Advances in Best-Worst Method: Proceedings of the Third International Workshop on Best-Worst Method (BWM2022) 3031248155, 9783031248153

Table of contents :
Preface
Organization
Scientific Committee
Organizing Committee
Contents
An Overview of the Applications of BWM in Health
1 Introduction
2 Best Worst Method (BWM)
3 Literature Review of Applications of BWM in Health
3.1 BWM in Healthcare System Evaluation Studies
3.2 BWM in Hospital, Performance and Service Quality Studies
3.3 BWM in Diagnosing and Treatment-Related Studies
3.4 BWM in Healthcare Supply Chain Studies
3.5 BWM in Healthcare Support Systems
3.6 BWM in Occupational Health and Safety
4 Observations and Concluding Remarks
References
A State-of the-Art Survey of Best-Worst Method Applications for the Problems Related to COVID-19
1 Introduction
2 Analysis of Literature
2.1 Descriptive Analyses
2.2 N-grams Application and Analyses
3 Conclusion
3.1 Implications
3.2 Limitations and Future Directions
References
Why Should Not a Decision Analyst be Content with Only (n-1) Pairwise Comparisons? Echoes from the Literature
1 Introduction
2 Preliminaries
3 The Agreement in the Literature
3.1 Normative Decision Theory
4 The Roles of Redundancy and Inconsistency
5 Conclusions
References
Identifying Relative Marginal Value Functions for Ranking
1 Introduction
2 Ranking Method Based on Relative Marginal Value Functions
3 Numerical Example
4 Conclusion and Future Work
References
A Consensus-Based Best-Worst Method for Multi-criteria Group Decision-Making
1 Introduction
2 Background
2.1 Group Decision-Making and Consensus
2.2 Best-Worst Method
3 Consensus-Based Best-Worst Method
4 Illustrative Example
5 Conclusions
References
A Fuzzy Best-Worst Method Based on the Fuzzy Interval Scale
1 Introduction
2 Fuzzy Cognitive Best Worst Method Under the Fuzzy Interval Scale
2.1 Fuzzy Cognitive Best Worst Method
2.2 Consistency Index and Consistency Ratio
3 Application
3.1 Comparative Analysis and Discussion
4 Conclusion
References
Integrating Sustainable Goals in Transmission System Operators’ Projects
1 Introduction
2 Literature Review
3 Methodology
3.1 Sustainable Decision Criteria – Aspects of Sustainability
3.2 Analysing Importance – The BWM
3.3 Analysing Performance – The Maturity Model
3.4 The Importance-Performance Analysis
4 Results and Discussion
5 Conclusion
References
A GIS-Based BWM Approach for the Location Selection of Solar Power Plant in Tunceli Province (Turkey)
1 Introduction
2 Literature Review
3 Research Methodology and Application Results
3.1 Criteria Used in the Location Selection
3.2 Weighting Criteria with the Best-Worst Method
3.3 Data Preparation for GIS Environment
3.4 Study Province
3.5 Integration of Criterion Weights to GIS Environment
4 Conclusion
References
A Fuzzy Best Worst Method Based Prioritization of Solar Panel Selection Criteria
1 Introduction
2 Literature Review
3 Methodology
4 Application
5 Conclusion
References
Prioritizing Competitive Capabilities in Additive Manufacturing Systems Using Best-Worst Method
1 Introduction
2 Literature Review
2.1 Additive Manufacturing Systems
2.2 Competitive Capabilities
3 Methodology
3.1 The Best-Worst Method
4 Results and Discussion
5 Conclusion and Implications
References
Identifying Impact of the Entrepreneurship Ecosystem on the Success of Entrepreneurial Start-Up Firms
1 Introduction
2 Theoretical Background
2.1 Entrepreneurship Ecosystem
2.2 The Lifecycle of Entrepreneurial Start-Up Firms
2.3 Success Measures of Start-Ups
3 Methodology
3.1 Data Collection
4 Results and Discussion
4.1 Bayesian Best-Worst Method
4.2 Importance-Performance Analysis
5 Conclusions
Appendix
References
Prioritizing the Distributor’s Key Performance Indicators and Constraints to Implement TOC-Based Solution for Outbound Supply Chain Network
1 Introduction
2 Literature Review
2.1 TOC in Supply Chain
2.2 Constraint to Implement TOC Solution in Outbound Supply Chain
2.3 KPIs of Distributors
3 Research Methodology
3.1 Procedure to Conduct BWM Method
3.2 Computing Consistency Ratio
4 Results and Discussion
5 Conclusion
References
Evaluating and Ranking the Supplier Selection Criteria for Additive Manufacturing Firms Using Best-Worst Method
1 Introduction
2 Literature Review
2.1 Gap in the Literature
3 Methodology
3.1 Best-Worst Method (BWM)
3.2 Steps of BWM
3.3 Consistency Measurement
4 Results and Discussion
5 Conclusion
References
Author Index

Citation preview

Lecture Notes in Operations Research

Jafar Rezaei Matteo Brunelli Majid Mohammadi   Editors

Advances in Best-Worst Method Proceedings of the Third International Workshop on Best-Worst Method (BWM2022)

Lecture Notes in Operations Research Editorial Board Members Ana Paula Barbosa-Povoa, University of Lisbon, Lisboa, Portugal Adiel Teixeira de Almeida

, Federal University of Pernambuco, Recife, Brazil

Noah Gans, The Wharton School, University of Pennsylvania, Philadelphia, USA Jatinder N. D. Gupta, University of Alabama in Huntsville, Huntsville, USA Gregory R. Heim, Mays Business School, Texas A&M University, College Station, USA Guowei Hua, Beijing Jiaotong University, Beijing, China Alf Kimms, University of Duisburg-Essen, Duisburg, Germany Xiang Li, Beijing University of Chemical Technology, Beijing, China Hatem Masri, University of Bahrain, Sakhir, Bahrain Stefan Nickel, Karlsruhe Institute of Technology, Karlsruhe, Germany Robin Qiu, Pennsylvania State University, Malvern, USA Ravi Shankar, Indian Institute of Technology, New Delhi, India Roman Slowiński, Poznań University of Technology, Poznan, Poland Christopher S. Tang, Anderson School, University of California Los Angeles, Los Angeles, USA Yuzhe Wu, Zhejiang University, Hangzhou, China Joe Zhu, Foisie Business School, Worcester Polytechnic Institute, Worcester, USA Constantin Zopounidis, Technical University of Crete, Chania, Greece

Lecture Notes in Operations Research is an interdisciplinary book series which provides a platform for the cutting-edge research and developments in both operations research and operations management field. The purview of this series is global, encompassing all nations and areas of the world. It comprises for instance, mathematical optimization, mathematical modeling, statistical analysis, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, decision analysis, supply chain management, transportation logistics, process design, operations strategy, facilities planning, production planning and inventory control. LNOR publishes edited conference proceedings, contributed volumes that present firsthand information on the latest research results and pioneering innovations as well as new perspectives on classical fields. The target audience of LNOR consists of students, researchers as well as industry professionals.

More information about this series at https://link.springer.com/bookseries/16741

Jafar Rezaei Matteo Brunelli Majid Mohammadi •

•

Editors

Advances in Best-Worst Method Proceedings of the Third International Workshop on Best-Worst Method (BWM2022)

123

Editors Jafar Rezaei Technology, Policy and Management Delft University of Technology Delft, The Netherlands

Matteo Brunelli Department of Industrial Engineering University of Trento Trento, Italy

Majid Mohammadi Vrije Universiteit Amsterdam (VU Amsterdam) Amsterdam, The Netherlands

ISSN 2731-040X ISSN 2731-0418 (electronic) Lecture Notes in Operations Research ISBN 978-3-031-24815-3 ISBN 978-3-031-24816-0 (eBook) https://doi.org/10.1007/978-3-031-24816-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book contains the proceedings of BWM2022, The Third International Workshop on Best-Worst Method. The workshop, hosted by Delft University of Technology, was organized hybrid on two days June 09 and 10, 2022. BWM2022 aims to bring together researchers working on theoretical, methodological, and application studies on the Best-Worst Method, a multi-criteria decision-making method that was developed in 2015 and that since then has gained a lot of attention among researchers and practitioners from many different fields. Researchers can share their latest findings with their peers and discuss avenues for future research. Four lectures were given on the foundations of BWM on the morning of the first day, and fourteen high-quality papers were accepted for presentation which were presented in eight sessions in two days chaired by the experts on different areas including supply chain management, health, energy, manufacturing, and entrepreneurship as well as methodological advancement. This book contains thirteen full papers. The first two published papers provide two literature reviews on the applications of the BWM in health, followed by four methodological contributions, and the other papers present applications of the BWM in different fields. We are very grateful to the authors for submitting their work and for having interactive discussions during the workshop. We also express our gratitude to the members of the scientific committee for reviewing the full papers. All papers were reviewed by at least two members of the scientific committee using single-blind peer-review process, and we did not use external reviewers. Reviewers evaluated the papers based on relevance, originality, rigor of the data collection and analysis, and presentation of the study. We are also grateful to Delft University of Technology for providing the infrastructure and to Springer for publishing the proceedings. June 2022

Jafar Rezaei Matteo Brunelli Majid Mohammadi

v

Organization

Scientific Committee Jafar Rezaei (Chair) Matteo Brunelli Majid Mohammadi Fuqi Liang Joseph Sarkis Salvatore Greco Negin Salimi Kannan Govindan Luis Martínez López Salvatore Corrente James Liou Himanshu Gupta Alessio Ishizaka Jingzheng Ren Simonov Kusi-Sarpong Huchang Liao

Delft University of Technology, The Netherlands University of Trento, Italy Vrije Universiteit Amsterdam, The Netherlands Shenzhen University, China Worcester Polytechnic Institute, USA University of Catania, Italy Wageningen University and Research, The Netherlands Southern Denmark University, Denmark University of Jaén, Spain University of Catania, Italy National Taipei University of Technology, Taiwan Indian Institute of Technology, Dhanbad, India NEOMA Business School, France The Hong Kong Polytechnic University, Hong Kong SAR, China University of Southampton, UK Sichuan University, China

Organizing Committee Jafar Rezaei Geqie Sun Pelin Gulum Tas

Delft University of Technology, The Netherlands Delft University of Technology, The Netherlands Delft University of Technology, The Netherlands

vii

Contents

An Overview of the Applications of BWM in Health . . . . . . . . . . . . . . . Pelin Gulum Tas

1

A State-of the-Art Survey of Best-Worst Method Applications for the Problems Related to COVID-19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . İbrahim Miraç Eligüzel and Eren Özceylan

19

Why Should Not a Decision Analyst be Content with Only (n 1) Pairwise Comparisons? Echoes from the Literature . . . . . . . . . . . . . . . . Matteo Brunelli

33

Identifying Relative Marginal Value Functions for Ranking . . . . . . . . . Majid Mohammadi and Jafar Rezaei A Consensus-Based Best-Worst Method for Multi-criteria Group Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Álvaro Labella, Diego García-Zamora, Rosa M. Rodríguez, and Luis Martínez A Fuzzy Best-Worst Method Based on the Fuzzy Interval Scale . . . . . . Nastaran Goldani and Mostafa Kazemi

41

48

59

Integrating Sustainable Goals in Transmission System Operators’ Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Georgios Athanasiou

74

A GIS-Based BWM Approach for the Location Selection of Solar Power Plant in Tunceli Province (Turkey) . . . . . . . . . . . . . . . . . . . . . . . Zekeriya Konurhan, Melih Yucesan, and Muhammet Gul

87

A Fuzzy Best Worst Method Based Prioritization of Solar Panel Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Kevser Arman and Nilsen Kundakcı

ix

x

Contents

Prioritizing Competitive Capabilities in Additive Manufacturing Systems Using Best-Worst Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Vishwas Dohale, Milind Akarte, and Priyanka Verma Identifying Impact of the Entrepreneurship Ecosystem on the Success of Entrepreneurial Start-Up Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Georgios Boutris and Negin Salimi Prioritizing the Distributor’s Key Performance Indicators and Constraints to Implement TOC-Based Solution for Outbound Supply Chain Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Chandrashekhar Chaudhari, Vivek Khanzode, Rauf Iqbal, and Vishwas Dohale Evaluating and Ranking the Supplier Selection Criteria for Additive Manufacturing Firms Using Best-Worst Method . . . . . . . . . . . . . . . . . . 161 Priya Ambilkar, Priyanka Verma, and Debabrata Das Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

An Overview of the Applications of BWM in Health Pelin Gulum Tas(B) Delft University of Technology, Delft, The Netherlands [email protected]

Abstract. This article presents an overview of the Best-Worst Method (BWM) applications in health and gives observations and concluding remarks about reviewed articles. BWM is a multi-criteria decision-making (MCDM) method developed to evaluate alternatives that a group of criteria characterizes. It has attracted the attention of many researchers from different disciplines. Sixty articles that applied BWM or one of the variants have been reviewed to provide an overview of the applications of BWM in the area of health. Investigated studies are divided into six groups: healthcare system evaluation studies, hospitals, performance and service quality studies, diagnosing and treatment-related studies, healthcare supply chain studies, healthcare support systems applications and occupational health and safety studies. Each article is analyzed in terms of specific application area in health, motivation of the study, integration of the BWM with other methods, if any, and essential application findings for both academicians and practitioners. With the motivation of giving a general idea of BWM applications in health, the impressions obtained and suggestions are presented at the end. The findings indicate that BWM is a favourable method for health-related decisionmaking problems, and it will be preferred more in health applications in the future due to its ability to adapt to other methods, practicality and reliable results. Keywords: Best-Worst Method (BWM) · Health · Multi-criteria decision making · Hospital performance analysis · Occupational health and safety

1 Introduction In problems where multiple alternatives and objectives should be considered simultaneously, the multi-criteria decision–making (MCDM) theory is used to compare the alternatives and make the best choice [1]. Different MCDM methods offer such an evaluation process in the literature, and Best-Worst Method (BWM) is one of them. BWM has been exposed to the intense interest of scholars since the time it emerged in 2015 and has taken place among the widely used MCDM methods [2]. This method identifies the best and worst criteria and then compares the others with the determined ones. Superior to other well-known MCDM methods in the literature, it requires fewer comparison data, turns into pairwise comparison steps time-efficient, and provides decision-makers with consistent and reliable results [1]. Because of its practicality, BWM is applied to various © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 1–18, 2023. https://doi.org/10.1007/978-3-031-24816-0_1

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P. Gulum Tas

problems from different research areas such as supply chain management [3], transportation and logistics [4], energy [5], sustainability [6], risk assessment [7], finance [8] and technology [9]. In addition to a well-known wide range of application areas, BWM is also constantly used in health and health-related decision-making problems. Healthcare management decisions have significant effects on countries’ budgets and are directly related to human life and well-being; therefore, they require a multidimensional and sensitive evaluation process [10]. In addition, the need for comprehensive healthcare services in societies, which has been increasing for years, obliges the authorities to make broader evaluations and improve their decision-making methods [11]. At this point, BWM stands out as a helpful tool and offers reliable and consistent results to decision-makers from different disciplines of healthcare. There are many health-related studies in which BWM is used, either purely or integrating with other decision-making methods [12]. The primary aim of this study is to present an overview of the applications of BWM in health. For this purpose, 60 published research that has applied BMW in health or health-related decision-making problem were investigated, and the main findings are briefly discussed. The remainder of the article is organized as follows. In Sect. 2, BWM application steps are briefly introduced, and then detailed literature research findings are presented in Sect. 3. The last section concludes the study by giving the observations and concluding remarks and suggestions for future research.

2 Best Worst Method (BWM) The Best-Worst Method (BWM) was developed by Rezaei [1] in 2015 as a novel MCDM method based on the pairwise comparison principle. This method has some significant advantages compared to others. It requires less pairwise comparison data than other MCDM methods, such as the Analytic Hierarchy Process (AHP). It is also less prone to some cognitive biases, such as anchoring bias and equalizing bias [2]. The steps of the BWM are as follows [1]: Step 1: The decision-maker identifies a set of criteria {c1 , c2 , . . . , cn } for evaluating the alternatives. Step 2: The best (e.g., the most important, most desirable) and the worst (e.g., the least important, least desirable) criteria are specified by the decision-maker. Step 3: Using a number between 1 and 9, the decision-maker expresses his/her preference for the criterion specified as the best overall the other criteria. As a result, the Best-to-Others (BO) vector is obtained and it is shown as: AB = (aB1 , aB2 , . . . , aBn ) where aBj shows the preference of the best criterion B, over criterion j. Step 4: Using a number between 1 and 9, the decision-maker expresses his/her preference of all criteria over the worst criterion, and as a result of that, the vector of Others-to-Worst (OW) is obtained, and it is shown as: AW = (a1W , a2W , . . . , anW ) where ajW shows the preference criterion j over the worst criterion W . Step 5: The optimal weights are calculated as wj∗ . The following requirements should be met by the optimal weights of the criteria:

An Overview of the Applications of BWM in Health

3

For each pair of wB /wj and wj /wW , the ideal situation is where wB /wj = aBj and should be found with wj /wW = ajW . To satisfy these conditions  for all j, a solution   wj  wB   maximum absolute differences  wj − aBj  and  wW − ajW  for all j be minimized. Under the conditions of non-negativity and unit-sum for weights, the following problem is obtained.      wB   wj  min max  − aBj ,  − ajW  j wj wW s.t. 

(1)

j

wj = 1

wj ≥ 0, for all j Equation (1) can be transformed to the following problem: min ξ,     wB − aBj  ≤ ξ, for all j, s.t. wj    wj    − a jW  ≤ ξ, for all j, w W  wj = 1

(2)

j

wj ≥ 0, for all j The optimal weights wj∗ and ξ ∗ are obtained after solving model (2). It can be stated that the smaller ξ ∗ , the higher the consistency of the provided pairwise comparisons, which means the higher the reliable comparison [1]. There are other variants of the BWM, such as the linear BWM [13], multiplicative BWM [14], Bayesian BWM [15], and belief-based BWM [16] which are suitable for different situations.

3 Literature Review of Applications of BWM in Health Providing a comprehensive, consistent, and high-quality healthcare service is one of the main challenges for authorities and countries [17]. In order to achieve this, health-related problems should be considered from all aspects, and BWM is a promising and effective method for that purpose. Researchers from different areas frequently prefer this method and its extensions for health problems such as hospital performance evaluation, location selection, disease diagnoses, and treatment comparison. This research focuses on the applications of BWM in health and attempts to present an overview. For a systematic review, we conducted a search on Google Scholar among 1,919 studies referring to the BWM [1]. We combined keywords referring to health and healthrelated operations (i.e., “healthcare “OR” health” OR “hospital “OR “treatment” OR “drug” OR “occupational health”). We considered articles published in peer-reviewed

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P. Gulum Tas

journals, conference papers and book chapters between 2015 and 2022. The initial search yielded 1,210 results, and then the abstracts of the articles were screened. We excluded studies that do not use the BWM or one of the variants and studies with no focus on health or health-related applications. This process resulted in 60 records investigated detailed in methodology, case study and conclusion remarks. As can be seen from Table 1, we grouped these 60 studies into six groups: healthcare system evaluation studies, hospitals, performance and service quality studies, diagnosing and treatment-related studies, healthcare supply chain studies, healthcare support systems applications and occupational health and safety studies. This grouping seeks to integrate and analyze the applications from an overall subject perspective according to their similarities. Table 1. BWM studies in health BWM application area

Number of studies References

Healthcare system evaluation

6

Torkayesh et el. [18], Cheraghalipour and Roghanian [19], Hasani and Mokhtari [20], Shojaei et al. [21], Kazancoglu et al. [22], Wang et al. [23]

Hospital, performance and service 21 quality

Sivakumar et al. [24], Demirel and Sahin [25], Liao et al. [26], Tahmasbi and Asgharpour [27], Nabeeh et al. [28], Yazdi et al. [29], Kheybari et al. [30], Aydin and Seker [31], Chen et al. [32], Talib et al. [33], Kaswan et al. [34], Ahmedinejad et al. [35], Amiri et al. [17], Sivakumar et al. [12], Ming et al. [36], Saner et al. [37], Momen et al. [38], Azizi et al. [39], Fei et al. [40], Luo et al. [41], Rowshan et al. [42]

Diagnosing and treatment-related

10

Basset et al. [43], Li et al. [44], Malakoutikhah et al. [45], Song et al. [46], Abellana [47], Naeini et al. [48], Edmerdash et al. [49], Almahdi et al. [50], Kundu et al. [51], Oztas et al. [52]

Healthcare supply chain

8

Chauhan et al. [53], Kaushik et al. [54], Raju et al. [55], Ishizaka et al. [56], Sabbagh et al. [57], Kavaliauskiene et al. [58], Yazdani et al. [59], Amini et al. [60] (continued)

An Overview of the Applications of BWM in Health

5

Table 1. (continued) BWM application area

Number of studies References

Healthcare support systems

6

Yazdani et al. [61], Tirkolaee and Torkayesh [62], Torkayesh et al. [63], Huang et al. [64], Chauhan et al. [65], Haghighi and Torabi [66]

Occupational health and safety

9

Khan et al. [67], Ak et al. [68], Gul and Ak [69], Valipour et al. [70], Ghoushchi et al. [7], Jain et al. [71], Mohandes and Zhang [72], Liu et al. [73], Nguyen et al. [74]

Figure 1 illustrates the distribution of the studies according to the six main groups. As can be seen from the graph, more than one-third of the studies investigate hospitals and performance-related problems. This category includes hospital location selection problems, medical service evaluations, and quality-related studies. When 17% of all studies are made up of diagnosing and treatment-related applications, 15% are about occupational health and safety applications.

BWM Applications in health Healthcare system evaluation studies 15%

Hospital, performance and service quality

10%

Diagnosing and treatment related studies

10% 35% 13% 17%

Healthcare supply chain studies Healthcare support systems applications Occupational health and safety studies

Fig. 1. Distribution of BWM applications in health

The healthcare support system group includes landfill area selection and evaluation of health support systems like telemedicine or information systems with 10%. While healthcare system evaluation studies focus on a general assessment, the healthcare supply

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P. Gulum Tas

chain applications consist of all activities such as medicine, food or medical device supplying related to health with 10% and 13%, respectively. Table 2. The country distributions of publications Country

Number of publications

Proportion

1

Canada

3

5%

2

China

9

15%

3

Egypt

3

5%

4

France

2

3.33%

5

India

8

13.33%

6

Iran

18

30%

7

Italy

1

1.67%

8

Korean

1

1.67%

9

Lithuania

1

1.67%

10

Malaysia

1

1.67%

11

Philippines

1

1.67%

12

Spain

3

5%

13

Turkey

8

13.33%

14

Vietnam

1

1.67%

Sum

60

100%

Regional distributions of the examined BWM application are provided in Table 2. As can be seen, Iran led with 18 publications, which contributed 30% of all papers. It is followed by China with 9 articles and made up 15% of the total. Turkey and India each have 8 publications with 13.33%. Similarly, Canada and Egypt each have 3 articles and contributed 5%. The other six countries each have only one publication which contributed 1.67%. Most of the scholars studying BWM in health are from Iran. China, India and Turkey have an influence in this field. The remaining part of this section includes six subsections. Each one deals with the groups and gives information about investigated problems, applications and integrated methods, and remarkable conclusions. 3.1 BWM in Healthcare System Evaluation Studies In a healthcare system, performance is always crucial for the service buyers and for the providers [75]. In order to increase the quality, authorities and policymakers should evaluate the systems using to proper tools and take the necessary precautions in advance. BWM is a helpful tool for this purpose, and there are substantial studies that investigated the factors and various measurements in the healthcare systems. For instance, Shojaei et al. [21] identified internal and external factors to evaluate and prioritize the changes

An Overview of the Applications of BWM in Health

7

that affect healthcare performance using BWM. They concluded that external factors such as economics and politics significantly impacted the healthcare system’s performance. They should be considered with the well-known internal factors to accomplish better performance. A similar study was conducted by Torkayesh et al. [18] to evaluate the healthcare sectors in Eastern Europe countries according to the pre-determines indicator weights. They proposed an integrated model using BWM and other MCDM tools and evaluated the healthcare systems of seven countries based on a real dataset. The study concluded that healthcare systems in Lithuania and Slovakia are better than in Poland and Estonia. Hasani and Mokhtari [20] considered the sustainability-related success of the healthcare systems. They proposed the Data Envelopment Analysis (DEA) integrated MCDM method, which included BWM, dynamic networks and other methods. The main contribution of the research was the integration of the hospital activities with sustainability and presenting to policymakers different alternatives. Wang et al. [23] considered the different strategies for the Covid-19 outbreak and proposed a methodology integrating BWM with other MCDM methods. In their real-life case study for Vietnam, they defined the availability of the health system as an important factor. From a different perspective, Cheraghalipour and Roghanian [19] focused on reengineering the internal processes and proposed a hybrid decision-making approach for optimal portfolio in healthcare management. In their problem of the state hospital, they weighted the organizational goals with fuzzy BWM. They solved the model that aimed to maximum value for the organization and the minimum employee resistance to the changes. It was founded that changes in the staff resistance directly affect the objective function and more participation is needed for a strategic evaluation. Kazancoglu et al. [22] evaluated the healthcare systems from the circular economy perspective, and they defined the circular economy barriers in the healthcare sector by applying big data, fuzzy BWM and fuzzy VIseKriterijumsa Optimizacija I Kompromisno Resenje (VIKOR). The high-cost requirements for the proposed technology for circular economy in health are defined as the most important barrier. On the other hand, the government-related barriers and lack of financial capabilities were the other essential factors. These were example studies from different perspectives investigating the healthcare system’s performance using BWM with other methods. They were mainly focused on the all system more than the activities or the processes related to healthcare. 3.2 BWM in Hospital, Performance and Service Quality Studies Hospitals are the main components of the healthcare system, and because of that, they need to be evaluated for consistent performance and quality. Decision-makers also should consider the performance of the smaller systems and assess the quality of the provided services as much as they care about the physical conditions and locations of the hospitals. There is considerable literature about BWM applications related to hospitals, performance and quality applications. For example, Liao et al. [26] investigated hospital performance by integrating hesitant fuzzy linguistic sets with BWM. The results of the applications revealed that the proposed method performed better than the interval BWM and fuzzy BWM methods. Amiri et al. [17] conducted a study using Group BWM and fuzzy preference programming methods to evaluate the hospital performance in Tehran. The proposed method covered the uncertainty and eliminated the need for consistency

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check calculations because of the group decision-making approach. Another study was conducted by Demirel and Sahin [25] in order to compare the performances of city hospitals in Turkey. In this study, BWM was integrated with other methods such as Stepwise Weight Assessment Ratio Analysis (SWARA), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Microsoft Excel Visual Basic for Applications (VBA) for establishing a visual decision support system. Also, Nabeeh et al. [28] proposed a hybrid methodology that is a combination of Multi-Attributive Border Approximation Area Comparison (MABAC), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE–II) and BWM for hospital service quality assessment. The Neutrosophic theory is also included in the methodology to overcome ambiguity and vagueness. In their case study, they compared five hospitals in Egypt and found that the performance of the private hospitals was better than the public hospitals. In another research, Fei et al. [40] proposed a novel evidential BWM integrating traditional BWM and belief function theory for hospital service evaluation. The proposed method was advantageous in dealing with uncertainty and less need for comparison. As a more up to date study, Tahmasbi and Asgharpour [27] focused on the difficulties of managing a healthcare centre during a pandemic period and used BWM with Fuzzy Cognitive Map Approach. They defined the “inadequate physical space” as the most critical challenge. In addition, the “manpower shortages” were among the essential difficulties. Sivakumar et al. [24] proposed a decision-making framework to improve healthcare service quality during Covid-19 pandemics and integrated BWM with Multi-Actor Multi-Criteria Analysis (MAMCA). To enhance the performance of intensive care units, they considered two scenarios from the stakeholders’ perspectives. The applications concluded that part-time physicians and medical staff had to be hired for better performance during the pandemics. Yazdi et al. [29] proposed a probabilistic-based model to evaluate the medical service quality, and they integrated fuzzy BWM and Bayesian networks. The application results of the proposed method were superior to the traditional MCDM methods in this field. As an essential problem in hospitals, Ahmadinejad et al. [35] studied a strategy for decreasing the effects of the pandemic on elective surgery operation rooms, and BWM is used for prioritizing the factors of Covid-19 transmissions. Personal protection, screening checklist and checking the body temperature were the most crucial prevention factors of the disease. Sivakumar et al. [12] investigated the intensive care units and proposed BWM- MAMCA method to include the stakeholders’ opinions to improve the quality. The applications showed that hiring part-time and full-time physicians and medical staff was the best solution for better quality. Another service quality research was conducted by Ming et al. [36] and they investigated patients’ satisfaction levels in the blood-collection room by extended linguistic BWM. Momen et al. [38] investigated the effects of surgical cancellations on management and patient levels. To achieve this, they evaluated the cancellation factors with integrated Failure Modes and Effect Analysis (FMEA) and fuzzy BWM approaches. They considered the psychological impact of the cancellations and found that high blood pressure and diabetes, high-risk surgery, unavailable intensive care unit beds, lack of staff and not receiving meditation were the main reasons. Rowshan et al. [42] investigated which factors affect outsourcing wards and units in public hospitals in their study. They use fuzzy BWM for prioritizing the 34 criteria defined by experts and

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hospital workers. Economic, services and management are found as the most important main criteria in such decisions. There are also quality management tool integrations with BWM in health. For example, Kaswan et al. [34] studied the just in time (JIT) elements for the healthcare units in India and used the BWM and AHP methods. The implementation of the JIT on healthcare affected many areas like patient care, costs, time and inventory management. In another research, Talib et al. [33] proposed a method to define and evaluate the Total Quality Management (TQM) enablers in the Indian healthcare system using BWM. The application showed that the leadership based enablers were the most important category for the implementation. Locations of the hospitals became essential decisions during the Covid-19 period, and there are BWM studies focused on this problem. Kheybari et al. [30], Aydin and Seker [31] and Chen et al. [32] investigated different location selection problems for hospitals. Kheybari et al. [30] focused on temporary hospitals and proposed a risk-averse BWM with a portfolio optimization model. They applied the method to the Mazandaran cities in Iran and searched locations for temporary pandemic hospitals. Aydin and Seker [31] also focused on the same problem for Turkey. They integrated Delphi, BWM and type-2 fuzzy TOPSIS to choose the pandemic hospital locations and the Ataturk Airport found the best alternative place. Chen et al. [32] investigated the same problem with BWM, DEA and fuzzy sets and applied it to the hospital location problem in Wuhan. The practical results of the proposed methodology showed that it can be used to evaluate hospital performance and solve other real-life issues. Saner et al. [37] used the Bayesian BWM, VIKOR and TOPSIS to assess hospitals’ preparedness levels in disaster situations. They calculated the personnel, equipment and transportation criteria as the most important ones for a preparedness level. 3.3 BWM in Diagnosing and Treatment-Related Studies Decision-makers sometimes face treatment selection or diagnosing problems, and they use different tools for making a decision. There are promising studies about diagnosing the diseases or comparing the treatment methods using BWM. For instance, in their research Basst et al. [43] argue a new model to differentiate Covid-19 and other similar viruses’ symptoms using computerized tomography (CT) scans and primary symptoms with the help of BWM and TOPSIS. They examined five chest diseases, and the proposed diagnosing model could detect Covid-19 in all cases. A similar study was conducted by Li et al. [44] and proposed a selection model of surgical treatments for early gastric cancer patients. They developed a framework that used subjective and objective criteria and combined different fuzzy sets to evaluate better. Early gastric cancer surgery options were assessed and weighted using BWM. The study results showed that the proposed method was helpful, especially when there was asymmetric information between doctors and patients. Song et al. [46] proposed a decision support system that simultaneously uses historical data and expert opinions and makes predictions about the risk level of the disease. They developed a system based on the principles of BWM and made applications in pregnancy diagnosing cases. Even if the system achieved good results, the honesty of the expert opinions was highlighted as a limitation.

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Abellana [47] investigated different types of dengue epidemic antecedents using fuzzy multi-attribute decision-making methods. This study adopted BWM and fuzzy BWM to define and evaluate the experts’ opinions about socioeconomic and environmental precursors. The study presented significant results because of the structured methodology and analysis of different dengue antecedents in the Philippines. Another study conducted by Naeini et al. [47] integrated Geographic Information System (GIS) with fuzzy BWM to evaluate the districts’ cardiovascular disease risk in Tehran. Cardiologists investigated the factors, and weighted results were used for prioritisation and mapping. The study results presented risk maps for the prevention of cardiovascular disease. From a different perspective on health Malakoutikhah et al. [45] focused on mental wellbeing and integrated a well-known workload measuring tool NASA-task load index (TLX) questionnaire, with fuzzy BWM. They made an application among medical students, and the results showed that the new method was more effective than the conventional workload tools in terms of realistic estimations. There are many drug and treatment evaluation applications using BWM. For instance, Oztas et al. [52] conducted a Covid-19 vaccine selection study using BWM and a questionnaire in another study. While efficacy was the most important criterion for the vaccine decision, participants determined the price and origin of the vaccine as the least important criteria. In another study, Edmerdash et al. [49] proposed a methodology that includes several MCDM methods such as BWM, MABAC and PROMETHEE with Neutrosophic Linguistic set for drug product selection. The suggested method accurately matched the patient’s needs with drug alternatives. Another selection problem considered by Almahdi et al. [50] proposed a framework for selecting mobile patient monitoring systems in telemedicine services using BWM and VIKOR. The proposed methodology integrated and evaluated the unmeasurable values with BWM and presented a benchmarking between different alternatives. Similarly, investigated the medical device selection problem for hospitals using different MCDM methods. The results of the Magnetic Resonance Imaging (MRI) selection problem compared with fuzzy BWM. 3.4 BWM in Healthcare Supply Chain Studies Healthcare management is a comprehensive and complex task and includes many systems and activities. The supply chain is one of the essential systems, and there are promising studies conducted using BWM about the healthcare supply chain. For instance, Chauhan et al. [53] investigated the pharmaceutical supplier selection problem in pandemics using the Bayesian BWM and MABAC. They evaluated eight criteria, and the results showed that lead time and quality were the most important parameters in conditions like a pandemic. A similar study is conducted by Kaushik et al. [54] about disruptions in the healthcare supply chain during the pandemic and epidemic. They used BWM to weigh predefined reasons and the “inefficient executive leadership” was the most important criterion in such crises. Yazdani et al. [59] integrated BWM with other decision-making methods to investigate the hospital supplier selection problem. The application results showed some critical insights about the understanding of the strong and the weak sides of the suppliers is essential in this problem. Ishizaka et al. [56] conducted another supplier selection research focused on closed-loop pharma supply chains. They used BWM with Geometrical Analysis for Interactive Aid (GAIA) to evaluate five

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suppliers and found the most important criterion on-time delivery. Raju et al. [55] used BWM to investigate the success of the Covid-19 vaccine distribution in India. They reached two important conclusions: For a successful implementation, the cold storage chain should be improved, and vaccine wastage needs to decrease. Sabbagh et al. [57] and Kavaliauskiene et al. [58] focused on blockchain technology in healthcare systems and studied the drug supply chain and blood supply chain. Sabbagh et al. [57] used BWM and VIKORSort methods and mainly focused on the risks of blockchain technology in the drug supply chain. They found three dangerous risks named “cyberattacks”, “double spending”, and “immutability”. Also, Kavaliauskiene et al. [58] studied the barriers to implementing blockchain technology in the blood supply chain using BWM and Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS). They specified the “business owners’ unwillingness” as the main barrier, and it should be considered for a successful implementation. In another research, Amini et al. [60] studied the food supplier selection problem for hospitals and evaluated seven criteria by applying the fuzzy BWM method. 3.5 BWM in Healthcare Support Systems The complex systems and organizations include many subsystems, and each plays a critical role in general performance. There are many subsystems like information, finance, and operational management for healthcare systems. These supportive subsystems may have different problems, and decision-makers should consider them. For instance, healthcare waste management is an essential issue for both hospital management and the environment, and there are studies in the literature using BWM to research this. Torkayesh et al. [63] focused on the problem of landfill location selection and presented a hybrid BWM and MARCOS model with GIS. They generated maps, and eight alternative locations were evaluated in terms of sustainable waste management. Another landfill selection method proposed by Yazdani et al. [61] was based on BWM and interval rough numbers. The method was applied to a hospital in Madrid and it revealed important conclusions for the decision-maker who may plan the hospital waste systems. Tirkolaee and Torkayesh [62] investigated the same problem and proposed a cluster-based decision support system. They integrated Stratified BWM with the K-means algorithm and other methods under the grey interval numbers. They applied the proposed method in Mazandaran province and found that local rules, policies, laws, and regulations are the most important criteria for the landfill location selection problem. Huang et al. [64] focused on the healthcare waste treatment technologies and proposed a decision support framework based on cloud model theory, BWM and other methods. Applying the method to empirical examples showed its feasibility and effectiveness compared to other methods. Another healthcare support system is information, and Haghighi and Torabi [66] proposed a framework for evaluating hospital information systems. They based their method on sustainability-resilience and integrated BWM with DEA and Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis. The result of the application revealed important ideas, especially for the system designers. A similar study was conducted by Chauhan et al. [65] about the performance of telemedicine services that were useful during the pandemics period. They integrated Bayesian BWM with The Decision Making Trial and Evaluation Laboratory (DEMATEL) and VIKOR methods to present an

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evaluation framework. According to the seven criteria, the evaluation of the six hospitals showed that the technological impact has the most impact when the environment has the least. 3.6 BWM in Occupational Health and Safety Establishing a safe and healthy work environment is critical for both managers and employees, and prioritizing the risk parameters is one of the main challenges [69]. BWM appears as a useful method for occupational health and safety problems, and there are studies using BWM with other methods in the literature. For instance, Khan et al. [67] investigated the risk factors for lower back pain, a common musculoskeletal disorder among workers, with BWM. The study results showed that occupational factors were the main risk factors for lower back pain. Jain et al. [71] focused on the un-ergonomic aspects of working from home style and proposed a method for identifying the musculoskeletal disorders of the handheld device users. They used BWM and VIKOR to weightage the risk factors and evaluate the user groups. While working durations, postures and work conditions were specified as the highest risk factors, the computer users were the riskiest working group. Ak et al. [68] proposed an occupational risk assessment method by integrating Bayesian BWM and VIKOR methods. In addition, there was a benchmark BWM-VIKOR against the Bayesian BWM-VIKOR method to demonstrate the proposed method’s practicality. Gul and Ak [48] proposed another occupational risk assessment method that considered the severity of the hazards by combining BWM and MultiAtributive IdealReal Comparative Analysis (MAIRCA) under a fuzzy environment. Their case study in the marble industry showed the performance of the proposed method in addition to benchmark and sensitivity analysis. Valipour et al. [70] presented another occupational risk assessment method by integrating fuzzy BWM with Fuzzy C-Means Algorithm and other MCDM methods to identify and prioritize the main risk factors in the automotive industry. Compared to traditional FMEA and other risk assessment methods proposed hybrid methodology was more reliable and presented important sights to the managers. A very similar risk assessment method was developed by Ghoushchi et al. [7], and it included FMEA, extended BWM based on G-number theory and the COmplex PRoportional ASsessment (COPRAS) method. The novelty of this method was the addition of the new risk criteria such as pollution ratio and cost, and application results revealed that FMEA and COPRAS methods have a good performance together. Nguyen et al. [74] investigated the risks of the hydrocarbon processing industry by proposing a method including Hazard and Operability (HAZOP) and BWANP which is the integration of the Analytic Network Process (ANP) and BWM. As a significant contribution, this method presented an economic loss perspective to show the financial aspects of the possible risks to decision-makers in that area. Liu et al. [73] considered the picture fuzzy sets, alternative queuing method and extension of BWM for a new risk assessment method. The case study in an excavation task in a construction area showed the method’s reliability and practicality in capturing the risks. Another risk assessment study for the construction workers was conducted by Mohandes and Zhang [72] and used the fuzzy BWM for defining the weights of the possible risks. The proposed method showed promising performance in overcoming the experts’ statistical data needs.

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4 Observations and Concluding Remarks This study, which was carried out with the motivation to give the decision-makers an overview of BMW applications in health, reached some conclusions and observations. Firstly, the BWM has been used in decision-making problems from almost every subunit of the healthcare system. The variety of the application areas shows that the BWM is a convenient method for representing and solving many health-related decision-making problems. Although it has a wide application area, this research reveals that it is preferred more frequently in problems like hospital and medical service performance evaluation, occupational health and risk assessment studies and diagnosing related decision-making problems. On the other hand, this research shows that BWM is suitable for use with other MCDM methods. Even though it can be used purely, its integration with other methods is common, and it shows the flexibility and integration capability of the BWM. Among the studies examined, VIKOR, DEMATEL, TOPSIS and FMEA were the most frequently used methods combined with the BWM for health applications. Also, using the BWM with fuzzy sets, Neutrosophic sets, or any other linguistic system was common integration. Bayesian BWM was preferred for the group decision-making problems, and some of the researchers extended the BWM based on different approaches. When it comes to countries, Iran, India, China and Turkey had more studies than others. There are many important BWM applications for the health system of these countries or related problems. Based on this review, the following predictions can be made for future BWM applications in health: • Its promising performance in disease diagnosis and evaluation of treatment alternatives shows that BMW may be applied more frequently in these areas in the future. • Due to its flexibility and integration capability with other methods, it is possible to see more health-related frameworks combining BWM with different approaches in the future. • The health-related studies have gained momentum in recent years because of the pandemics and increased service quality expectations. BWM applications yielded highly reliable and practical results, and because of that, it is expected that the BWM method will grab more attention in healthcare performance evaluation studies in the future. • Bayesian BWM in health revealed promising results in group decision-making. We believe that it will be used more in the future, especially for strategic health decisions that include many stakeholders. For future studies, considering other databases in addition to Google Scholar search for BWM applications in health can be beneficial. On the other hand, instead of manual screening of the abstracts, using more up-to-date techniques like text-mining can provide a wider search and richer outputs.

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35. Ahmadinejad, B., Shabani, A., Jalali, A.: Implementation of clean hospital strategy and prioritizing Covid-19 prevention factors using best-worst method. Hosp. Top. 1–11 (2021). https:// doi.org/10.1080/00185868.2021.1997129 36. Ming, Y., Luo, L., Wu, X., Liao, H., Lev, B., Jiang, L.: Managing patient satisfaction in a blood-collection room by the probabilistic linguistic gained and lost dominance score method integrated with the best-worst method. Comput. Ind. Eng. 145, 106547 (2020). https://doi. org/10.1016/j.cie.2020.106547 37. Saner, H.S., Yucesan, M., Gul, M.: A Bayesian BWM and VIKOR-based model for assessing hospital preparedness in the face of disasters. Nat. Hazards 111(2), 1603–1635 (2021). https:// doi.org/10.1007/s11069-021-05108-7 38. Momen, S., Tavakkoli-Moghaddam, R., Ghasemkhani, A., Shahnejat-Bushehri, S., TavakkoliMoghaddam, H.: Prioritizing surgical cancellation factors based on a fuzzy best-worst method: a case study. IFAC-PapersOnLine 52(13), 112–117 (2019). https://doi.org/10.1016/j.ifacol. 2019.11.161 39. Azizi, F., Tavakkoli-Moghaddam, R., Hamid, M., Siadat, A., Samieinasab, M.: An integrated approach for evaluating and improving the performance of surgical theaters with resilience engineering. Comput. Biol. Med. 141, 105148 (2022). https://doi.org/10.1016/J.COMPBI OMED.2021.105148 40. Fei, L., Lu, J., Feng, Y.: An extended best-worst multi-criteria decision-making method by belief functions and its applications in hospital service evaluation. Comput. Ind. Eng. 142, 106355 (2020). https://doi.org/10.1016/J.CIE.2020.106355 41. Luo, Y., Chen, X., Sun, Y.: A fuzzy linguistic method for evaluating doctors of online healthcare consultation platform using BWM and prospect theory. In: 2019 IEEE 6th International Conference on Industrial Engineering and Applications (ICIEA 2019), pp. 506–510 (2019). https://doi.org/10.1109/IEA.2019.8715035 42. Rowshan, M., Shojaei, P., Askarifar, K., Bahmaei, J.: Outsourcing model in public hospitals HMIS health management and information science designing a multi-criteria decision-making framework for selecting wards and units in public hospitals: a case of Shiraz Zeinabieh hospital. Health Man Info. Sci. 8(3) (2021). https://doi.org/10.30476/jhmi.2022.91372.1085 43. Abdel-Basst, M., Mohamed, R., Elhoseny, M.: A model for the effective COVID-19 identification in uncertainty environment using primary symptoms and CT scans. Health Inform. J. 26(4), 3088–3105 (2020). https://doi.org/10.1177/1460458220952918 44. Li, D.P., He, J.Q., Cheng, P.F., Wang, J.Q., Zhang, H.Y.: A novel selection model of surgical treatments for early gastric cancer patients based on heterogeneous multicriteria group decision-making. Symmetry 10(6), 223 (2018). https://doi.org/10.3390/sym10060223 45. Malakoutikhah, M., Kazemi, R., Rabiei, H., Alimohammadlou, M., Zare, A., Hassanipour, S.: Comparison of mental workload with N-Back test: a new design for NASA-task load index questionnaire. Int. Arch. Health Sci. 8(1), 7–13 (2021). https://doi.org/10.4103/IAHS. IAHS_126_20 46. Song, K., Zeng, X., Zhang, Y., De Jonckheere, J., Yuan, X., Koehl, L.: An interpretable knowledge-based decision support system and its applications in pregnancy diagnosis. Knowl. Based Syst. 221, 106835 (2021). https://doi.org/10.1016/j.knosys.2021.106835 47. Abellana, D.P.: Modelling the interdependent relationships among epidemic antecedents using fuzzy multiple attribute decision making (F-MADM) approaches. Open Comput. Sci. 11(1), 305–329 (2021). https://doi.org/10.1515/comp-2020-0213 48. Bonyadi Naeini, A., Mojaradi, B., Zamani, M.: Prevention of cardiovascular diseases by combining GIS and fuzzy best-worst decision-making algorithm in areas of Tehran. Int. J. Ind. Eng. Prod. Res. 30(3), 255–271 (2019). https://doi.org/10.22068/ijiepr.30.3.255 49. Edmerdash, M., Rushdy, E.: An efficient framework for drug product selection–DPS according to neutrosophic BWM, MABAC and PROMETHEE II methods. Neutrosophic Sets Syst. 45(1), 19 (2021)

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50. Almahdi, E.M., Zaidan, A.A., Zaidan, B.B., Alsalem, M.A., Albahri, O.S., Albahri, A.S.: Mobile-based patient monitoring systems: a prioritisation framework using multi-criteria decision-making techniques. J. Med. Syst. 43(7), 1–19 (2019). https://doi.org/10.1007/s10 916-019-1339-9 51. Kundu, P., Görçün, Ö.F., Küçükönder, H.: Medical device selection in private hospitals by integrated fuzzy MCGDM methods: a case study in choosing MRI (Magnetic Resonance Imaging) system. J. Oper. Res. Soc. 73(9), 2059–2079 (2022). https://doi.org/10.1080/016 05682.2021.1960910 52. Özta¸s, G.Z., Bars, A., Genç, V., Erdem, S.: Criteria assessment for Covid-19 vaccine selection via BWM. In: Rezaei, J., Brunelli, M., Mohammadi, M. (eds.) BWM 2021. LNOR, pp. 228– 237. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-89795-6_16 53. Chauhan, A., Jakhar, S.K., Mangla, S.K.: Socio-technological framework for selecting suppliers of pharmaceuticals in a pandemic environment. J. Enterp. Inf. Manag. (2022). https:// doi.org/10.1108/JEIM-02-2021-0081/FULL/PDF 54. Kaushik, A., Mishra, S.K., Yadav, R., Kumar, G.: Managing healthcare supply chain during epidemic and pandemic. In: Singari, R.M., Kankar, P.K., Moona, G. (eds.) Advances in Mechanical Engineering and Technology. LNME, pp. 307–317. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-9613-8_28 55. Raju, T.B., Kumar, V., Jalil, S.A., Sivakumar, S.: Ranking of factors affecting Covid-19 vaccine distribution using BWM method. In: Rezaei, J., Brunelli, M., Mohammadi, M. (eds.) BWM 2021. LNOR, pp. 238–251. Springer, Cham (2022). https://doi.org/10.1007/978-3030-89795-6_17 56. Ishizaka, A., Khan, S.A., Kheybari, S., Zaman, S.I.: Supplier selection in closed loop pharma supply chain: a novel BWM–GAIA framework. Ann. Oper. Res. 1–24 (2022). https://doi.org/ 10.1007/s10479-022-04710-7 57. Sabbagh, P., et al.: Evaluation and classification risks of implementing blockchain in the drug supply chain with a new hybrid sorting method. Sustainability 13(20), 11466 (2021). https:// doi.org/10.3390/SU132011466 58. Meidute-Kavaliauskiene, I., Yazdi, A.K., Mehdiabadi, A.: Integration of blockchain technology and prioritization of deployment barriers in the blood supply chain. Logistics 6(1), 21 (2022). https://doi.org/10.3390/LOGISTICS6010021 59. Yazdani, M., Torkayesh, A.E., Chatterjee, P.: An integrated decision-making model for supplier evaluation in public healthcare system: the case study of a Spanish hospital. J. Enterp. Inf. Manag. 33(5), 965–989 (2020). https://doi.org/10.1108/JEIM-09-2019-0294/FULL/PDF 60. Amini, A., Abdollahzadeh, S., Teymourlu, M.: A model for evaluating and selecting the food suppliers for hospitals in indeterminate conditions. Health Res. J. 5(1), 16–31 (2019). https:// doi.org/10.29252/hrjbaq.5.1.16 61. Yazdani, M., Tavana, M., Pamuˇcar, D., Chatterjee, P.: A rough based multi-criteria evaluation method for healthcare waste disposal location decisions. Comput. Ind. Eng. 143, 106394 (2020). https://doi.org/10.1016/j.cie.2020.106394 62. Tirkolaee, E.B., Torkayesh, A.E.: A cluster-based stratified hybrid decision support model under uncertainty: sustainable healthcare landfill location selection. Appl. Intell. 52, 13614– 13633 (2022). https://doi.org/10.1007/s10489-022-03335-4 63. Torkayesh, A.E., Zolfani, S.H., Kahvand, M., Khazaelpour, P.: Landfill location selection for healthcare waste of urban areas using hybrid BWM-grey MARCOS model based on GIS. Sustain. Cities Soc. 67, 102712 (2021). https://doi.org/10.1016/j.scs.2021.102712 64. Huang, R.L., Deng, M.H., Li, Y.Y., Wang, J.Q., Li, J.B.: Cloud decision support framework for treatment technology selection of health-care waste. J. Intell. Fuzzy Syst. 1–26 (2022). https://doi.org/10.3233/JIFS-212065

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A State-of the-Art Survey of Best-Worst Method Applications for the Problems Related to COVID-19 ˙Ibrahim Miraç Eligüzel(B)

and Eren Özceylan

Industrial Engineering Department, Gaziantep University, 27100 Gaziantep, Turkey [email protected]

Abstract. The best-worst method (BWM) and its variations have been widely utilized in decision making problems since 2015. During the COVID-19 pandemic, several problems occurred considering the decision making related to legislative, health system, precautions, transportation, and economic decisions. The aim of this paper is to analyze the state-of the-art survey of BWM applications for the problem related to COVID-19. To do so, a bibliographic analysis of literature is conducted. “COVID-19” and “best-worst method” are searched in the Scopus database as keywords, and 40 studies out of 47 studies are taken into consideration. Keywords and abstracts of these studies are analyzed with the N-grams approach and VOSviewer software. In addition, a descriptive analysis is done focusing on the authors’ information and journals. The descriptive analysis demonstrates the topics in the retrieved studies comprehend COVID-19 and BWM with sustainable development goals, healthcare technology, supply chain, risk management, energy consumption, and logistics topics. The descriptive analysis part reveals that supply chain, service quality, social sustainability, supplier selection, sustainable development, green supply, and energy usage are the main topics in the considered literature. Keywords: Best-Worst method · COVID-19 · Pandemic · MCDM · Literature review

1 Introduction Decision making processes have become crucial steps in the COVID-19 pandemic as a solution method for confronted problems. Decision making process is utilized considerably through daily problems in several ways in order to help investigate complex decisions and fortify effective and efficient decision processes. Various intriguing narratives appear to influence decision-making on risk reduction and management strategies to deploy. Municipalities or governments frequently act in an uncoordinated manner, which leads to several inefficient and ineffective management measures in disaster risk reduction during the COVID-19 pandemic. The reason behind considering the BWM on the COVID-19 pandemic is as follows: the BWM can produce ideal weight coefficient values; inconsistencies during the comparison of criteria are decreased by removing a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 19–32, 2023. https://doi.org/10.1007/978-3-031-24816-0_2

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small number of pairwise comparisons; this has a further impact on producing more dependable results, as transitivity relationships are less harmed, resulting in higher consistency of outcomes [1]. From the COVID-19 pandemic point of view, governments and local municipalities have struggled to make decisions to handle healthcare, vaccination, and implement restrictions. Therefore, this kind of situation must be supported in a more systematic way, like through the utilization of BWM. All in all, BWM can offer an efficient and effective process for a situation such as the COVID-19 pandemic. In addition, a study that considers the BWM application on issues related to the COVID-19 pandemic has not been conducted to demonstrate the general view of the application of BWM during the COVID-19 pandemic. The proposed study also aims to fill the aforementioned gap in the literature. In order to achieve a given aim, a systematic approach to analysis of the literature is provided. Therefore, the best-worst method (BWM) and its application during COVID-19 are taken into consideration. To tackle multi-criteria decision-making problems, the BWM is proposed, and a number of choices are weighed against a set of criteria in order to choose the best one (s) [2]. According to BWM, the decision-maker identifies the best (e.g. most desirable, most important) and worst (e.g., least desirable, least important) factors first. After that, pairwise comparisons between each of these two criteria (best and worst) and the other criteria are made. In that aspect, a descriptive analysis of literature is proposed in this study in order to highlight the usage of BWM in multi-criteria decision making during the COVID-19 pandemic. To accomplish the given aim, “COVID-19” and “best-worst method” are searched in the Scopus database. There are 36 studies in total. Retrieved studies are mostly related to determining hospital location, identification and prioritization of strategies, prioritizing economic sectors, circular economy goals, epidemic presentations, supplier selection, and supply-chain management (food and medical). In this study, N-gram is applied in both keywords and abstracts. The N-gram is a phrase that can also refer to any co-occurring character combination in a string [3] and combination that allows understanding of a text in a useful context. N-grams are also referred to as text categorization methodology, which is one of the most effective and widely used methods for analyzing English texts [4]. From that application, the main characteristics of considered studies are retrieved and demonstrated. In that way, BWM application areas are gathered during the COVID-19 pandemic. From this point of view, several studies are proposed in the literature. One of the studies proposed by Petrudi et al. [5] focuses on the social sustainability innovation framework for assessing suppliers. From the same perspective, designing supplier selection strategies is investigated [6], analysis of key success points for sustainable initiatives in supply chains is conducted [7], and mitigating risks in perishable food supply chains is investigated [8]. Also, there are studies related to the healthcare system that utilizes BWM. Some of these studies are proposed by Chen et al. [9], which investigates multi-criteria group decision making for makeshift hospital selection, and Chauhan et al. [10], which comprises identifying group key success factors and computing the relevant significance of these factors. Another study intends to incorporate a multi-criteria decision making approach based on linguistic hesitant fuzzy sets to evaluate and select the best e-learning website [11]. Another example considers the banking industry [12], in which the main consequences of the COVID-19 epidemic on the financial sector were attempted to be understood. As a result, a hybrid strategy is used, which includes a

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novel and extended intuitionistic fuzzy best-worst method for determining the essential components’ weights, as well as a fuzzy inference system for calculating the banking sector’s performance index. Lastly, energy planning of off-grid locations [13], deciding priorities of important factors for developing multi-model transport [14], identifying barriers for digitalization in the supply chain [15], and assessing the measures implemented by the Ready-Made Garments sector [16] are the other application areas in the literature during the COVID-19 pandemic. The aforementioned studies are the instances of BWM application in different areas during the COVID-19 pandemic. In order to have a deep insight into studies related to BWM and COVID-19 in the literature, descriptive and bibliographic analyses are proposed in this study. Analyses are proposed in the second section, with two sub-sections. In the first sub-section, descriptive analysis is given and N-grams application with analyses is given in the second sub-section. Lastly, a conclusion is given.

2 Analysis of Literature Both descriptive analysis and N-grams application to the literature are given in this section. Utilized studies in the proposed study are retrieved from the Scopus database by searching for “COVID-19” and “best-worst method” keywords. Search is done on abstracts, keywords, and titles of studies conducted in English. The Scopus database is used because it is one of the largest compiled abstract and citation databases, with a worldwide scope of scientific publications, conference papers, as well as book chapters, by ensuring only the highest quality data is indexed. After that, the abstracts and keywords of 36 studies are gathered for descriptive analysis. A year-wise publication trend according to subject areas is given in Fig. 1.

Fig. 1. Documents by subject area 2021–2022

In Fig. 1, subject areas of documents are given with respect to 2021–2022. From the Fig. 1, subject areas that are computer science and business management have increased. However, mathematics has decreased, and health professions and economics subject areas are not observed in 2022. The retrieved studies are given in Table 1. The given literature consists of studies conducted until May 10, 2022. The given literature in Table 1 comprehends the BMW method and its variations as a solution methodology. The scope of the literature in

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Table 1 can be expressed as supply-chain management, location selection, determining strategies, and prioritization of economic sectors. Table 1. Brief illustration of literature on BWM with COVID-19. Study

Scope

Methodology

Study

Scope

Methodology

Rezaei (2015)

Method comparison

BWM and AHP

Petrudi et al. (2021)

Social sustainability innovation and supplier assessment

Grey BWM

Abdel-Basst et al. (2020)

A model to BWM and differentiate TOPSIS between COVID-19 and other four viral chest diseases under uncertainty environment

Rajak et al. (2021)

Identifying the stakeholders’ requirements and critical success factors for sustainable supply chain

Hybrid quality function deployment BWM

Moslem et al. (2020)

Transportation modes

Ranjbari et al. (2021)

Agenda for sustainable development

Modified Delphi method, fuzzy inference system and BWM

Ahmad et al. (2021)

Identification and A Sarker et al. Prioritization Of Group-BWM (2021) Strategies To Based MCDM Tackle COVID-19

Flexible Supply Chain Management

BWM

Aydin and Seker (2021)

Determining the location of isolation hospitals

BWM, interval Seyfi-Shishavan Type-2 fuzzy et al. (2021) technique, TOPSIS

Effects of COVID-19 pandemic on the banking sector

Intuitionistic fuzzy best-worst method

Ayyildiz (2021)

Green supply chain

BWM Sharma et al. integrated (2021) interval valued intuitionistic fuzzy AHP

Exploring the priorities for retail supply chains

FUCOM and BWM

Chang et al. (2021)

High-tech industry during the COVID-19 pandemic

BWM and modified VIKOR

Su et al. (2021)

Sustainable supply chain

BWM

Duan et al. (2021)

Risk evaluation of electric power grid

Bayesian BWM and improved MEEM

Wan et al. (2021) Hospital selection

BWM

Integrated trapezoidal interval type-2 fuzzy technique with VIKOR and BWM

(continued)

A State-of the-Art Survey of Best-Worst Method Applications

23

Table 1. (continued) Study

Scope

Foong et al. (2021)

Gong et al. (2021)

Methodology

Study

Scope

Methodology

Prioritizing BWM economic sectors for post-crisis recovery in oleo-chemical industry based on a sector criticality index

Ali et al. (2022)

Energy planning in off-grid locations

Fuzzy optimistic BWM

Evaluating and selecting the best e-learning website for network teaching

Afrasiabi et al. (2022)

Sustainable and resilient supplier selection

Fuzzy BWM and TOPSIS

Linguistic hesitant fuzzy sets and the TODIM

Gupta and Critical success BWM Singh (2021) factors for achieving circular economy goals through emerging technologies during pandemic

Charoennapharat Determining the Fuzzy BWM and Chaopaisarn priorities of (2022) factors for developing and improving multimodal transport

Haqbin et al. (2021)

Identifying and prioritizing recovery solutions for small and medium-sized enterprises

Rough BWM

Chauhan et al. (2022)

Selecting Bayesian BWM suppliers of and pharmaceuticals multi-attributive border approximation area comparison

Hsu et al. (2021)

Epidemic prevention

Bayesian BWM

Chauhan et al. (2022)

Sustainable healthcare operations via telemedicine services

Bayesian BWM

Ilyas et al. (2021)

Supplier selection strategies

BWM and Chen et al. Fuzzy TOPSIS (2022)

Makeshift hospital selection

BWM and data envelopment analysis in trapezoidal interval type-2 fuzzy environment

Jain et al. (2021)

Identifying the risk level of musculoskeletal disorders

BWM and VIKOR

Barrier identification in digitalization technology of supply chain logistic

Bayesian BWM

Gupta et al. (2022)

(continued)

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˙I. M. Eligüzel and E. Özceylan Table 1. (continued)

Study

Scope

Kheybari et al. (2021)

Kumar et al. (2021)

Methodology

Study

Scope

Methodology

Selection of Hybrid temporary risk-averse hospital locations BWM

K.E.K et al. (2022)

Medical oxygen BWM and supply chain Fuzzy technique for order performance

Perishable Food Supply Chains Risk Mitigation

Fuzzy BWM

Munim et al. (2022)

Supply Chain Disruption and Risk Management

Bayesian BWM

Kumar and Developing Kumar Singh resilience in (2021) agri-food supply chains

BWM and Quality function deployment

Sivakumar et al. (2022)

Improving healthcare service quality

BWM and multi-objective linear programming

Pamucar et al. (2021)

Zero-carbon city

BWM-D and TODIM-D based fuzzy MCDM approach

Tapsall et al. (2022)

COVID-19 risk of ocean cruising

Best-worst scaling

Paul et al. (2021)

Key supply chain BWM strategies

Yalcin Kavus et al. (2022)

Evaluating airline service quality

Interval-valued neutrosophic AHP and BWM

2.1 Descriptive Analyses Descriptive is a quantitative analysis-based science that intersects and combines fields such as mathematics, information science, and statistics. Descriptive methods are used to gain insights such as network visualization and citation analysis, as well as to increase the objectivity of the study. In this part, the keyword network of considered studies and the number of studies with respect to journals are illustrated. Next, the number of documents for the first ten authors and the citation network of authors who have more than 15 cites in retrieved literature are demonstrated. From the keyword network of given literature (see Fig. 2), it can be said that COVID19 and BWM are the main focuses of retrieved literature. Sustainable development goals, healthcare technology, supply chain, risk management, energy consumption, and logistics are some of the other topics utilized with COVID-19 and BWM. In Fig. 2, the size of the bubble indicates the weight of the assigned topic in the given data and each color indicates one cluster. Also, risk management, risk mitigation, and supply chain topics have the biggest size aside from COVID-19 and BWM in assigned color. Therefore, it can be concluded that several application areas have a place in the literature. In detail, supply chain management and risk management are the areas that are most utilized with COVID-19 and BWM from Fig. 2. When the retrieved literature is considered, the list of the journals and the number of publications can be seen in Fig. 3. According to Fig. 3, the highest number of publications is observed in “Applied Soft Computing” and “Sustainability” journals. After these

A State-of the-Art Survey of Best-Worst Method Applications

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Fig. 2. Network illustration of keywords.

Fig. 3. Number of studies according to journals.

journals, 7 journals take their place with two publications. Lastly, the rest of the journals in Fig. 3 have only one publication about a given topic in the proposed study. According to Fig. 4, Moktadir has the most publications, followed by seven writers, each of whom has two. (Specifically, Ali, Ayyildiz, Chauhan, Chen, Dong, Jakhar, Paul).

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Fig. 4. Number of documents for first 10 authors.

Fig. 5. Citation network of authors.

Figure 5 shows the citation network of authors in the retrieved literature. From the general view, a total of three clusters emerge, and each cluster is represented with different colors. Rezaei, Paul, and Sarkis are the authors who take the central positions in each cluster. Furthermore, the top five cited writers in a given period of literature are: Rezaei with 120 cites, Paul with 50 cites, Moktadir with 40 cites, Ivanov with 40 cites, and Sarkis with 40 cites. 2.2 N-grams Application and Analyses In this part of the proposed study, descriptive analysis is implemented through the Ngrams application. As an objective, an N-gram model is constructed by counting the number of times word sequences appear in corpus text. The N-gram model is defined as the neighboring sequences of items in a document in technical terms. In order to apply the mentioned analysis, Python 3.7 programming with the “nltk” library is utilized. Throughout the N-grams application, it aimed to deduct modification to BWM and application areas of BWM during the COVID-19 pandemic. Two separate applications are implemented as keyword and abstract applications. The reason behind considering abstracts and keywords separately derives from the purposes of these parts in the articles. Abstract reflects the general overview of the study, which can lead a main idea behind

A State-of the-Art Survey of Best-Worst Method Applications

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a study, and a keyword reflects the scope of the study. In the keyword application, main aims of the studies are attempted to be extracted. In the keyword analysis, the values of n are decided as one and two because of the limited number of keywords. After the keyword analysis, abstract analysis is implemented in order to gather better understanding of the retrieved literature. In this application, n values are set to one, two, and three, respectively, because an increase in n values leads to a decrease in output, which effects the performance of the analysis. Therefore, application areas and utilized methods (variations of BWM) are gathered and demonstrated. Before the application of the N-grams algorithm, it is necessary to clean the text from stop words. After that, lemmatization is applied to gather more accurate results. Lemmatization enables us to obtain the lemma of a given word. Continuous sequences of words, symbols, or tokens in a document are known as N-grams. These can be regarded as the adjacent sequences of items in a document in technical terms. The basic illustration of N-grams is given in Fig. 6.

Fig. 6. Illustration of N-grams application on the sentence for N = 1, 2, 3

Fig. 7. N-grams application on keywords, n = 1.

From Fig. 7, it can be underlined that the COVID-19 pandemic is the main topic of the studies. After that, “supply” and “chain” words take their place, which indicates that the supply chain is also in the focus of the retrieved literature. From the perspective of methodology, the words are gathered as “fuzzy” and “best-worst”. These words indicate that BWM with a fuzzy approach is mostly utilized as a method of multi-criteria decision making.

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Fig. 8. N-grams application on keywords, n = 2.

In Fig. 8, N-grams are applied with n equals to 2. From Fig. 8, it can be underlined that the COVID-19 pandemic is the main focus. The supply chain is an application area that is mostly investigated. In addition, success factors, critical success, and relational analysis are the other topics. Considering the methods of given studies, BWM is utilized and a fuzzy set approach is integrated.

Fig. 9. N-grams application on abstracts, n = 1.

Figure 9 demonstrates the result of N-grams (n = 1) application on abstracts of retrieved literature. It can be seen that the COVID-19 pandemic is again the focus of studies. Other areas can be expressed as supply chain, risk management, suppliers, and sustainability. From Fig. 10, the supply chain is again the most considered area with COVID-19 and BWM. Besides the supply chain topic, service quality, social sustainability, supplier selection, sustainable development, green supply, and energy consumption are the areas that fall into the scope of the retrieved literature. Also, the “trit2F weight” term is observed to be related to methodology. Figure 11 shows the application of N-grams with n equals three. Through this application, one can gather the general view of a given literature due to the triple combination

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Fig. 10. N-grams application on abstracts, n = 2.

Fig. 11. N-grams application on abstracts, n = 3.

of words. Figure 11 illustrates that the power grid is the most focused concern in the studies. It can be deduced that the green supply chain is another application area. From the aspect of methodological approach; fuzzy technique order, order preference similarity, and interval type 2 fuzzy are the terms generally used.

3 Conclusion To conclude, the main aim of this study is to illustrate the analysis of studies related to COVID-19 and BWM in the literature. In order to accomplish the given aim, the Scopus database is utilized and search is implemented with “COVID-19” and “best worst method” keywords. From this search, 43 studies are found and 36 of them are retrieved to conduct analyses. In the proposed study, analyses consist of two main parts. In the first part of the analysis, a bibliometric analysis is applied, which comprehends keyword networks, number of studies with respect to journals, number of documents for the first ten authors, and the citation networks of authors who have more than 15 citations.

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3.1 Implications From the bibliometric analysis, it can be said that studies include the topics covering COVID-19 and BWM, as well as sustainable development goals, healthcare technology, supply chain, risk management, energy consumption, and logistics topics. Additionally, J. Rezaei, S.K. Paul, and J. Sarkis are the authors with the most citations. In the second phase of the analysis, descriptive analysis is performed using the N-grams application on both keywords and abstracts of retrieved literature of this part indicates that the subjects covered by the collected literature include supply chain, service quality, social sustainability, supplier selection, sustainable development, green supply, and energy usage. In addition, it can be said that fuzzy approaches are integrated into BWM to be applied to multi-criteria decision making. 3.2 Limitations and Future Directions One of the limitations of the proposed study is the limited number of word sequences of words in keywords and abstracts to have a comprehensive analysis. Because of this, values of n are limited to 3 in the case of abstract analysis and to 2 in keyword analysis. Another limitation in this study is the availability of research studies. Therefore, 40 studies out of 47 are considered. For future studies, topic modeling methods can be utilized to have a deeper analysis of the mentioned studies.

References 1. Pamuˇcar, D., Ecer, F., Cirovic, G., Arlasheedi, M.A.: Application of improved best worst method (BWM) in real-world problems. Mathematics 8(8), 1342 (2020) 2. Rezaei, J.: Best-worst multi-criteria decision-making method. Omega 53, 49–57 (2015) 3. Cavnar, W.B., Trenkle, J.M.: N-gram-based text categorization n-gram-based text categorization. In: Proc. Third Annu. Symp. Doc. Anal. Inf. Retr., pp. 1–14 (2001) 4. Gurcan, F., Cagiltay, N.E.: Research trends on distance learning: a text mining-based literature review from 2008 to 2018. Interact. Learn. Environ. 1–22 (2020) 5. Petrudi, S.H.H., Ahmadi, H.B., Rehman, A., Liou, J.J.H.: Assessing suppliers considering social sustainability innovation factors during COVID-19 disaster. Sustain. Prod. Consum. 27, 1869–1881 (2021) 6. Ilyas, M., Carpitella, S., Zoubir, E.: Designing supplier selection strategies under COVID-19 constraints for industrial environments. Procedia CIRP 100, 589–594 (2021) 7. Rajak, S., et al.: Issues and analysis of critical success factors for the sustainable initiatives in the supply chain during COVID-19 pandemic outbreak in India: a case study. Res. Transp. Econ. 93, 101114 (2021). https://doi.org/10.1016/j.retrec.2021.101114 8. Kumar, A., Mangla, S.K., Kumar, P., Song, M.: Mitigate risks in perishable food supply chains: learning from COVID-19. Technol. Forecast. Soc. Change 166, 120643 (2021) 9. Chen, Z.H., Wan, S.P., Dong, J.Y.: An efficiency-based interval type-2 fuzzy multi-criteria group decision making for makeshift hospital selection. Appl. Soft Comput. 115, 108243 (2022) 10. Chauhan, A., Jakhar, S.K., Jabbour, C.J.C.: Implications for sustainable healthcare operations in embracing telemedicine services during a pandemic. Technol. Forecast. Soc. Change 176, 121462 (2022)

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11. Gong, J.W., Liu, H.C., You, X.Y., Yin, L.: An integrated multi-criteria decision making approach with linguistic hesitant fuzzy sets for e-learning website evaluation and selection. Appl. Soft Comput. 102, 107118 (2021) 12. Seyfi-Shishavan, S.A., Gündo˘gdu, F.K., Farrokhizadeh, E.: An assessment of the banking industry performance based on Intuitionistic fuzzy Best-Worst method and fuzzy inference system. Appl. Soft Comput. 113, 107990 (2021) 13. Ali, T., Aghaloo, K., Chiu, Y.R., Ahmad, M.: Lessons learned from the COVID-19 pandemic in planning the future energy systems of developing countries using an integrated MCDM approach in the off-grid areas of Bangladesh. Renew. Energy 189, 25–38 (2022) 14. Charoennapharat, T., Chaopaisarn, P.: Factors affecting multimodal transport during CoViD19: a Thai service provider perspective. Sustainability 14(8), 4838 (2022) 15. Gupta, H., Yadav, A.K., Kusi-Sarpong, S., Khan, S.A., Sharma, S.C.: Strategies to overcome barriers to innovative digitalisation technologies for supply chain logistics resilience during pandemic. Technol. Soc. 69, 101970 (2022) 16. Munim, Z.H., Mohammadi, M., Shakil, M.H., Ali, S.M.: Assessing measures implemented by export-oriented RMG firms in an emerging economy during COVID-19. Comput. Ind. Eng. 165, 107963 (2022) 17. Abdel-Basst, M., Mohamed, R., Elhoseny, M.: A model for the effective COVID-19 identification in uncertainty environment using primary symptoms and CT scans. Health Inform. J. 26, 3088–3105 (2020) 18. Moslem, S., et al.: Best-worst method for modelling mobility choice after COVID-19: evidence from Italy. Sustainability 12, 1–19 (2020) 19. Ranjbari, M., Shams Esfandabadi, Z., Scagnelli, S.D., Siebers, P.O., Quatraro, F.: Recovery agenda for sustainable development post COVID-19 at the country level: developing a fuzzy action priority surface. Environ. Dev. Sustain. 23, 16646–16673 (2021) 20. Ahmad, N., Hasan, M.G., Barbhuiya, R.K.: Identification and prioritization of strategies to tackle COVID-19 outbreak: a group-BWM based MCDM approach. Appl. Soft Comput. 111, 107642 (2021) 21. Sarker, M.R., Moktadir, M.A., Santibanez-Gonzalez, E.D.R.: Social Sustainability Challenges Towards Flexible Supply Chain Management: Post-COVID-19 Perspective. Glob. J. Flex. Syst. Manag. 22, 199–218 (2021). https://doi.org/10.1007/s40171-021-00289-3 22. Aydin, N., Seker, S.: Determining the location of isolation hospitals for COVID-19 via Delphibased MCDM method. Int. J. Intell. Syst. 36(6), 3011–3034 (2021). https://doi.org/10.1002/ int.22410 23. Ayyildiz, E.: Interval valued intuitionistic fuzzy analytic hierarchy process-based green supply chain resilience evaluation methodology in post COVID-19 era. Environ. Sci. Pollut. Res. 1–19 (2021).https://doi.org/10.1007/s11356-021-16972-y 24. Sharma, M., Luthra, S., Joshi, S., Kumar, A.: Accelerating retail supply chain performance against pandemic disruption: adopting resilient strategies to mitigate the long-term effects. J. Enterp. Inf. Manag. 34, 1844–1873 (2021) 25. Chang, S.C., Lu, M.T., Chen, M.J., Huang, L.H.: Evaluating the application of csr in the high-tech industry during the covid-19 pandemic. Mathematics 9, 1–16 (2021) 26. Su, Z., Zhang, M., Wu, W.: Visualizing sustainable supply chain management: a systematic scientometric review. Sustainability 13(8), 4409 (2021) 27. Duan, Y., et al.: Risk evaluation of electric power grid investment in China employing a hybrid novel MCDM method. Mathematics 9, 1–23 (2021) 28. Wan, S.P., Chen, Z.H., Dong, J.Y.: An integrated interval type-2 fuzzy technique for democratic–autocratic multi-criteria decision making. Knowl.-Based Syst. 214, 106735 (2021) 29. Foong, S.Z.Y., et al.: A criticality index for prioritizing economic sectors for post-crisis recovery in oleo-chemical industry. J. Taiwan Inst. Chem. Eng. 130, 103957 (2021)

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30. Afrasiabi, A., Tavana, M., Di Caprio, D.: An extended hybrid fuzzy multi-criteria decision model for sustainable and resilient supplier selection. Environ. Sci. Pollut. Res. 29, 37291– 37314 (2021). https://doi.org/10.1007/s11356-021-17851-2 31. Gupta, A., Singh, R.K.: Applications of emerging technologies in logistics sector for achieving circular economy goals during COVID 19 pandemic: analysis of critical success factors. Int. J. Logist. Res. Appl. 1–22 (2021) 32. Haqbin, A., Shojaei, P., Radmanesh, S.: Prioritising COVID-19 recovery solutions for tourism small and medium-sized enterprises: a rough best-worst method approach. J. Decis. Syst. 31, 102–115 (2021) 33. Chauhan, A., Jakhar, S.K., Kumar Mangla, S.: Socio-technological framework for selecting suppliers of pharmaceuticals in a pandemic environment. J. Enterp. Inf. Manag. (2022). https:// doi.org/10.1108/JEIM-02-2021-0081 34. Hsu, W.C.J., Lo, H.W., Yang, C.C.: The formulation of epidemic prevention work of covid-19 for colleges and universities: priorities and recommendations. Sustainability 13, 1–19 (2021) 35. Jain, R., Rana, K.B., Meena, M.L.: An integrated multi-criteria decision-making approach for identifying the risk level of musculoskeletal disorders among handheld device users. Soft Comput. (2021).https://doi.org/10.1007/s00500-021-05592-w 36. Kheybari, S., Ishizaka, A., Salamirad, A.: A new hybrid risk-averse best-worst method and portfolio optimization to select temporary hospital locations for Covid-19 patients. J. Oper. Res. Soc. 1–18 (2021) 37. Vimal, K.E.K., et al.: Modelling the strategies for improving maturity and resilience in medical oxygen supply chain through digital technologies. J. Glob. Oper. Strateg. Sourc. (2022). https://doi.org/10.1108/JGOSS-10-2021-0088 38. Kumar, P., Kumar Singh, R.: Strategic framework for developing resilience in agri-food supply chains during COVID 19 pandemic. Int. J. Logist. Res. Appl. 1–24 (2021) 39. Sivakumar, G., Almehdawe, E., Kabir, G.: Developing a decision-making framework to improve healthcare service quality during a pandemic. Appl. Syst. Innov. 5, 1–21 (2022) 40. Pamucar, D., Deveci, M., Canıtez, F., Paksoy, T., Lukovac, V.: A novel methodology for prioritizing zero-carbon measures for sustainable transport. Sustain. Prod. Consum. 27, 1093– 1112 (2021) 41. Tapsall, S., Soutar, G.N., Elliott, W.A., Mazzarol, T., Holland, J.: COVID-19’s impact on the perceived risk of ocean cruising: a best-worst scaling study of Australian consumers. Tour. Econ. 28, 248–271 (2022) 42. Paul, S.K., Moktadir, M.A., Ahsan, K.: Key supply chain strategies for the post-COVID-19 era: implications for resilience and sustainability. Int. J. Logist. Manag. (2021). https://doi. org/10.1108/IJLM-04-2021-0238 43. Yalcin Kavus, B., Gulum Tas, P., Ayyildiz, E., Taskin, A.: A three-level framework to evaluate airline service quality based on interval valued neutrosophic AHP considering the new dimensions. J. Air Transp. Manag. 99, 102179 (2022)

Why Should Not a Decision Analyst be Content with Only (n − 1) Pairwise Comparisons? Echoes from the Literature Matteo Brunelli(B) Department of Industrial Engineering, University of Trento, Trento, Italy [email protected]

Abstract. More and more often, scholars in the field of multi-criteria decision analysis (MCDA) seem to be overly adverse towards inconsistency. While this has some reasonable justifications, hiding the dirt under the rug, by not even trying to let possible inconsistencies emerge, can have negative effects on the decision process. In other words, there may be some merit in having a decision maker being consistent when he is given the possibility of being inconsistent, but there isn’t any in having a fully consistent decision maker when he cannot be inconsistent. In the latter case, consistency of preferences cannot, by all means, be associated to the reliability of judgements. These concepts are illustrated by taking into account some recently introduced methods whose common inspiration is the Best-Worst Method.

Keywords: Pairwise comparisons

1

· Inconsistency · Preferences

Introduction

One of the main concerns which can be found in the literature on Multi-Criteria Decision Making (MCDM) methods is the reduction of the cognitive effort of experts to a tolerable level. Prominent examples are the Best Worst Method (BWM) [18] and others, as for instance, the methods by Harker [9] and Shiraishi et al. [22] used to reduce the required number of pairwise comparisons in the Analytic Hierarchy Process (AHP). A survey on the issue of incomplete preferences was offerted by Urena et al. [26]. Recently, at least four methods—the Full Consistency Method (FUCOM) [17], the Best Only Method (BOM) [16], the Base Criterion Method (BCM) [10], and the Level Based Weight Assessment (LBWA) [28]—reduced the number of comparisons required from an expert to the minimum necessary number. That is, given n entities to be compared, then (n − 1), properly chosen, comparisons are necessary and required by the above mentioned methods. Such methods, which are all referring to the Best Worst Method as the main inspiration and yardstick, can be briefly described as follows. In the following sections we shall review the methods and analyze they suitability for decision analysis. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 33–40, 2023. https://doi.org/10.1007/978-3-031-24816-0_3

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Preliminaries

As recalled, there are at least four methods which have been recently proposed and require only (n − 1) pairwise comparisons: FUCOM assumes the existence of an a priori established order relation (in terms of importance) on the set of criteria. Given a set of criteria C = {c1 , . . . , cn }, the criteria are ordered from the most to the least important and ties are possible. Then, given this ranking, each criteria is compared to its successor, in terms of importance, and a set of (n − 1) pairwise comparisons are obtained. In the original paper, Pamucar et al. [17] considered the absence of inconsistencies as a validation point for their method and a sign of its greater reliability. At present, FUCOM has been applied to real-world problems in human resource evaluation [23] and in supplier selection [3], to cite only a couple of application domains. BCM requires the expert or the analyst to select a criterion in the set C and use it as a yardstick with which the other (n − 1) criteria are then compared. According to Haseli et al. [10] “The final weights derived from BCM are very reliable because the comparisons are fully consistent”. BOM requires the identification of a “best” criterion which, in turn, is compared to all the other (n − 1) criteria. Indeed, BOM appears to be a special case of BCM. In the original paper, Mostafa [16] considered the consistency of the set of pairwiese comparisons an indicator of the greater reliability of his method with respect to other methods such as BWM and AHP. LBWA is substantially more complex than the three previous methods, and for this reasons, its description is omitted. Nevertheless, also in this case, this method “eliminates inconsistencies which may occur with models using the pairwise comparison technique” [4]. Some comments are in order. If we represent criteria c1 , . . . , cn as nodes of a graph and pairwise comparisons aij between them as edges, all the above mentioned methods consider spanning trees of the graph, as for instance those in Fig. 1. Given the fact that, by definition, a spanning tree does not allow cycles, we can deduce that these approaches do not detect inconsistencies, simply because inconsistencies are not allowed to be exposed. Bringing this to the extreme consequences, each of the three above-mentioned methods considers every set of (n−1) pairwise comparisons as fully consistent, even if these were given randomly. Let us incidentally remark that, in the first three methods listed above, optimization problems are proposed to estimate the weight vector from the (n − 1) pairwise comparisons. However, in none of them it is necessary to solve an optimization problem to find the best fitting weights. In fact, in all cases, the pairwise comparisons, together with the normalization constraint, form a system of equations with a unique solution. However, the focal issue, and the main concern of this note, is that, besides their minimal requests in terms of the number of questions asked to a decision

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Fig. 1. Two sets of (n − 1) comparisons seen as spanning trees.

maker, these methods, according to their proponents, have the particular and appealing feature of reducing inconsistencies to zero. We will argue that (i) such a full consistency is not an intrinsic merit of the method, but it is instead a weakness caused by the impossibility to even measure inconsistency and that (ii) the literature, instead, encourages redundancy of judgments to find and possibly correct inconsistencies.

3

The Agreement in the Literature

There are very few ideas which, to some extent, permeate all the perspectives on decision theory. The existence of inconsistencies—and the inconvenience of hiding them—is one of them. This section recalls, by means of an extensive use of quotations, the position which seems to have been reached in the literature. Descriptive Decision Theory Descriptive decision theory is concerned with the analysis of how decisions are actually made in real-world situations. In this field of study, rationality, expressed in various forms of transitivity and consistency, and its violation is one of the objects under study. This is self-evident if we consider the nature of the inquiry and seminal works such as those by Tversky [25] and Edwards [5]. Prescriptive Decision Theory Scholars in prescriptive decision analysis, which is probably the area closer to MCDA, as it employees a constructive approach, recommends to give the experts the opportunity to express their inconsistencies. In their reference book on multiattribute value and utility theory, Keeney and Raiffa [11, p. 123] encourage experts to provide more than (n − 1) comparisons:

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We repeat that it may be desirable to ask additional questions thereby getting an over-determined system of equations, fully expecting that the set of responses would be inconsistent in practice. These inconsistencies can be used by the analyst to “force” the decision maker to rethink through his preferences. Hopefully, reasons for the original inconsistencies can be found, and from this a consistent set of preferences established. Keeney and Raiffa are fully aware that inconsistencies are related with the redundancy of comparisons, and can be exploited in favor of the decision analyst [11, p. 302]: Concerning overdetermination with inconsistencies, the desire is clearly to have the decision maker reflect on the inconsistencies which perhaps can be illuminated by the analyst and change some responses to imply a consistent set of preferences. Most, if not all, of the other reference books on the same subject maintain the same view. For instance, according to Eisenfuhr et al. [6, p. 138]: It is sensible not to limit ourselves to the determination of m − 1 tradeoffs to generate a consistent system of equations but to deliberately create more than the minimal required number of trade-off measurements in order to check for consistency of the statements. In their behaviorally-oriented textbook, Von Winterfeld and Edwards [27, p. 290] acknowledged that expecting all the possible comparisons would be asking too much, but they also encourage to seek redundancy. In fact, they remark the following: Some redundancy is a good idea, since it can be used to find inconsistent judgments. Finally, even Belton and Stewart [1, p. 141] raised the same point: It is good practice to carry out more than the minimum number of comparisons necessary to specify the set of criteria weights, thus building in a check on the consistency of the decision makers’ judgements. It is important to note that all the above mentioned key references encourage redundancy so that possible inconsistencies are discovered. That is, inconsistencies are not only accepted but also exploited to improve the decision process. 3.1

Normative Decision Theory

Normative decision theory is concerned on how decisions should be made in an ideal world and should, by definition, be the most conservative in terms of accepting violations of the principle of transitivity. Nevertheless, scholars in this field have often expressed concern in not considering inconsistencies and intransitivities. For example, the personal position of Fishburn [7] was the following:

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Transitivity is obviously a great practical convenience and a nice thing to have for mathematical purposes, but long ago this author ceased to understand why it should be a cornerstone of normative decision theory. Such a personal view is compatible with the position expressed by Luce and Raiffa [14] in their book on game theory and decisions, in which they wrote that “No matter how intransitivities arise, we must recognize that they exist”. It is therefore evident that the taboo of inconsistency and intransitivity has fallen, long ago, also in the realm of normative decision theory.

4

The Roles of Redundancy and Inconsistency

Consider now a linear regression problem in y = ax + b with x ∈ Rn−1 and n points in Rn . Obviously, when we try to find the linear relation by minimizing the least squares, or any other reasonable metric, we will always find an hyperplane which perfectly fits the given n points, and the sum of the squared residuals is equal to 0. Does this entail that the estimated relation is a reliable and robust representation of the considered phenomenon? What if some of the n points were outliers or were not obtained with due care and diligence? For a more tangible idea of this issue, one can refer to Fig. 2. With only two datapoints a linear regression y = ax + b with x ∈ R has always zero residuals, but the addition of more points, while yielding some residuals can significantly affect the final result and increase its reliability. y

y

x

x

Fig. 2. Linear regression with and without redundancy.

Let us note that comparing this regression problem with the problem of pairwise comparisons it not too far from a true interpretation of the problem. In fact pairwise comparison matrices have often been seen as collections of datapoints for linear regression [8,12,24]. Thus, we can conclude that, in the case of only (n − 1) pairwise comparisons, having zero inconsistencies does not imply a greater reliability of the results and

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of the method used to obtain them. On the contrary, having more comparisons enhances the reliability and the robustness of the results and yields an estimation of the degree of inconsistency of preferences. This value, similarly to the sum of the squared residuals in linear regression, has an intrinsic value. In fact, studies have shown that (in)consistency can be used as a criterion to judge whether someone is an expert [21]. More precisely, it is a necessary condition for expertise. So, if we do not even attempt to measure it, then we neglect a possible way to estimate levels of expertise. Another related issue regards the existence of possible biases in the judgement of experts [15]. One example is the so called anchoring bias which can arise when a single anchor/yardstick is used to perform the comparisons. Unlike the BWM [19,20], it is likely that some of the methods using (n − 1) comparisons and a single pivot criteria, e.g. BOM, may be affected by this bias, thus reducing the reliability of the obtained results.

5

Conclusions

We have considered the problem of how many questions should be asked to an expert to elicit his/her preferences, and we focused on the case when the least possible amount of questions, (n − 1), are asked. The proponents of recent weighting methods using (n − 1) comparisons often refer to the BWM as the inspiration or as a yardstick for their proposals, possibly thanks to the fact that, unlike complete pairwise comparison matrices, which require n(n − 1)/2 comparisons, the BWM requires only (2n − 3) comparisons, which is a linear function of n. However, the BWM considers the consistency checks a necessary step [13] and therefore it can hardly be taken as an inspiration to reduce the number of comparisons to (n − 1). In conclusion, it seems reasonable to discourage the use of methods which do not allow the estimation of inconsistencies. Using them, would be like flying an airplane without warning lights and think that, for this reason, everything must be fine. Future studies could also focus on the other side of the coin. Namely, the marginal value of the information gained by asking additional pairwise comparisons is certainly decreasing, so that after a while no more comparisons are really necessary. In this case, the danger is represented by cognitive overload. Well-known studies on this topic, e.g. [2], can be updated considering the most recent methods and findings in the literature.

References 1. Belton, V., Stewart, T.: Multiple Criteria Decision Analysis: An Integrated Approach. Springer, Heidelberg (2002). https://doi.org/10.1007/978-1-4615-1495-4 2. Carmone Jr., F.J., Kara, A., Zanakis, S.H.: A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP. Eur. J. Oper. Res. 102(3), 538–553 (1997)

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ˇ Chatterjee, P., Vasiljevi´c, M., Tomaˇsevi´c, M.: Sustainable 3. Durmi´c, E., Stevi´c, Z, supplier selection using combined FUCOM-Rough SAW model. Rep. Mech. Eng. 1(1), 34–43 (2020) 4. Ecer, F., Pamucar, D., Mardani, A., Alrasheedi, M.: Assessment of renewable energy resources using new interval rough number extension of the level based weight assessment and combinative distance-based assessment. Renew. Energy 170, 1156–1177 (2021) 5. Edwards, W.: Behavioral decision theory. Annu. Rev. Psychol. 12(1), 473–498 (1961) 6. Eisenf¨ uhr, F., Weber, M., Langer, T.: Rational Decision Making. Springer, Heidelberg (2010) 7. Fishburn, P.C.: Nontransitive preferences in decision theory. J. Risk Uncertain. 4(2), 113–134 (1991) 8. Gulliksen, H.: A least squares solution for paired comparisons with incomplete data. Psychometrika 21(2), 125–134 (1956) 9. Harker, P.T.: Incomplete pairwise comparisons in the analytic hierarchy process. Math. Modell. 9(11), 837–848 (1987) 10. Haseli, G., Sheikh, R., Sana, S.S.: Base-criterion on multi-criteria decision-making method and its applications. Int. J. Manag. Sci. Eng. Manag. 15(2), 79–88 (2020) 11. Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Trade-Offs. Cambridge University Press, Cambridge (1993) 12. Laininen, P., H¨ am¨ al¨ ainen, R.P.: Analyzing AHP-matrices by regression. Eur. J. Oper. Res. 148(3), 514–524 (2003) 13. Liang, F., Brunelli, M., Rezaei, J.: Consistency issues in the best worst method: measurements and thresholds. Omega 96, 102175 (2020) 14. Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. Dover Publications, Mineola (1989) 15. Montibeller, G., Von Winterfeldt, D.: Cognitive and motivational biases in decision and risk analysis. Risk Anal. 35(7), 1230–1251 (2015) 16. Mostafa, A.M.: An MCDM approach for cloud computing service selection based on best-only method. IEEE Access 9, 155072–155086 (2021) ˇ Sremac, S.: A new model for determining weight coefficients 17. Pamuˇcar, D., Stevi´c, Z, of criteria in MCDM models: Full consistency method (FUCOM). Symmetry 10(9), 393 (2018) 18. Rezaei, J.: Best-worst multi-criteria decision-making method. Omega 53, 49–57 (2015) 19. Rezaei, J.: Anchoring bias in eliciting attribute weights and values in multiattribute decision-making. J. Decis. Syst. 30(1), 72–96 (2021) 20. Rezaei, J., Arab, A., Mehregan, M.: Equalizing bias in eliciting attribute weights in multiattribute decision-making: experimental research. J. Behav. Decis. Mak. 35(2), e2262 (2022) 21. Shanteau, J., Weiss, D.J., Thomas, R.P., Pounds, J.C.: Performance-based assessment of expertise: how to decide if someone is an expert or not. Eur. J. Oper. Res. 136(2), 253–263 (2002) 22. Shiraishi, S., Obata, T., Daigo, M.: Properties of a positive reciprocal matrix and their application to AHP. J. Oper. Res. Soc. Jpn. 41(3), 404–414 (1998) ˇ Brkovi´c, N.: A novel integrated FUCOM-MARCOS model for evaluation 23. Stevi´c, Z, of human resources in a transport company. Logistics 4(1), 4 (2020) 24. Sugihara, K., Ishii, H., Tanaka, H.: Interval priorities in AHP by interval regression analysis. Eur. J. Oper. Res. 158(3), 745–754 (2004)

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25. Tversky, A.: Intransitivity of preferences. Psychol. Rev. 76(1), 31 (1969) 26. Ure˜ na, R., Chiclana, F., Morente-Molinera, J.A., Herrera-Viedma, E.: Managing incomplete preference relations in decision making: a review and future trends. Inf. Sci. 302, 14–32 (2015) 27. Von Winterfeldt, D., Edwards, W.: Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge (1986) ˇ zovi´c, M., Pamucar, D.: New model for determining criteria weights: level based 28. Ziˇ weight assessment (LBWA) model. Decis. Making Appl. Manag. Eng. 2(2), 126– 137 (2019)

Identifying Relative Marginal Value Functions for Ranking Majid Mohammadi1(B) and Jafar Rezaei2 1

Vrije Universiteit Amsterdam, Amsterdam, The Netherlands [email protected] 2 Delft University of Technology, Delft, The Netherlands

Abstract. The current multi-criteria decision-making (MCDM) ranking methods provide suggestions on the superiority of an alternative to other alternatives mainly based on the alternatives’ performance difference and the weights (relative importance) of the criteria as absolute values, while the aim of the MCDM is to only provide the relative importance of criteria/alternatives for the decision under study. In this paper, we put forward a way for ranking alternatives with respect to multiple criteria that considers only the relative importance of every pair of criteria/alternatives and provides a ranking that is agnostic to the alternative performance normalization and prevents the rank reversal phenomenon. We apply the proposed procedure to an example to show its inner mechanism. Keywords: Ranking utility

1

· Normalization-agnostic · Relative marginal

Introduction

Making decision in the presence of multiple criteria is a challenging task due to the possible trade-off between the criteria and difference of the performance of the alternatives under study. Multi-criteria decision-making (MCDM) considers such decision problems and provides the decision-makers (DMs) with proper procedure to deal with conflicting criteria. Often, the relative importance (weight) of the criteria is identified through some questions from the DMs, according to which a preference model is created (e.g., weights or marginal value functions of criteria). According to such a model, the available alternatives could be ranked or sorted, so that the (set of) best alternative(s) could be selected and offered to the DMs [2]. Generally speaking, what makes an alternative preferred to another alternative is a function of the alternatives performance difference and the relative importance (weights) of the criteria. In most MCDM methods, the criteria weights are deemed absolute values, that is in contrast to the nature of the criteria weights as a representation of the relative importance of criteria. Considering: (i) the performance difference, and (ii) weights as absolute numbers, c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 41–47, 2023. https://doi.org/10.1007/978-3-031-24816-0_4

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are the reasons that most MCDM methods are sensitive to the normalization of alternative performance, and cannot deal with the rank reversal if a new alternative/criterion is added. In this paper, we put forward a new way for comparing alternatives based on two crucial principles. First, the criteria weights only convey the relative importance of criteria, and this fact is reflected by assuming that weights are nonnegative and constant-sum (usually unit-sum). Statistically speaking, weights are compositional data [1] and any proper function to process them should be based on the ratios between its different part. This means that any approach based on the absolute values of the criteria weights is not correct, since the compositional data like criteria weights are only a way to represent the relative information. The second principle of our proposal is to consider the relative performance of each alternative over a criterion, not their differences. A by-product of such a principle is that we cannot evaluate the alternatives independently, but rather with respect to another alternative. This principle aligns with the first one as well: Since we know only the relative importance of criteria, we can only know the relative preferences of alternatives as well. Based on this principle, we develop a procedure to elicit the marginal value functions of the ratios between the alternative performance. Along with the criteria weights, we finally arrive at a set of ranking between different alternatives. The proposed approach is agnostic to the normalization of the alternative performance scores, since only the ratios between the scores are considered. In addition, the rank reversal phenomenon is avoided because of considering only the relativity of criteria weights and alternative performance scores. So, suppose that a new alternative is added. We can calculate the ratio between its performance scores with those of others and calculate its relative preferences with other alternatives. However, the new alternative does not influence the ratios of other alternatives, in contrast to other methods that use a normalization of performances. This paper is structured as follows. Section 2 includes the proposal on using the relative marginal value functions for developing a ranking method. Section 3 includes solving an example by the proposed method. Section 4 concludes the paper and put forwards lines for future research.

2

Ranking Method Based on Relative Marginal Value Functions

The ranking methods take, as input, the criteria weights as well as the performance matrix, and provide a ranking of alternatives accordingly. Let A ∈ Rm×n be the performance matrix of m alternatives with respect to n criteria. The criteria are shown by C = {c1 , c2 , ..., cn } with weights w = {w1 , w2 , ..., wn }. The criteria weights are non-negative and unit-sum. The data with such constraints are called composition [1], whose statistical analyses are different than other data with no constraints. The underlying idea of doing such analyses on compositional data is that the relative ratios of different parts (or different

Identifying Relative Marginal Value Functions for Ranking

43

weights in the MCDM case) should be taken into account, not their absolute magnitude. For the MCDM, it means that the criteria weights represent the relative importance of the criteria. Therefore, any function or method processing the criteria weights must use the ratios of the weights [4]. The MCDM methods typically process the criteria weights as absolute, the consequence of which is the occurrence of rank reversal [3]. Also, what should be expected from a ranking method is to provide us with a ratio between alternatives, since the criteria weights are also relative. That being said, we develop a method that tries to identify the relative marginal value functions, where it identifies the relative importance of alternatives over a criterion. For doing so, we propose to compare the best and the worst performance over each criterion and then find the relative marginal value function by interpolation. Accordingly, the relative importance of each pair of alternatives could be simply computed. In summary, the steps required to apply the proposed way of ranking method is as follows: Step 1: For each criterion cj ∈ C, identify the best and the worst performance. For the benefit criteria, it is computed as: Bj = max Aij , i

Wj = min Aij , i

(1)

and for the cost criteria it is computed as: Bj = min Aij , i

Wj = max Aij , i

(2)

where Bj and Wj are the best and the worst performance for criterion j. Step 2: Ask the decision-maker to compare the best to the worst performance of each criterion and express their preferences by a number, shown here by Mj for criterion j: Mj =

Bj , Wj

j = 1, . . . , n,

(3)

where Mj > 1 indicates how much Bj is more important than Wj . For example, M1 = 3 means that B1 is three times more important than W1 . Step 3: Interpolate linearly the marginal value function based on Mj . For doing so, we know that the ratio of alternatives with equal performance is one, and the ratio between the best and the worst performance is Mj for criterion j. We show the linear interpolated function as fj (., .) that takes as input the performance of two alternatives and returns a ratio. Figure 1 shows a linear interpolated function based on Mj . Step 4: For given weights w, we compute the weight factors w ˆ as: w w ˆ= , (4) wmin where wmin is the minimum weight of criteria.

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Fig. 1. A relative marginal value function with linear interpolation.

Step 5: We now compute the pairwise ratios of each pair of alternatives based on the weight factor and relative marginal value function. For two alternatives Ai and Ak , we compute the ratio as:  ˆj fj (Aij , Akj ) Ai j∈Ti/k w , (5) = Ak ˆj fj (Akj , Aij ) j∈Tk/i w where Ti/k = {t|ct (Ai ) > ct (Ak )}. Given the five steps presented above, several points deserve proper attention. We present some of the most important points in the following. Remark 21. In Step 2, we only ask the DM to compare the best performance of alternatives to the worst over a criterion. We can indeed ask more from the DM so that the interpolation of the value function will be more accurate. However, demanding more answers from the DM might not always be possible. Here, we only present the minimal procedure for interpolating the value function. Remark 22. The linear interpolation is only one type of shapes that the value function can attain. Any other value function could also be used, but the procedure remain the same. See [5] for more types of value functions. Remark 23. The best performance as presented in Step 1 could be replaced by the best nominal values for the corresponding criteria. Also, it is possible to think that the values more than a threshold have the same performance for the associated criterion. Therefore, the best Bj for criterion j could be replaced by a value less than or more than the values in the performance matrix. The same applies for the worst performance of criterion j. Remark 24. The proposed procedure is robust to rank reversal when an alternative is added or removed. This is because we consider the ratio between the performance of different alternatives over criteria.

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45

Numerical Example

In this section, an example is solved by using the proposed procedure. Assume that we have three criteria C = {c1 , c2 , c3 } (all benefit) and three alternatives A = {A1 , A2 , A3 } with performance matrix presented in the first three rows of Table 1. Also the weights of criteria are w = [0.5, 0.3, 0.2]. Table 1. The performance matrix of the example. c1 c2 c3 A1 2 A2 4 A3 8

7 3 2

5 4 1

B 8 W 2

7 2

5 1

We first identify the best and the worst performance of alternatives for each criterion, here shown by two vectors B and W . The last two rows of Table 1 show the best and the worst performance of alternatives for each criterion. We now ask a DM to compare the best and the worst performance over each criterion. Assume that the following answers are elicited from the DM: M1 =

B1 = 3, W1

M2 =

B2 = 4, W2

M3 =

B3 = 5. W3

(6)

As a result, the relative marginal value functions are interpolated as in Fig. 2.

Fig. 2. The relative marginal value functions for the example.

For comparing any pairs of alternatives, we need to first find the line equation for each of the relative marginal value function. Figure 3 shows the line equation of the value functions. So, for comparing alternatives A1 and A2 , we have:

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Fig. 3. The relative marginal value function with line equations for the example.

5 , 3 13 f2 (A1 , A2 ) = f1 (7, 3) = , 5 5 f3 (A1 , A2 ) = f1 (5, 4) = , 4 f1 (A2 , A1 ) = f1 (4, 2) =

(7)

where the first equation compare the performance of A2 over A1 since A2 has a higher performance over A1 with respect to c1 , and the other two comparisons are in favor of A1 . The computed ratios in Eq. (7) are also shown in Fig. 3. The weight factors are also computed as: w ˆ=

w = [2.5, 1.5, 1]. 0.2

(8)

Accordingly, the final ratio between two alternatives A1 and A2 is computed as: A1 = A2

13 5

× 1.5 × 54 × 1 = 1.71, 5 3 × 2.5

which means that A1 is preferred to A2 . Similarly, the ratios between the other pairs of alternatives are computed as: 4 × 1.5 × 5 A1 = 4, = A3 3 × 2.5 8 × 1.5 × 4 A2 = 5 5 = 2.3. A3 3 × 2.5

(9)

As a result, the ranking is obtained as: A1 > A2 > A3 .

4

Conclusion and Future Work

In this paper, we presented a ranking method based on learning the relative marginal value function for each criterion. The underlying idea of the proposed approach is that we need to compute the relative importance of alternatives, since we do so for the criteria. Based on this assumption, we develop a method that compares the best and the worst performance of alternatives over each criterion

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and uses linear interpolation to construct the relative marginal value function. According to such functions, the alternatives could be ranked. The proposed procedure does not require normalization, which makes it robust against the rank reversal phenomenon. For future, one can extend the proposed procedure for nonlinear value function and study different ways for eliciting the relative marginal value functions. Also, the outranking methods could be revised according to the proposed framework so that they could be agnostic to the normalization technique and robust against rank reversal.

References 1. Aitchison, J.: The statistical analysis of compositional data. J. Roy. Stat. Soc. Ser. B (Methodol.) 44(2), 139–160 (1982) 2. Ehrgott, M., Figueira, J., Greco, S.: Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Cham (2005) 3. Mohammadi, M., Rezaei, J.: Ratio product model: a rank-preserving normalizationagnostic multi-attribute decision-making method. J. Multi-Criteria Decis. Anal. (2022) 4. Mohammadi, M., Tamburri, D., Rezaei, J.: Unveiling and unraveling aggregation and dispersion fallacies in group MCDM. Group Decis. Negot. (2022) 5. Rezaei, J.: Piecewise linear value functions for multi-criteria decision-making. Expert Syst. Appl. 98, 43–56 (2018)

A Consensus-Based Best-Worst Method for Multi-criteria Group Decision-Making ´ Alvaro Labella(B) , Diego Garc´ıa-Zamora , Rosa M. Rodr´ıguez , and Luis Mart´ınez University of Ja´en, Campus Las Lagunillas s/n, 23071 Ja´en, Spain {alabella,dgzamora,rmrodrig,martin}@ujaen.es

Abstract. The resolution of Multi-criteria Decision-Making (MCDM) problems driven by human knowledge involves collecting their opinions, which usually implies the emergence of inconsistencies. The Best-Worst Method (BWM) was proposed to reduce such inconsistencies and, consequently, obtain more reliable solutions for MCDM problems. Classically, the BWM finds the optimal weights for a set of criteria from the preferences of only one stakeholder, but lately it has been extended to deal with multi-criteria group decision-making (MCGDM) problems. However, when several Decision-Makers (DMs) take part in a decision process, disagreements may appear among them. If these conflicts are neglected, experts may feel unsatisfied with the solution chosen by the group or even question the decision process. Therefore, this contribution proposes an extension of the BWM to smooth disagreements and obtain consensual solutions in MCGDM problems. To do so, an optimization model is introduced which derives a collectively agreed solution for the criteria weights. Additionally, such an optimization model is based on linear programming, which provides accurate results and the ability to deal with hundreds or thousands of DMs.

Keywords: Best-worst method decision-making · Consensus

1

· Multi-criteria group

Introduction

The use of human knowledge in some decision-making problems is essential in contexts in which the available information is neither objective nor quantitative, but uncertain and qualitative [18,25]. In this regard, group decision-making (GDM) problems aim at improving decision processes by taking into account the points of view of multiple experts to make a decision. However, when multiple DMs are involved in the resolution of a decision-making problem, the emergence of conflicts among them is unavoidable [7]. Therefore, it is usual to include a consensus mechanism in the GDM process to soften these discrepancies and provide a collectively agreed solution for the group decision situation [13]. According to Mart´ınez and Montero [16], the most popular methodology to manage the idea c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 48–58, 2023. https://doi.org/10.1007/978-3-031-24816-0_5

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of consensus may be the notion of Soft Consensus, proposed by Kacprzyk [11], which is based on the concept of fuzzy majority. On the other hand, when a human stakeholder is asked to give his/her opinion using pairwise comparison matrices [26], the DM usually does not provide such comparisons consistently, but by incurring some contradictions. Due to the fact that such inconsistencies would negatively affect the decision process, the BestWorst Method (BWM) [20] was initially proposed as an algorithm to solve some behavioral errors in similar Multi-criteria Decision-Making (MCDM) methods and, consequently, reduce the number of pairwise comparisons and inconsistencies. Concretely, the BWM aims at deriving the weights of the criteria in a MCDM problem by just considering the pairwise comparisons between the best and the worst criteria with all the others. To do so, BWM considers an optimization model whose solution provides weights for the criteria that are similar to the original preferences elicited from the DM. Even though there are some proposals which aim at adapting the BWM to GDM [15,17], they neglect the notion of Soft Consensus [11] and the use of consensus measures [19] to manage the disagreements among DMs. Therefore, this contribution aims to simultaneously deal with both the inconsistencies in the preferences given by human DMs and the conflicts that appear among the participants in GDM problems. To do so, here it is proposed a reformulation of classic BWM which allows managing several DMs to provide agreed collective weights derived from pairwise comparisons involving their opinions about the best and the worst criteria. Furthermore, the proposed Consensus-based BWM (C-BWM) is stated in terms of pairwise comparisons given in a 0–1 scale, which allow linearizing the optimization model to obtain more accurate results than the ones provided by nonlinear solvers (see Fig 1).

Fig. 1. Scheme of C-BWM model

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In addition, this linearization improves the computational performance with respect to model resolution, and consequently qualifies the proposal to quickly manage GDM problems involving hundreds or thousands of DMs [23]. The remainder of the contribution is organized as follows: Sect. 2 reviews basic concepts related to GDM, consensus, and BWM. Section 3 introduces the proposal, a C-BWM for MCGDM. In Sect. 4, the performance of the proposal is shown through the resolution of a MCGDM problem. To conclude, Sect. 5 draws some conclusions together with future research lines.

2

Background

This section is devoted to revising some basic concepts related to the proposal. 2.1

Group Decision-Making and Consensus

Different situations in real-world contexts, such as business, work, social or personal life, require making a choice among different options [1,9]. Even though sometimes the available information regarding such decisions is objective, when the accessible data is vague or uncertain, the complexity of the decision process increases, and it is necessary to take into account the knowledge of a group of human experts to consider multiple views [13,18]. In particular, when a group of experts E = {E1 , E2 , . . . , Em } is asked to evaluate possible alternatives A = {A1 , A2 , . . . Ar } according to different criteria C = {C1 , C2 , . . . , Cn }, the decision problem is a MCGDM problem [10,12]. Despite the participation of several DMs in the decision process presents several advantages, it also gives rise to a relevant phenomenon: the emergence of disagreements between them [13]. If disagreements are not properly managed before selecting a solution for the decision problem, such a solution may not satisfy some experts, which could question the trustworthiness of the process [7]. To overcome this drawback, Consensus Reaching Processes (CRPs) are performed before choosing the best alternative to smooth out the possible conflicts among experts’ opinions and, in this way, achieve an agreed solution for the decision problem [8,18]. In a CRP, experts talk to each other, exchange views, and, if they consider, change their initial opinions to increase the level of agreement within the group. This process is usually driven by a moderator, who is in charge of identifying conflicts and suggesting changes to experts about their opinions [14]. Several consensus approaches have been proposed in the specialized literature [19]. Some of them include feedback mechanisms, in which experts are asked if they want to change their preferences [22]. On the other hand, other proposals provide an automatic process in which experts are not questioned about modifying their preferences, but they are automatically modified [2] (see Fig. 2).

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Fig. 2. Schemes of CRPs with and without feedback mechanisms

2.2

Best-Worst Method

The classic BWM [6,20,21] aims to determine the priority of the criteria C = {C1 , C2 , . . . , Cn } in a certain MCDM problem by reducing inconsistencies in the elicitation process and obtaining more consistent solutions.

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To do so, the DM should provide, according to his point of view, the best and the worst criteria, which are denoted CB and CW , respectively. Furthermore, such DM must point out the comparison of CB and the remaining criteria to obtain the Best-to-Others (BO) vector, BO = {aB1 , aB2 , . . . , aBn }, where aBi ∈ [1, 9] ∩ N denotes the degree of preference of CB over the criterion Ci . In the same way, the DM also compares all criteria with CW to obtain the Others-to-Worst (OW) vector, OW = {a1W , a2W , . . . , anW }, where aiW ∈ [1, 9] ∩ N denotes the preference degree of the criterion Ci over CW . These values are then used as the input of an optimization model to obtain the weights for the criteria {w1∗ , w2∗ , . . . , wn∗ }:   wB wi min max |, |aiW − | |aBi − w i=1,2,...,n wi wW  (BWM) n i=1 wi = 1, s.t. wi ≥ 0, ∀ i = 1, 2, ..., n, Due to the full consistency of a multiplicative pairwise comparison matrix in 1–9 Saaty’s scale [24] is given by aij = aik akj ∀ i, j, k ∈ {1, 2, ..., n}, the weights obtained as output from the BWM allow constructing a fully consistent wi ) which is close to the multiplicative pairwise comparison matrix (ˆ aij := w j original preferences BO and OW given by the DM.

3

Consensus-Based Best-Worst Method

Let us consider a MCGDM problem in which a group of m ∈ N experts E = {E1 , E2 , ..., Em } wants to reach a collective agreed solution about the importance of n ∈ N criteria. To do so, each expert provides his/her opinions using BestWorst preferences, i.e., each expert Ek points out which are the best (B k ) and the worst (W k ) criteria according to his/her point of view and also provides two pairwise comparison vectors: for the best criteria CB k BOk = (aB k 1 , aB k 2 , ..., aB k n ) and for the worst criteria CW k OW k = (a1W k , a2,W k , ..., an,W k ) These preferences are given by experts using a 1–9 Saaty scale [24]. To simplify the notation and linearize the optimization model, this information is first remapped into a linear scale by using the function f : [ 19 , 9] → [0, 1] defined as f (x) = 12 (1 + log9 (x)) ∀ x ∈ [ 19 , 9], and then it is stored as follows:

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53

– A matrix P ∈ Mm,n containing the preferences BOk , where Pki = f (aB k i ) ∀ 1 ≤ k ≤ m, 1 ≤ i ≤ n, – A matrix Q ∈ Mm,n containing the preferences OW k , where Qki = f (aiW k ) ∀ 1 ≤ k ≤ m, 1 ≤ i ≤ n, – A vector B = (B 1 , B 2 , ..., B m ) ∈ Rm , B k ∈ {1, 2, ..., n}, containing the best criterion for each expert, – A vector W = (W 1 , W 2 , ..., W m ) ∈ Rm , W k ∈ {1, 2, ..., n}, containing the worst criterion for each expert. In the same way, the solution for the collective BWM problem is stored in a matrix with the corresponding individual weights (wki ) ∈ Mm×n ([0, 1]), where wki represents the individual weight of the expert Ek for the criterion Ci . Respecn tively, the mcollective weights are provided in a vector (g1 , g2 , ..., gn ) ∈ R , where 1 gi = m k=1 wki i ∈ {1, 2, ..., n} satisfy the consensus constraint |wki − gi | ≤ ε ∀ i = 1, 2, ..., n, k = 1, 2, ..., m. and ε ∈]0, 1]. When using ratings on a 0 − 1 linear scale, the distance between the weights that the method aims to obtain and the original preferences elicited from the experts can be defined by ξ : Mm,n × Mm,n × Rn × Rn × Mm,n → R+ ξ(P, Q, B, W, w) =

m  n 

(|Pki − 0.5 − wkB k + wki | + |Qki − 0.5 − wki + wkW k |)

k=1 i=1

Remark 1. Note that the function ξ stands for an additive distance in a 0– 1 scale, easier to linearize than the original multiplicative distance for a 1–9 Saaty’s scale. Therefore, for fixed values P, Q, B, W , the C-BWM is defined as min ξ(P, Q, B, W, w) w,g ⎧n ⎪ i=1 wki = 1, ∀ k = 1, 2, ..., m ⎪ ⎪ ⎨w ≥ 0, ∀ i = 1, 2, ..., n, k = 1, 2, ..., m, ki s.t. m 1 ⎪ = g i ⎪ k=1 wki ∀ i = 1, 2, ..., n, m ⎪ ⎩ |wki − gi | ≤ ε ∀ i = 1, 2, ..., n, k = 1, 2, ..., m.

(C-BWM)

The output of this model consists of individual and collective weights which minimize the distance function ξ for the given preferences and satisfy a consensus condition. In addition, the presented model allows considering both preferences elicited in a 1−9 Saaty’s scale [24] and preferences in the range [0−1] (see Fig. 1). Furthermore, the proposed model substitutes the original objective function in BWM [20] for another one based on linear combinations and absolute values, which facilitates the linearization of the model to deal with hundreds or even thousands of DMs and provide more precise results in the numeric resolution [23].

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Remark 2. Note that the optimization model C-BWM provides a consensual solution in which the DMs’ preferences are modified as little as possible, since it minimizes the distance between the weights that the method obtains and the original preferences given by the DMs. Remark 3. Note that this model considers the function f to remap the 1–9 multiplicative scale into a 0–1 additive scale. Consequently, quotient-based expressions in traditional BWM are now expressed in terms of sums and differences. For this reason, the aggregation of the weights has been conducted using an arithmetic mean instead of the geometric mean.

4

Illustrative Example

In this section, the proposed model is applied to select the agreed criteria weights in a MCGDM problem. The soft drink company BAT-Cola has started the recruitment process for a marketing manager. The recruitment team, formed by five experts E = {E1 , E2 , E3 , E4 , E5 }, considers that four key aspects should be taken into account in the selection process: C={C1 : Proficiency in languages, C2 : Work experience, C3 : Leadership capacity, C4 : Age}. However, experts have different opinions about the importance of these aspects in selecting the best candidate, and the company would prefer an agreed importance of these criteria. For this reason, before the selection process, the company asks the team to provide their preferences about the importance of the skills and, from them, obtain collective consensual weights for each aspect. These preferences are compiled in Tables 1 and 2. Table 1. BO preferences in 1–9 Saaty’s scale. BO C1 C2 C3 C4 Best E1 E2 E3 E4 E5

1 8 1 4 4

2 1 3 1 1

6 6 6 8 4

3 3 3 8 5

1 2 1 2 2

Table 2. OW preferences in 1–9 Saaty’s scale. OW C1 C2 C3 C4 Worst E1 E2 E3 E4 E5

6 1 6 2 4

3 8 5 8 5

1 2 1 1 4

2 6 3 5 1

3 1 3 3 4

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Table 3. BO preferences in 0–1 scale. BO C1

C2

C3

C4

Best

E1 E2 E3 E4 E5

0.66 0.5 0.75 0.5 0.5

0.91 0.91 0.91 0.97 0.82

0.75 0.75 0.75 0.97 0.87

1 2 1 2 2

0.5 0.97 0.5 0.82 0.82

Table 4. OW preferences in 0–1 scale. OW C1

C2

C3

C4

Worst

E1 E2 E3 E4 E5

0.75 0.97 0.87 0.97 0.87

0.5 0.66 0.5 0.5 0.82

0.66 0.91 0.75 0.87 0.5

3 1 3 3 4

0.91 0.5 0.91 0.66 0.82

Experts have provided their preferences using the 1–9 Saaty scale, which are transformed into a 0–1 scale using the function f : [ 19 , 9] → [0, 1] defined as f (x) = 12 (1 + log9 (x)) ∀ x ∈ [ 19 , 9] (see Tables 3 and 4) to apply the C-BWM lately and derive the consensual weights. From the experts’ preferences, the C-BWM allows obtaining consensual collective weights (ε = 0.05). The approximated results of the optimization model are shown in Table 5. To obtain the results, we have used the solver Clp for the Julia 1.6 programming language [3] on the cloud service Google Colaboratory [4] (2.20 GHz Intel(R) Xeon(R) CPU and 13 GB RAM). Table 5. Results. Weights

C1

C2

C3

C4

E1 E2 E3 E4 E5

0.42 0.32 0.42 0.32 0.37

0.4 0.5 0.4 0.5 0.45

0.01 0.09 0.01 0.03 0.1

0.17 0.09 0.17 0.15 0.08

Collective 0.37 0.45 0.05 0.13

Therefore, according to the optimization model, the most relevant criterion is C2 : Work Experience (0.45), which makes sense taking into account that the majority of experts in the group think that this aspect is the most important.

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Fig. 3. Graphic MDS [5] visualization showing the relative distances between the DMs represented in two dimensions.

In the same sense, C3 : Leadership capacity (0.05) is selected as the worst rated criterion by the majority of the experts, and this is reflected in the consensual collective weight. It should be highlighted that, even though some experts have had to modify their original preferences (for example, E2 ), these modifications are the minimum required to satisfy the consensus condition. To graphically show the significance of including consensus in the classical BWM approach, the individual weights obtained by applying the classical BWM to the BO and OW preferences (ε = 1 in the C-BWM) have been compared with the modified agreed opinions obtained by using the C-BWM with ε = 0.05. Figure 3 shows the multidimensional scaling (MDS) representation [5] of both non-agreed and agreed preferences and their respective collective opinion. As expected, the figure indicates that the preferences corresponding to the consensual approach are much closer to the group opinion.

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To sum up, the introduced optimization model is able to detect and smooth disagreements in the experts’ preferences in a GDM problem and provide an agreed solution to derive the criteria weights when managing multiple DMs.

5

Conclusions

This contribution has introduced an extension of BWM for MCGDM, which allows obtaining agreed weights for the given criteria according to the preferences of several experts. To do so, the original optimization-based BWM proposal [20] has been modified to take into account the preferences of several experts and provide a collectively agreed solution to weight the considered criteria. In addition, this proposal has been presented in terms of linear variables, objective function, and constraints, which allow providing more precise results than when using nonlinear optimization. Furthermore, this linear approach also implies an improvement of computational efficiency, which guarantees the good performance of the model when dealing with decision problems which consider hundreds or thousands of experts. Future studies should focus on exploring the relationship between this proposal and the recently proposed Comprehensive Minimum Cost Consensus (CMCC) models [13] as well as introducing new BWM-CMCC models which could be based on multi-objective optimization or bilevel optimization. Acknowledgements. This work is partially supported by the Spanish Ministry of Economy and Competitiveness through the Spanish National Project PGC2018099402-B-I00, and the Postdoctoral fellow Ram´ on y Cajal (RYC-2017-21978), the FEDER-UJA project 1380637 and ERDF, by the Spanish Ministry of Science, Innovation and Universities through a Formaci´ on de Profesorado Universitario grant (FPU2019/01203) and by the Junta de Andaluc´ıa, Andalusian Plan for Research, Development, and Innovation (POSTDOC 21-00461).

References 1. Belton, V., Stewart, T.: Multiple Criteria Decision Analysis: An Integrated Approach. Springer Science & Business Media, Heidelberg (2002) 2. Ben-Arieh, D., Easton, T.: Multi-criteria group consensus under linear cost opinion elasticity. Decis. Support Syst. 43(3), 713–721 (2007) 3. Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017). https://doi.org/10.1137/ 141000671 4. Bisong, E.: Building Machine Learning and Deep Learning Models on Google Cloud Platform. Springer, Heidelberg (2019) 5. Borg, I., Groenen, P.J.: Modern Multidimensional Scaling: Theory and Applications. Springer Science & Business Media, Heidelberg (2005) 6. Brunelli, M., Rezaei, J.: A multiplicative best-worst method for multi-criteria decision making. Oper. Res. Lett. 47(1), 12–15 (2019)

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7. Butler, C.L., Rothstein, A.: On Conflict and Consensus: A handbook on Formal Consensus Decisionmaking. Citeseer (2007) 8. Garc´ıa-Zamora, D., Labella, A., Rodr´ıguez, R.M., Mart´ınez, L.: Nonlinear preferences in group decision-making. extreme values amplifications and extreme values reductions. Int. J. Intell. Syst. 36(11), 6581–6612 (2021) 9. Greco, S., Figueira, J., Ehrgott, M.: Multiple Criteria Decision Analysis, vol. 37. Springer, Heidelberg (2016) 10. Ishizaka, A., Nemery, P.: Multi-criteria Decision Analysis: Methods and Software. John Wiley & Sons, Hoboken (2013) 11. Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18(2), 105–118 (1986) 12. Kilgour, D.M.: Group decisions: choosing multiple winners by voting. In: Kilgour, D.M., Eden, C. (eds.) Handbook of Group Decision and Negotiation, pp. 439–460. Springer, Cham (2021) 13. Labella, A., Liu, H., Rodr´ıguez, R.M., Mart´ınez, L.: A cost consensus metric for consensus reaching processes based on a comprehensive minimum cost model. Eur. J. Oper. Res. 281, 316–331 (2020) 14. Labella, A., Liu, Y., Rodr´ıguez, R.M., Mart´ınez, L.: Analyzing the performance of classical consensus models in large scale group decision making: A comparative study. Appl. Soft Comput. 67, 677–690 (2018) 15. Liang, F., Verhoeven, K., Brunelli, M., Rezaei, J.: Inland terminal location selection using the multi-stakeholder best-worst method. Int. J. Logistics Res. Appl. pp. 1– 23 (2021) 16. Mart´ınez, L., Montero, J.: Challenges for improving consensus reaching process in collective decisions. New Math. Nat. Comput. 3(02), 203–217 (2007) 17. Mohammadi, M., Rezaei, J.: Bayesian best-worst method: a probabilistic group decision making model. Omega 96, 102075 (2020) 18. Palomares, I., Rodriguez, R.M., Martinez, L.: An attitude-driven web consensus support system for heterogeneous group decision making. Expert Syst. Appl. 40, 139–149 (2013) 19. Palomares, I., Estrella, F., Martinez, L., Herrera, F.: Consensus under a fuzzy context: taxonomy, analysis framework afryca and experimental case of study. Inf. Fusion 20, 252–271 (2014) 20. Rezaei, J.: Best-worst multi-criteria decision-making method. Omega 53, 49–57 (2015) 21. Rezaei, J.: Best-worst multi-criteria decision-making method: some properties and a linear model. Omega 64, 126–130 (2016) ´ Tr´e, G.D., Mart´ınez, L.: A large scale consensus 22. Rodr´ıguez, R.M., Labella, A., reaching process managing group hesitation. Knowl.-Based Syst. 159, 86–97 (2018) ´ Dutta, B., Mart´ınez, L.: Comprehensive minimum 23. Rodr´ıguez, R.M., Labella, A., cost models for large scale group decision making with consistent fuzzy preference relations. Knowl.-Based Syst. 215, 106780 (2021) 24. Saaty, T.L.: How to make a decision: the analytic hierarchy process. Eur. J. Oper. Res. 48(1), 9–26 (1990) 25. Sun, Y., He, S., Leu, J.: Syndicating web services: a QoS and user-driven approach. Decis. Support Syst. 43, 243–255 (2007) 26. Thurstone, L.L.: A law of comparative judgment. Psychol. Rev. 34(4), 273 (1927)

A Fuzzy Best-Worst Method Based on the Fuzzy Interval Scale Nastaran Goldani(B)

and Mostafa Kazemi

Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran [email protected], [email protected]

Abstract. The best worst method (BWM) has been regarded as an ideal alternative to the analytic hierarchy process (AHP) between multi-criteria decision making (MCDM) methods since it reduces the number of pairwise comparisons and maintains the consistency between judgments. In real decision-making problems, decision-makers are not always sure about their decisions and mainly express their preferences with degrees of uncertainty. Moreover, they often face problems that must distinguish a prominent alternative among a shortlist with similar traits, which raises the severity of decision making in an uncertain environment. To deal with these situations, we propose a new linear fuzzy BWM based on a fuzzy interval scale, which is called fuzzy additive BWM. The proposed method maintains the features of the original BWM and also decreases the complexity of fuzzy calculations by eliminating the fuzzy multiplication operation. In addition, a fuzzy consistency index is proposed to check the validity of the input data. Also, fuzzy consistency ratio and total deviation are introduced for evaluating the obtained results by the fuzzy additive BWM. An example is applied and solved by the fuzzy additive BWM to indicate the method’s efficiency. Finally, comparative analyses are conducted to show the advantages and suitability of the new BWM method. Keywords: Best-worst method · Fuzzy interval scale · Multicriteria decision making

1 Introduction The analytic hierarchy process (AHP) [1] is one of the essential methodologies in multicriteria decision making (MCDM), which performs based on the pairwise comparison tool. Since its proposal, it has been applied to solve different decision-making problems, such as health-care [2], logistics [3, 4], business [5], agriculture [6]. In order to deal with imprecision and vagueness in decision-making, which is a direct effect of the rapid industrialization of societies, some researchers have extended the classical AHP under different theories, such as fuzzy set [7–9], interval type 2 fuzzy set [10, 11], intuitionistic fuzzy sets [10–14], interval-valued intuitionistic fuzzy sets [12], and hesitant fuzzy sets [15, 16].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 59–73, 2023. https://doi.org/10.1007/978-3-031-24816-0_6

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Despite the vast application of AHP in different domains, much research has been done to criticize its different characteristics. Wang et al. [17] defined some examples to prove the non-efficiency of the extent analysis method (EAM), one of the most wellknown extensions of AHP, and the revised EAM. Yuen [18] argued that the ratio scale used in AHP is not an appropriate scale to show the human cognition for all pairwise comparison problems and is very likely to produce exaggerated results, especially when there is a small and homogeneous group of competitive alternatives which are needed to be evaluated. For an example, if person A is 60 kg and person B is 61 kg, B is slightly heavier than A. Considering the ratio scale or fuzzy ratio scale, B is two times heavier than A, which indicates that his/her weight is equal to 120 kg based on the ratio scale and is (60, 120, 180) based on the fuzzy ratio scale. In order to avoid this exaggeration, Yuen introduced the interval scale, which is defined based on the differences between utilities, not the ratios of weights [19]. In this case, the slightly heavier is indicated by one, so the weight of B is correctly calculated as 61 kg, based on the interval scale or is (60, 61, 62) based on the fuzzy interval scale. Based on AHP, all criteria and alternatives are pairwise compared by experts or decision-makers (DMs). In this case, for n criteria (n2 −n)/2 comparisons must be done, which leads to imprecision in the subjective judgments and great value of consistency ratio. In order to ignore this issue, Rezaei [20] introduced the Best Worst Method (BWM). In the proposed method, the number of pairwise comparisons is reduced to 2n − 3. BWM is based on the reference comparisons, in which the best and the worst criterion are first distinguished by DMs, and then the comparisons are made between the best criterion to others and other criteria to the worst. Hence, the results of BWM are more consistent than that of AHP, which persuades DMs to investigate it under different types of fuzzy set theories [21, 22]. The original BWM is constructed based on a non-linear programming model, and many other extensions are direct extensions of the original one [21–24]. Rezaei [25] proposed a linear form of the original BWM. This linear programming model is based on the Least Worst Absolute Error investigated by Choo and Wedley [26], stated as one of the difficult to solve models. Zhang et al. [27] proposed a cognitive BWM (CBWM) that uses the interval scale to show human cognition. They illustrated the superiority of their linear model to AHP and BWM by applying it to a case study. Brunelli and Rezaei [28] introduced a new multiplicative BWM based on the algebraic approach. However, it was mentioned that the proposed model is mathematically simple; there is a need for logarithmic transformation to obtain the optimal weights of criteria and consistency ratio, which makes it complicated. Guo and Zhao [21] extended the original model to fuzzy context. Nevertheless, there have been some mathematical errors in their study, which are mentioned in [29, 30], and deeply discussed in [31]. In this paper, we propose a new linear BWM based on the fuzzy interval scale, which is more straightforward in calculating fuzzy weights.

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The rest of this study is organized as follows. In Sect. 2, the definitions of fuzzy interval scale are briefly introduced. A new consistency index based on the input data, and the fuzzy cognitive BWM (FCBWM) are presented. In addition, to check the model’s output, a new consistency ratio is also introduced in this section. In Sect. 3, an example is illustrated. Besides, the obtained results are compared with the results of CBWM and the original BWM. Finally, Sect. 4 gives conclusions of the research.

2 Fuzzy Cognitive Best Worst Method Under the Fuzzy Interval Scale Let (X , N) is a measurement scale schema based on the interval scale and maps the linguistic variables to the corresponding numerical variables. The numerical representation is in the following form.     iκ  X = αi = ∀i ∈ −τ , . . . , −1, 0, 1, . . . , τ , κ0 (1) τ where κ is the crisp normal utility that is used to adjust an interval scale to a fuzzy triangular number, and 2τ + 1 is the number of measurements in the scale schema. To simplify the computations, it is assumed that max(X ) = κ and κ = τ . The interval and ratio scale schema are shown in Table 1. Table 1. Ratio and interval rating scale schemas Scale

Notation

Fuzzy ratio scales

Fuzzy interval scale

Absolutely important

8

(8,9,9)

(7 κ8 , 8 κ8 , 8 κ8 )

Outstandingly important

7

(7,8,9)

Significantly important

6

(6,7,8)

Strongly important

5

(5,6,7)

Highly important

4

(4,5,6)

Fairly important

3

(3,4,5)

Moderately important

2

(2,3,4)

Slightly important

1

(1,2,3)

(0, κ8 , 2 κ8 )

Equally important

0

(1,1,1)

(0, 0, 0)

(6 κ8 , 7 κ8 , 8 κ8 ) (5 κ8 , 6 κ8 , 7 κ8 )

(4 κ8 , 5 κ8 , 6 κ8 ) (3 κ8 , 4 κ8 , 5 κ8 )

(2 κ8 , 3 κ8 , 4 κ8 )

( κ8 , 2 κ8 , 3 κ8 )

Definition 1. Let B˜ = (b˜ ij )n×n be a fuzzy pairwise opposite matrix (FPOM), when b˜ ij = (bl , bm , bu ) is a fizzy preference degree of i over j for all i, j = 1, 2, . . . , n. ij

ij

ij

B˜ = (b˜ ij )n×n is a fuzzy complement matrix, if: b˜ ij + b˜ ji = 0, b˜ ii = 0.

(2)

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Definition 2. A FPOM is perfectly consistent if it satisfies the following additive transitivity, for all i, j, k = 1, 2, . . . , n: b˜ ik + b˜ kj = b˜ ij .

(3)

Definition 3. Let B˜ = (b˜ ij )n×n is a consistent FPOM and V˜ = (˜v 1 , v˜ 2 , . . . , v˜ n ) is a fuzzy utility vector, then: b˜ ij = v˜ i − v˜ j , i, j = 1, 2, . . . , n

(4)

  Definition 4 [19]. Let V˜ = v˜ 1 , . . . , v˜ j , . . . , v˜ n , v˜ j = (vjl , vjm , vju ), be the triangular ∼

fuzzy utility vector, for all j = 1, 2, . . . , n, and κ= (κ l , κ m , κ u ) be the fuzzy normal utility. The rescaled vector of V˜ , is: 



ϑil ϑim ϑiu l m u l m u ˜ = { w˜ = wi , wi , wi | wi , wi , wi = , , , (i = 1, . . . , n)} (5) W nκ u nκ u nκ u   ˜ = w˜ 1 , . . . , w˜ j , . . . , w˜ n , w˜ j = (wl , wm , wu ), be a triangular Definition 5 [32]. Let W j j j fuzzy weight vector. It is called a normalized triangular fuzzy weight/priority vector if and only if the following conditions hold:

n wju + wl ≤ 1, i=j,i=1 i

n (6) wm = 1, i=1 i

n wjl + wiu ≥ 1. i=j,i=1

2.1 Fuzzy Cognitive Best Worst Method BWM is a weighting method based on pairwise comparisons. Unlike matrix-based methods, BWM needs two pairwise vectors to derive the criteria weights. In the following, we propose the fuzzy cognitive best-worst method (FCBWM). The basic steps of the original BWM and FCBWM are the same, so to avoid redundancy, we propose the steps of FCBWM. Step 1. Determine a set of criteria Step 2. Determine the best and the worst criteria from the set of criteria.

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Step 3. Conduct the pairwise comparisons between the best criterion and the other criteria. The interval scale is used to determine the Best-to-Others (BO) vector ABO = l , a m , a u ) denotes the preference degree of the (˜aB1 , a˜ B2 , . . . , a˜ Bn ), where a˜ Bj = (aBj Bj Bj best criterion to criterion j, j = 1, 2, . . . , n. It is clear that a˜ BB = (0, 0, 0). Step 4. Conduct the pairwise comparisons between the worst criterion and the other criteria. The interval scale is used to determine the Others-to-Worst (OW) vector AOW = l , a m , a u ) denotes the preference degree of (˜a1W , a˜ 2W , . . . , a˜ nW ), where a˜ jW = (ajW jW jW criterion j to the worst criterion, j = 1, 2, . . . , n. It is clear that a˜ WW = (0, 0, 0). Step 5. Determine the optimal weights of criteria. To derive the optimal weights of criteria, a˜ Bj = v˜ B − v˜ j and a˜ jW = v˜ j − v˜ W should  be satisfied. So, we  minimize the maximum absolute differences of a˜ Bj − v˜ B + v˜ j  and a˜ jW − v˜ j + v˜ W  for all j. Therefore, the following optimization problem is defined to derive the optimal weights of criteria.     min maxj {a˜ Bj − v˜ B + v˜ j , a˜ jW − v˜ j + v˜ W }

wjl wjl

=

ϑjl

, nκ u m ϑj wjm = u , nκ ϑju wju = u , nκ

n u wj + wl ≤ 1 i=j,i=1 i

n wm = 1 i=1 i

n wjl + wiu ≥ 1 wjl

≤

wjm

(7)

i=j,i=1 ≤ wju ,

≥ 0, (j = 1, 2, . . . , n).

    ∼ ∼ where κ= (κ l , κ m , κ u ) is the fuzzy normal utility. κ m = max X and κ= (max X −     δ, max X , max X + δ) is a fuzzy form of κ, δ is the average of the difference of the ∼

modal values of the adjacent atomic terms. n κ= (nκ l , nκ m , nκ u ) is the fuzzy population utility.

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Equation 6 can be transformed into the following programming model. min ε    l  aBj − vBl + vjl  < ε,    m  aBj − vBm + vjm  < ε,    u  aBj − vBu + vju  < ε,    l l  ajW − vjl + vW  < ε,    m m ajW − vjm + vW  < ε,    u u  ajW − vju + vW  < ε, wjl =

ϑjl

, nκ u ϑjm wjm = u , nκ ϑju u wj = u , nκ u wj + (in =j,i=1) wil ≤ 1,

(8)

n wim = 1, i=1

wjl + in=j,i=1 wiu ≥ 1, wjl ≤ wjm ≤ wju , wjl ≥ 0, (j = 1, 2, . . . , n) where ε˜ = (ε, ε, ε) is Solving problem (8) the optimal

a fuzzy triangular deviation. ∗ = w˜ ∗ , . . . , w˜ ∗ , . . . , w˜ n∗ and ε∗ = (ε∗ , ε∗ , ε∗ ) are derived. fuzzy weights W 1 j 2.2 Consistency Index and Consistency Ratio 1- input-based consistency index The fuzzy input-based consistency index (ICI), which is based on the input data provided by DM, is proposed to measure the inconsistency between a˜ BW , and its estimated values, a˜ Bj + a˜ jW .

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65

 2   n  l  n  m m − a m 2  1 a + al − al  1 aBk + akW BW BW Bk kW   = ( ICI , , n κu n κu k=1 k=1   n  u  2 u − au  1 aBk + akW BW  ) n κu

(9)

k=1

The graded mean integration representation (GMIR) [33] method is applied to obtain the crisp ICI. It is evident that ICI ≥ 0, and the ICI → 0, show more consistency in DM’s pairwise comparisons. 2- Consistency ratio Pairwise comparisons based on the fuzzy interval scale are fully consistent when a˜ Bk + a˜ kW = a˜ BW , where a˜ Bk , a˜ kW , and a˜ BW are the fuzzy interval preference of the best criterion over criterion j, the fuzzy interval preference of criterion j over the worst criterion, and the fuzzy interval preference of the best criterion over the worst criterion, respectively. The maximum inconsistency occurs when both a˜ Bk and a˜ kW are equal to a˜ BW , so, to reach the equality, the following equation must be satisfied. (10) a˜ BW − ξ˜ + a˜ BW − ξ˜ = a˜ BW + ξ˜ ,  l   l m u m , au where ξ˜ = ξ , ξ , ξ , and a˜ BW = aBW , aBW BW . To simplify the Eq. (10), the maximum elements of fuzzy values are just considered, so in this case, Eq. (10) is converted into u u u − ξ + aBW − ξ = aBW + ξ. aBW

(11)

By solving Eq. (11) for different buBW , the maximum consistency index (MCI) is determined and indicated in Table 2. Table 2. Consistency index table u aBW

0

1

2

3

4

5

6

7

8

MCI

0

0.333

0.667

1

1.333

1.667

2

2.333

2.667

Then, the consistency ratio (CR) is calculated by ε∗ MCI where ε∗ is the optimal deviation derived by (8). CR =

(12)

3 Application In this section, an example is illustrated to compare the proposed method with BWM and CBWM.

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A company needs to conclude a contract with a transportation company to ship its goods. There are four alternatives {T1 , T2 , T3 , T4 } which are evaluated on different criteria {transportation cost (TC), tardiness rate (TR), defective rate (DR), flexibility (F), documentation ability (DA)}. Figure 1 shows the hierarchical structure of the problem. The pairwise comparison vectors mentioned in the FCBWM steps are represented in Table 3 to Table 5.

Fig. 1. The hierarchy structure of the problem

Table 3. Evaluation of criteria to the reference criteria under fuzzy ratio and interval scales Criteria

Fuzzy interval scale

Fuzzy ratio scale

Best criterion: TC

Worst criterion: DA

Best criterion: TC

Worst criterion: DA

TC

0

8

1

9

DR

4

6

5

7

TR

2

6

3

7

F

4

7

5

8

DA

8

0

9

1

A Fuzzy Best-Worst Method Based on the Fuzzy Interval Scale

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Table 4. BO vectors for comparing alternatives under fuzzy ratio and interval scales Criteria

Best alternative

TC

T4

TR

T1

DR

T3

F

T3

DA

T2

Fuzzy interval scale   7, 1, 6, 0   0, 6, 2, 4   5, 2, 0, 7   2, 7, 0, 6   4, 0, 2, 2

Fuzzy ratio scale   8, 2, 7, 1   1, 7, 3, 5   6, 3, 1, 8   3, 8, 1, 7   5, 1, 3, 3

Table 5. OW vectors for comparing alternatives under fuzzy ratio and interval scales Criteria

Worst alternative

TC

T1

TR

T2

DR

T4

F

T2

DA

T1

Fuzzy interval scale   0, 6, 0, 7   6, 0, 4, 2   1, 6, 7, 0   5, 0, 7, 2   0, 4, 2, 2

Fuzzy ratio scale   1, 7, 1, 8   7, 1, 5, 3   2, 7, 8, 1   6, 1, 8, 3   1, 5, 3, 3

Considering the hierarchical structure of the problem, six different problems appear. The fuzzy ICI is calculated according to Eq. (9), and GMIR is applied to defuzzify the fuzzy ICI. The defuzzified values are indicated in Fig. 2. All values are less than or equal to 0.1, which verifies the consistency of input data. By solving the constraint optimization problem (8), the optimal weights of criteria/ alternatives are determined. The CR values of the problems are calculated by Eq. (12). Table 5 shows the values of CR and the weights of the criteria. The ranking order of alternatives is calculated by Eq. (13), and GMIR is applied to transform the fuzzy values of weights into crisp values. So, the ranking order is T3 > T1 > T2 > T4 , which indicates that T3 is preferred to all others.

n w˜ T = w˜ i w˜ T (i) (13) i=1

where n and T are the numbers of criteria and alternatives, w˜ i indicates the fuzzy weight of criterion i, w˜ T (i) is the relative fuzzy weight of alternative T for criterion i, and w˜ T is the fuzzy priority weight of the T -th alternative. 3.1 Comparative Analysis and Discussion In this section, FCBWM is compared with BWM, and CBWM in four aspects: ranking order of alternatives, TD values, CR values, standard deviation, and range of the obtained results.

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0.12 0.1

ICI

0.08 0.06 0.04 0.02 0 Main

TC

DR

TR

F

DA

Fig. 2. Derived ICI for different problems

Table 6. Fuzzy triangular weights and CRs TC

DR

TR

F

DA

(0.172,0.275, 0.324)

(0.125,0.213, 0.246)

(0.156,0.244, 0.277)

(0.125,0.213, 0.246)

(0,0.056, 0.059)

T1

(0,0.152, 0.208)

(0.141,0.344, 0.438)

(0.031,0.203, 0.276)

(0.125,0.297, 0.365)

(0,0.188, 0.245)

T2

(0.156,0.34, 0.427)

(0,0.156, 0.203)

(0.125,0.297,0.37)

(0,0.141, 0.177)

(0.078,0.313,0.417)

T3

(0,0.152, 0.208)

(0.094,0.281, 0.359)

(0.172,0.359, 0.448)

(0.188,0.359,0.458)

(0.031,0.25, 0.339)

T4

(0.156,0.355,0.458)

(0.031,0.219,0.297)

(0,0.141, 0.182)

(0.031,0.203, 0.271)

(0.031,0.25, 0.339)

CR

0.374

0.187

0.374

0.374

0.299

w

1. Ranking order Regarding Table 1, it can be seen that the ranking order of alternatives obtained by CBWM and FCBWM are the same, but there is a slight difference with the results derived by BWM. The ranking order of T1 and T4 derived by CBWM and FCBWM is vice versa in BWM. A thorough investigation of the obtained results of BWM reveals that the ranking order of alternatives is affected by the weights of criteria. Their priority is changed after multiplying the weights of the main criteria. Considering Fig. 4, the value of CR, 0.252, obtained by BWM for solving the main criteria problem, is greater than that of CBWM and FCBWM, 0.123 and 0.1873, respectively. This issue plays a significant role in changing the priority order of alternatives. The order was the same as the order obtained by CBWM and FCBWM before involving weights of the main criteria.

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2. Total deviation Furthermore, the fuzzy total deviation (FTD) is introduced for fuzzy interval scale, Eq. (14), to measure the total differences between the obtained utilities and preferences degrees. The crisp equivalent is compared with the results of TDs gained by BWM [20], and CBWM [27] and depicted in Fig. 3.     1 n wB 2 wi 2 ( aBi − + aiW − ) TDBWM = i=1 2n wi wW 1 n TDCBWM = ((aBi − wB + wi )2 + (aiW − wi + wW )2 ) 2n i=1

l m u TDFCBWM = ( TDFCBWM | , TDFCBWM , TDFCBWM

2 2 1 n l l l l TDFCBWM = ( aBj − vBl + vjl + ajW − vjl + vW ) i=1 2n

2

2 1 n m m m m TDFCBWM = ( aBj − vBm + vjm + ajW − vjm + vW ) i=1 2n n

2

2 1 u u u u = ( aBj − vBu + vju + ajW − vju + vW )) TDFCBWM 2n

(14)

i=1

According to Fig. 3, all TD values derived by CBWM and FCBWM are less than that of BWM. However, it was half expected that the results of FCBWM be more significant than the obtained results in the crisp environment. TD values derived by FCBWM are less than TD values obtained by CBWM in half cases, and all are less than that of BWM. It can be considered another justification to verify the validity of the proposed method. Also, it can validate the acceptability of pairwise comparisons discussed by ICI and indicated in Fig. 2, when all obtained values are less than or close to 0.1. 3. Consistency ratio Another comparison is made between the values of CR obtained by the mentioned methods. According to Fig. 4, in five problems out of six, CBWM presented better values of CR than BWM. However, comparing the results of Table 6 and Fig. 4 indicates that the values of CR obtained by the proposed method are greater than CBWM. It can be justified as a direct effect of the extension of CBWM in an uncertain environment. So, considering it as a reason for the weak performance of FCBWM cannot be acceptable. Table 7. Results of FCBWM, BWM, and CBWM Method

Priorities of alternatives

BWM

T3 > T2 > T4 > T1 T3 > T2 > T1 > T4 T 3 > T2 > T1 > T4

CBWM Proposed method

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1.4 1.2 1 0.8 0.6 0.4 0.2 0 main

F

TR

DR

BWM CBWM FCBWM TC

DA

Fig. 3. The value of TD obtained by FCBWM, CBWM, and BWM for calculating the weights of criteria and alternatives

4. Standard deviation and range Finally, to show that the proposed method is applicable for a homogeneous list of alternatives, as mentioned in Sect. 1, the standard deviation and the range of weight of alternatives corresponding to each criterion produced by BWM, CBWM, and FCBWM are calculated and indicated in Fig. 5. According to Fig. 5, the standard deviation and range gained by solving FCBWM are less than BWM, but they are greater than CBWM. Since FCBWM is a direct extension of CBWM in a fuzzy environment, these deviations can be interpreted as an uncertain interval neglected in CBWM. In sum, it shows that this method will be meaningful and applicable for the problems in which DMs cannot distinguish the alternatives readily.

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0.3 0.25 0.2 CBWM

0.15

BWM 0.1 0.05 0 main

F

TR

DR

TC

DA

Fig. 4. CR values obtained by CBWM and BWM for calculating the weights of criteria and alternatives

0.250

0.600 0.500 SD.FCBWM 0.400

0.150 0.300 0.100 0.200 0.050

0.100

0.000

SD.BWM Range

Standard deviation

0.200

SD.CBWM R.FCBWM R.BWM R.CBWM

0.000 TC

DR

TR

F

DA

Fig. 5. The standard deviation and range of weights derived by BWM, CBWM, and FCBWM

4 Conclusion In this paper, we have proposed a new BWM, called fuzzy cognitive BWM (FCBWM), based on the fuzzy interval scale. FCBWM holds all the excellent features of the original BWM and can overcome the mathematical errors of the fuzzy BWM [21], which leads to misleading results. A new consistency index based on the input data is presented to check the validity of the provided preferences. A new consistency ratio based on additive transitivity and total deviation factor is introduced according to the fuzzy interval scale.

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N. Goldani and M. Kazemi

In the end, the efficiency of FCBWM is illustrated by conducting some comparative analyses with BWM and CBWM. However, this paper introduced a new fuzzy BWM. It is needed to apply the method to real-world problems in different application areas such as healthcare management, environmental management, and logistics to investigate how this method can solve the problems more efficiently. Moreover, the combination of FCBWM with other theories and other MCDM methods such as TOPSIS, MULTIMOORA, and ELECTRE could be interesting future research topics.

References 1. Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York, 324 (1980) 2. Lee, C.W., Kwak, N.: Information resource planning for a health-care system using an AHPbased goal programming method. J. Oper. Res. Soc. 50(12), 1191–1198 (1999) 3. Yayla, A.Y., et al.: A hybrid data analytic methodology for 3PL transportation provider evaluation using fuzzy multi-criteria decision making. Int. J. Prod. Res. 53(20), 6097–6113 (2015) 4. Prakash, C., Barua, M.K.: An analysis of integrated robust hybrid model for third-party reverse logistics partner selection under fuzzy environment. Resour. Conserv. Recycl. 108, 63–81 (2016) 5. Lee, J., Cho, H., Kim, Y.S.: Assessing business impacts of agility criterion and order allocation strategy in multi-criteria supplier selection. Expert Syst. Appl. 42(3), 1136–1148 (2015) 6. Liu, Y., et al.: A fuzzy decision tool to evaluate the sustainable performance of suppliers in an agrifood value chain. Comput. Ind. Eng. 127, 196–212 (2019) 7. Choudhary, D., Shankar, R.: An STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: A case study from India. Energy 42(1), 510–521 (2012) 8. Kuo, R.J., Chi, S.-C., Kao, S.-S.: A decision support system for selecting convenience store location through integration of fuzzy AHP and artificial neural network. Comput. Ind. 47(2), 199–214 (2002) 9. Kwong, C.-K., Bai, H.: A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment. J. Intell. Manuf. 13(5), 367–377 (2002). https://doi.org/10.1023/A:1019984626631 10. Ayodele, T.R., et al.: A multi-criteria GIS based model for wind farm site selection using interval type-2 fuzzy analytic hierarchy process: the case study of Nigeria. Appl. Energy 228, 1853–1869 (2018) 11. Celik, E., Akyuz, E.: An interval type-2 fuzzy AHP and TOPSIS methods for decision-making problems in maritime transportation engineering: the case of ship loader. Ocean Eng. 155, 371–381 (2018) 12. Wu, J., Huang, H.-B., Cao, Q.-W.: Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Appl. Math. Model. 37(24), 9898–9906 (2013) 13. Sadiq, R., Tesfamariam, S.: Environmental decision-making under uncertainty using intuitionistic fuzzy analytic hierarchy process (IF-AHP). Stoch. Env. Res. Risk Assess. 23(1), 75–91 (2009). https://doi.org/10.1007/s00477-007-0197-z 14. Xu, Z., Liao, H.: Intuitionistic fuzzy analytic hierarchy process. IEEE Trans. Fuzzy Syst. 22(4), 749–761 (2013) 15. Acar, C., Beskese, A., Temur, G.T.: Sustainability analysis of different hydrogen production options using hesitant fuzzy AHP. Int. J. Hydrogen Energy 43(39), 18059–18076 (2018)

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16. Öztaysi, B., et al. Hesitant fuzzy analytic hierarchy process. in 2015 IEEE international conference on fuzzy systems (FUZZ-IEEE). 2015. IEEE 17. Wang, Y.-M., Luo, Y., Hua, Z.: On the extent analysis method for fuzzy AHP and its applications. Eur. J. Oper. Res. 186(2), 735–747 (2008) 18. Yuen, K.K.F.: Cognitive network process with fuzzy soft computing technique in collective decision aiding (2009) 19. Yuen, K.K.F.: Fuzzy cognitive network process: comparisons with fuzzy analytic hierarchy process in new product development strategy. IEEE Trans. Fuzzy Syst. 22(3), 597–610 (2013) 20. Rezaei, J.: Best-worst multi-criteria decision-making method. Omega 53, 49–57 (2015) 21. Guo, S., Zhao, H.: Fuzzy best-worst multi-criteria decision-making method and its applications. Knowl.-Based Syst. 121, 23–31 (2017) 22. Mou, Q., Xu, Z., Liao, H.: An intuitionistic fuzzy multiplicative best-worst method for multicriteria group decision making. Inf. Sci. 374, 224–239 (2016) 23. Aboutorab, H., et al.: ZBWM: the Z-number extension of best worst method and its application for supplier development. Expert Syst. Appl. 107, 115–125 (2018) 24. Ali, A., Rashid, T.: Hesitant fuzzy best-worst multi-criteria decision-making method and its applications. Int. J. Intell. Syst. 34(8), 1953–1967 (2019) 25. Rezaei, J.: Best-worst multi-criteria decision-making method: some properties and a linear model. Omega 64, 126–130 (2016) 26. Choo, E.U., Wedley, W.C.: A common framework for deriving preference values from pairwise comparison matrices. Comput. Oper. Res. 31(6), 893–908 (2004) 27. Zhang, H., et al.: Cognitive best worst method for multiattribute decision-making. Mathematical Problems in Engineering, 2017 (2017) 28. Brunelli, M., Rezaei, J.: A multiplicative best–worst method for multi-criteria decision making. Oper. Res. Lett. 47(1), 12–15 (2019) 29. Mi, X., et al.: The state-of-the-art survey on integrations and applications of the best worst method in decision making: why, what, what for and what’s next? Omega 87, 205–225 (2019) 30. Dong, J., Wan, S., Chen, S.-M.: Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Inf. Sci. 547, 1080–1104 (2021) 31. Brunelli, M., Mezei, J.: An inquiry into approximate operations on fuzzy numbers. Int. J. Approximate Reasoning 81, 147–159 (2017) 32. Wang, Y.-M., Elhag, T.M.: On the normalization of interval and fuzzy weights. Fuzzy Sets Syst. 157(18), 2456–2471 (2006) 33. Chen, S.H., Hsieh, C.H.: Representation, ranking, distance, and similarity of LR type fuzzy number and application. Aust. J. Intell. Process. Syst. 6(4), 217–229 (2000)

Integrating Sustainable Goals in Transmission System Operators’ Projects Georgios Athanasiou1,2(B) 1 Delft University of Technology, Mekelweg 5, 2628 CD Delft, The Netherlands

[email protected] 2 Springer Heidelberg, Tiergartenstr. 17, 69121 Heidelberg, Germany

Abstract. Transmission System Operators (TSOs) are responsible for the construction, maintenance, and operation of the high-voltage grid. The Dutch TSO TenneT, has been appointed by the Dutch government to oversee all the projects required for the connection of the offshore wind farms in the North Sea with the high-voltage grid. An important step in the lifecycle of such projects is the invitation to tender and the selection of the awarded contractor, based on different exclusion, selection, and award criteria. This study focuses on identifying such sustainable criteria suitable for the TSO market and proposes a multi-criteria decision-making process based on the Best-Worst Method (BWM) for assessing their importance. Additionally, this study proposes using a Maturity Model for evaluating the performance of existing sustainable measures, related to sustainable goals. Next, following an Importance-Performance Analysis (IPA), the study concludes by identifying and proposing which sustainable goal can be prioritised. TenneT is used as a case study where its experts helped identify the research problem and took part in the IPA, helping to identify the sustainable goals to be prioritised. Keywords: Best-Worst Method (BWM) · Importance-performance analysis · Decision-making · Transmission system operators · Sustainability

1 Introduction Sustainability is seen as one of the most important challenges the world needs to address today (Silvius 2017) and sustainable development is becoming the leading model of development for organisations and nations as a response to the environmental crisis and the adverse social inequalities which are prevalent in the world (Waas et al. 2014). Selecting and awarding infrastructure projects was traditionally done based on monetary competition and the cheapest available offers. Technical and time-related criteria were later implemented with the latest addition being sustainable criteria and added value. The Most Economically Advantageous Tender or MEAT award criteria, and other exclusion and selection criteria are now necessary for contracting authorities that operate within the European Union. This applies to TSOs since these companies need to procure for infrastructure projects that often exceed the monetary thresholds of Public Procurement Law (Chao-Duivis 2013). The exclusion, selection and award criteria © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 74–86, 2023. https://doi.org/10.1007/978-3-031-24816-0_7

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entailed in Public Procurement regulation can range from technical criteria (e.g., reliability,) environmental (e.g., CO2 emissions) to social characteristics and objectives (e.g., employment conditions). Thus, TSOs need to account for and include these sustainable characteristics and objectives in their contractor and supplier tender selection process. There are many definitions of sustainability in the literature, however, most authors agree that sustainability essentially is balancing the environmental, social, and economic aspects and consequences of any action (Talbot and Venkataraman 2011). Elkington’s (1998) definition of sustainability is widely accepted and used by various groups and nations as the prevalent definition of sustainability and as a roadmap for sustainable development. The Triple Bottom Line (TBL), or the equal attention to Planet, People and Profit was juxtaposed against the Bottom Line, often used by corporations to measure success, and make decisions. To improve the sustainable performance of TSOs this study focuses on a methodology which can identify opportunities for sustainable goal integration in projects, considering the capabilities and limitations of the market. TSOs operate under several unique conditions which make the integration of sustainable objectives in their projects and the associated decision-making processes challenging. TSOs operate in a complex global market and are involved with projects which can have adverse effects and consequences on the environment and society. Additionally, the current high demand for offshore projects makes it easier for contractors and suppliers to choose not to tender for a specific TSO’s projects if they deem the sustainable goals and requirements excessive. All these challenges make the integration of sustainable goals in projects difficult and can hinder the decision-making process leading to the tender of a project. They raise the need for a systematic approach which can be used by decision-makers to ease the process of integrating sustainable goals in the company’s projects. Such an approach requires the comparison of sustainable goals and existing sustainable measures, associated with them, and the selection of some of these goals and measures to be integrated in an incremental manner. The importance of sustainable goals, in their ability to promote sustainability in projects can capture the urgency of certain goals and their preference by the decision-makers. Additionally, the performance of existing measures can provide an additional understanding of the current situation of these measures and reveal whether the company is on the right track to achieve its goals. By analysing these two characteristics, the several sustainability goals of TSOs can be assessed in terms of their importance and their real-life performance. This can reveal possible ways and strategies to be followed according to each sustainable goal’s score, following the Importance-Performance Analysis (IPA) developed by Martilla and James (1977). IPA aims at supporting companies improve and gain a competitive advantage by identifying the aspects that they should focus on more, and the areas where they may be consuming too many resources on. The integration of sustainable objectives and measures in projects by TSOs constitutes a MCDA problem, since it requires the identification of goals to be achieved, the selection of associated sustainability measures, and their integration in the tender process. Decisions are being made at every step as decision makers decide between what is relevant to projects, what can be achieved and try to balance technical requirements

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with all three aspects of sustainable development (Azapagic and Perdan 2005) and other constraints, specific to the context of TSOs. MCDA is also shown in the literature to help with the identification of important sustainability goals and their integration in projects (Carboni et al. 2016; Labuschagne and Brent 2005) and (Salimi 2021). This paper aims at studying the tender process for TSO projects and the need for sustainable criteria integration in that process. Using the BWM and its pairwise comparison process, important sustainable goals were ranked according to their ability to influence sustainability in a project. Existing measures that related to the sustainable goals were then ranked in terms of maturity and sustainable performance in real life. Finally, the study offered the Importance-Performance Analysis which can help TSOs identify which sustainable goals they need to prioritise according to the company’s experts and their perception of sustainability and the TSO market. Section 2 introduces the findings of the literature review regarding sustainable goals. Scientific articles and initial conversations with Supply Chain Management and Procurement experts from TenneT allowed the identification of sustainable goals as well as real-life hindrances and difficulties in integrating these goals in the company’s tender process and the projects themselves. Section 3 presents the Methodology used in this study to help TSOs identify important sustainable goals that lack behind in terms of performance and introduces TenneT as the paper’s case study. Section 4 presents the results of this study and Sect. 5 concludes the study by summarizing the findings of the Importance-Performance Analysis, other related findings, and the study’s limitations.

2 Literature Review An extensive literature review was performed to identify sustainable criteria associated with the TSO market, the selection of bidding contractors and the final contract award. TenneT was used as a case study for this paper where its own sustainable goals, existing measures and experts were used to collect data and perform the Importance Performance Analysis. A decision-tree diagram is presented in Fig. 1 where the sustainable goals identified from the literature review and used in this study are presented. This section additionally provides a literature review to identify possible existing sustainability-related measures that TSOs to promote sustainability in projects. Table 1 presents a list of existing sustainable measures identified through the literature review and their associated sustainable goal(s).

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Table 1. Existing sustainability measures identified through the literature review Existing sustainability measures

Description

Associated sustainable goal

Authors

Environmental Cost Index (ECI)

Monitors the emission of Greenhouse Gas (GHG) emissions and the use of polluting materials and assigns monetary cost to each pollutant

Emissions, Energy Consumption

Silvius and Schipper (2015), Montalban-Domingo et al. (2020), Carboni et al. (2016)

Raw Material Passport (RMP)

Monitors the origin of materials used in projects and whether they derive from raw or recycled sources

Circularity and Waste, Materials and Natural Resources

Silvius and Schipper (2015), Montalban-Domingo et al. (2020), Carboni et al. (2016)

Supplier Code of Conduct (SCC)

Must-sign document for potential suppliers and contractors adhering to environmental, ethical and work-condition related principles

Human Rights, Labour Conditions & Decent Work

Silvius and Schipper (2015), Montalban-Domingo et al. (2020), Carboni et al. (2016), Labuschagne et al. (2005)

Safety Cultural Ladder (SCL)

Must-obtain certificate for potential suppliers and contractors adhering to TenneT’s strict safety policy

Health & Safety

Montalban-Domingo et al. (2020), Labuschagne et al. (2005)

Total Cost of Ownership (TCO)

Technical measure focusing on minimising energy losses in cable projects

Emissions, Energy Consumption

Silvius and Schipper (2015), Montalban-Domingo et al. (2020), Carboni et al. (2016)

Nature Inclusive Design (NID)

Includes a variety of solutions that can protect and enhance biodiversity and restore nature to its original state

Biodiversity

Silvius and Schipper (2015). Montalbán-Domingo et al. (2020), García-Segura et al. (2020)

Stakeholders & Society

Measures taken in the Stakeholders & Society early stages of projects to inform, discuss, and consult with local communities and Non-Government Organisations (NGOs) regarding issues they deem important

Silvius and Schipper (2015), Montalban-Domingo et al. (2020)

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3 Methodology This section presents the methodology used in the study and its goals of i) Identifying relevant sustainable decision criteria (sustainable goals), ii) Ranking these goals in terms of Importance using the BWM, iii) Ranking TenneT’s existing sustainable measures (associated with the sustainable goals) in terms of Performance and iv) Identifying the aspect(s) that need to be prioritised and integrated in the TenneT’s coming projects, using IPA. TenneT is the sole TSO in the Netherlands and one of four TSOs in Germany and is responsible for connecting the new offshore wind farms to the high-voltage grid through a series of platform, cable, and land station projects. TenneT’s employees are responsible for (among other things) researching the market, discussing, and negotiating with existing or potential suppliers and/or contractors, identifying potential problems and hindrances regarding a project’s goals, and putting the company’s projects to tender. TenneT’s experts from different departments were contacted and agreed to take part in the study. Experts from the Supply Chain Management/Procurement department were interviewed to discuss the tender process, TenneT’s sustainable goals, possible hindrances, and the market’s ability to become more sustainable. Through the interviews and discussions, the research problem was formulated. TenneT wishes to become more sustainable, lead the energy transition and stimulate sustainability in its supply chain and in the TSO market. The main obstacles identified were the plethora of available offshore projects, meaning that contractors can opt to bid for other projects if they find TenneT’s requirements strenuous and sustainable investments are often costly for contractors and suppliers. Focusing on certain sustainable goals at a time and integrating more of these goals in an incremental fashion was shared by all interviewees as a preferred strategy for the company. This study aims offering a structured approach through which TSOs can prioritise the integration of sustainable goals in projects focusing on the importance of the goals (using BWM) and their performance (using the Maturity Model) and following IPA. This structured approach can help resolve the two main issues mentioned earlier and help TSOs improve their sustainability performance. Five experts took part in the IPA, coming from the Corporate Social Responsibility department, the Supply Chain Management/Procurement department, the 2GW offshore wind program and from individual project teams. These experts had experience on offshore wind projects, had knowledge of the TSO market and were personally motivated in improving the company’s sustainability performance. The experts took part in an online workshop to discuss the sustainable goals identified from literature and compared them with TenneT’s own goals. Sustainable goals that were deemed important by three or more experts were selected and used in the IPA. These goals are presented in Fig. 1. Next, these experts were asked to perform the BWM and assess the importance of the sustainable goals. Finally, the experts received the Maturity Model questionnaire which was tailored to the company’s existing sustainable measures and were asked to assess the real-life performance based on their experience.

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3.1 Sustainable Decision Criteria – Aspects of Sustainability The sustainability aspects were derived in combination from the literature review, an initial discussion with procurement professionals from TenneT and the online workshop organised with TenneT’s experts. The sustainable goals are presented in Fig. 1, in a decision-tree scheme and are based on the TBL approach.

Fig. 1. The sustainable aspects and goals as they were identified in this study.

3.2 Analysing Importance – The BWM The BWM method was used to assess the importance of the identified sustainable goals, as perceived by the company experts. Since, the TBL is divided into three aspects, the comparisons were performed three times. Once for the three main aspects of sustainability (People, Planet and Profit) and two more times for the sub-aspects of People and Planet. The Best-Worst method was selected as the preferred MCDA method for this research, as it offers clarity and structure, allowing a decision-maker to offer consistent comparisons. This is achieved by selecting the best and worst criteria in the beginning of the process, which reduces anchoring bias, as the two opposite reference points (the best

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and worst) are considered (Rezaei 2022). The BWM has been already implemented in various problems relating sustainability, such as assessing social sustainability in supply chains (Rezaei et al. 2017; Ahmadi et al. 2020) and sustainability in location selection problems (Rezaei et al. 2020). Additionally, it is very data-efficient as well as timeefficient, as it requires fewer comparisons than some MCDA methods (Rezaei 2015) and (Salimi 2021). BWM is a pairwise comparison-based method which helps the decisionmaker/expert to find the weights of the criteria. To do so, the expert/decision-maker is asked to choose the best (most important) and worst (least important) criteria from among a list of criteria and conduct a pairwise comparison among these two reference points and the remaining criteria. Formulating and solving a minmax problem the weights of the criteria can be calculated. In this study, the linear version of BWM was used. The BWM can be divided into six subsequent steps: 1) Determine a set of decision-making criteria {c1 , c2 , . . . , cn } by experts/decisionmakers. These criteria may be presented at different levels. 2) Have experts/decision-makers identify the best (B) and worst (W) criteria. In this study, the best criterion refers to the most important sustainable goals in terms of its ability to stimulate sustainability in TSO-related projects and consequently, the worst criterion refers to the sustainability goal least able to do so. 3) Determine the preference of the best over all the other criteria by a number from 1 to 9 (where 1 is “equally important” and 9 is “extremely more important”) by the expert(s)/decision-maker(s). The result of best-to-others comparisons is the BO vector: BO = (aB1 , aB2 , . . . , aBn )

(1)

where, aBj shows the preference of criterion B over criterion j. 4) Determine the preference of all the criteria over the worst criterion selected by the expert(s)/decision-maker(s). The result of others-to-worst comparisons is the OW vector: OW = (a1W , a2W , . . . , anW )

(2)

where, ajW refers to the preference of criterion j over criterion W.  5) Compute the optimal weights w1∗ , w2∗ , . . . , wn∗ . The optimal weights are calculated by minimizing the maximum absolute differences of:     wB − aBj wj , wj − aiW ww  (3) For all j, which is translated into the following optimization problem:     min max wB − aBj wj , wj − aiW ww  w

j

(4)

Such that: n j=1

wj = 1wj ≥ 0, forallj.

(5)

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Model 5 is converted into min ξ such that   wB − aBj wj  ≤ ξ for all j   wj − ajW wW  ≤ ξ for all j n wj = 1 wj ≥ 0, for all j j=1

(6)

  w∗ = w1∗ , w2∗ , . . . , wn∗ that is the optimal weight of the criteria is the result of model 6. ξ ∗, the optimal value of objective function in model 6, indicates the consistency ratio. This study deals with a Multi-Criteria Decision-Making problem with more than one level. Thus, the results of Model 6 are called local weights. To determine the global weight of sub-criteria in the last level of the hierarchical tree, their local weight is multiplied by the weight of the category (main aspect of Sustainability) to which they belong. Checking the reliability of the pairwise comparisons is an important step before solving the optimisation problem and can help the decision-maker/expert to confront any inconsistencies of his/her answers as soon as they arise. Liang et al. (2020) have identified the thresholds for the different combinations of decision criteria and the scale on which they are compared. The input-based CR proposed by Liang et al. (2020) can immediately indicate a decision-maker’s/expert’s consistency level by using the input (preference) he/she provides. The input-based consistency ratio is formulated as follows: CRI = max CRIj

(7)

j

where

 CRIj

=

|aBj −ajW −aBW | aBW ×aBW −aBW , aBW 0,

aBW

>1 =1

In the comparison of the three main aspects of sustainability (People, Planet, and Profit) the acceptable threshold and the input-based CR derived from each decisionmaker’s/expert’s preferences are presented in Table 2. All input based CRs are lower than the corresponding threshold, thus acceptable.

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Table 2. Input-based consistency ratio for each expert’s comparisons based on 3 decision-criteria and a 9-scale rank Expert

Input-based CR

Threshold

A

0.0238

0.1294

B

0.0139

0.1359

C

0.1667

0.1667

D

0.0500

0.1354

E

0.1190

0.1294

3.3 Analysing Performance – The Maturity Model A Maturity Model developed by Silvius and Schipper (2015) designed to assess the performance of sustainable goals was selected for this study. A Maturity Model questionnaire was sent to TenneT’s experts who were asked to assess the performance of the company’s existing measures (see Table 1). The Maturity Model divides the performance of the sustainability measures into four levels which are explained below: Level 1: This aspect is considered implicitly, in compliance with laws and (company) regulations. No specific policies are applied in the project. Level 2: This aspect is considered explicitly, but reactively, and with the intention to not compromise the interests of different stakeholders of the project. Level 3: This aspect explicitly considered as one of the areas that the project contributes to. Level 4: Contributing to this aspect is one of the drivers behind the project and included in the justification of the project. 3.4 The Importance-Performance Analysis Two important stages in the formulation of any strategy are the identification of the set of factors or aspects that an organisation deems important (e.g., quality, cost etc.) and the assessment of the company’s performance relating to these goals and factors (Slack 1994). Salimi (2021) argues that only identifying the goals a company deems important does not guarantee business success. Aspects that already perform well may not be the optimal choice for investing valuable time and resources for their improvement. Importance-Performance Analysis (IPA) suggests various strategies which organisations can use to achieve their goals, depending on the level of importance of a specific goal and its real-life performance. Implementing IPA to integrate sustainable goals in TSO projects requires placing these goals in one of four quadrants of the IPA matrix. The matrix divided by the axes of Importance (High or Low) and Performance (High or Low) and depending on each goal’s placement in the matrix, an appropriate response strategy is proposed. The BWM weights and the Maturity Level scores were used to create the IPA matrix and plot the sustainable goals.

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4 Results and Discussion The weights produced from each decision-maker’s/expert’s preferences were aggregated using the geometric mean and were then corrected (if the summation of all aspects did not equal to 1). Global weights were calculated by multiplying the local weights to the weight of the main aspect. The BWM analysis showed that the Planet aspect was the most important one for stimulating sustainability. Additionally, the aspect of Reducing Emissions was selected as the most important sub aspect while in the People aspect, Health and Safety ranked first (Table 3). Table 3. BWM local and global weights from the experts Aspect

Weight

People

0.2734

Planet

0.5635

Sub-aspect

Local weight

Health and safety

0.3496

0.0956

Human rights

0.2205

0.0603

Labour conditions and decent work

0.1977

0.0540

Stakeholders

0.2323

0.0635

Energy consumption

0.1437

0.0810

Reducing emissions

0.3559

0.2006

Biodiversity

0.1466

0.0826

Materials and nat. resources

0.1454

0.0820

0.2083

0.1174

1

0.1631

Circularity and waste Profit

Global weight

0.1631

The Maturity Model questionnaire results (presented in Fig. 2) showed that the least integrated goals in projects are Human Rights, Labour Conditions and Decent

Maturity Model - Performance Assessment Circularity and Waste Materials and Natural Resources Biodiversity Reducing Emissions Energy Consumpon Stakeholders and Society Labour Condions and Decent Work Human Rights Health and Safety 0

1

2

3

4

Fig. 2. The maturity level scores for each sustainable goal as perceived by the experts.

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Work, reducing Energy Consumption, Materials and Natural Resources and Circularity and Waste ranking the lowest. To improve the performance of Circularity and Waste, TenneT’s existing measures can be integrated further into the company’s projects. This can be achieved by using already existing sustainable measures such as the Raw Material Passport (RMP) in the tender process, as entry requirements with specific targets to be met, or as award criteria, aiming to create added value for the project, can stimulate the contractors and suppliers act more sustainably. This can improve TenneT’s sustainable performance and help the company meet its own sustainable targets. Combining the results from both the Importance and Performance analyses Fig. 3 was created, identifying the sustainability goal “Circularity and Waste” as a priority for the next projects. Goals that fall within Quadrant A need to be prioritised according to IPA since they offer the greater opportunity for improvement. Reducing Emissions and Health and Safety are placed in Quadrant B which means that they are important to TenneT and receive adequate attention since they perform well in real-life. The remaining sustainable goals are placed in quadrant D, which according to IPA means that TenneT can benefit more from focusing elsewhere.

Importance - Performance Matrix 0.2000

Importance

0.1500

Reducing Emissions

Quadrant B

Quadrant A Circularity & Waste

Health & Safety

Materials & Natural Resources

0.1000 Circularity & Waste Human Rights

0.0500

0.0000

Biodiversity

Quadrant C

0

Stakeholders & Society

Labour Condions & Decent Work

1

Quadrant D

2

3

4

Performance Fig. 3. The IPA matrix as a result of the BWM and the maturity model

What is also worth mentioning is that the different decision-makers had different perspectives on sustainable goals and their associated issues in projects. In both the importance assessment and the performance assessment of the goals and measures, decision-makers graded the same aspects with a different importance and/or performance score. This difference in the perception of sustainability between the different decisionmakers can possibly be tracked between the different departments of the company as well. The different understanding of sustainability makes difficult to develop a companywide sustainability culture and can lead to lengthy discussions since different people have

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different views on the matter and perceive the goals and actions necessary to achieve these goals.

5 Conclusion Integrating sustainable goals in the tender process of projects can help TSOs improve their sustainable performance and influence their market towards sustainable development. The different criteria of the tender process (exclusion, selection, and award) offer many opportunities for sustainable goal integration. Identifying these sustainable goals however and agreeing on which ones can and should be integrated in a project can be time-consuming process with arguments from employees with different backgrounds and points of view. This study offers a structured methodology which TSOs can follow to identify which sustainable goals can be integrated in their projects, based on their importance and their performance. The methodology used in this study was based on Importance-Performance Analysis and the use of the BWM and a Maturity model for capturing the importance and performance of sustainable goals accordingly. The study concluded based on the IPA that TenneT can begin integrating sustainable goals in its projects, prioritizing Circularity and Waste. Additionally, this study identified the difference in perception between the experts in terms of the importance and performance they attached to each sustainable goal and associated measure. Thus, the BWM can be further utilised to investigate the size and origins of the different perceptions, values and understanding of sustainability within TSOs. The usage of only five company experts and the lack of a sensitivity analysis, checking the IPA conclusions, are the major limitations of this study.

References Azapagic, A., Perdan, S.: An integrated sustainability decision-support framework part II: problem analysis. Int. J. Sustain. Dev. World 12(2), 112–131 (2005). https://doi.org/10.1080/135045005 09469623 Carboni, J., Young, M., Milsom, P., Gonzalez, M.: The GPM global P5 standard for sustainability in project management. Release 1(5), 35 (2016) Chao-Duivis, M.A.B., Koning, A.Z.R., Ubink, A.M.: A Practical guide to dutch building contracts (2013) Elkington, J.: Partnerships from cannibals with forks: the triple bottom line of 21st-century business. Environ. Qual. Manage. 8(1), 37–51 (1998). https://doi.org/10.1002/tqem.331008 0106 Ahmadi, H.B., Lo, H.W., Gupta, H., Kusi-Sarpong, S., Liou, J.J.: An integrated model for selecting suppliers on the basis of sustainability innovation. J. Clean. Prod. 277, 123261 (2020) Ahmadi, H.B., Kusi-Sarpong, S., Rezaei, J.: Assessing the social sustainability of supply chains using best worst method. Resour. Conserv. Recycl. 126, 99–106 (2017) Labuschagne, C., Brent, A.C.: Sustainable project life cycle management: the need to integrate life cycles in the manufacturing sector. Int. J. Proj. Manage. 23(2), 159–168 (2005). https://doi. org/10.1016/j.ijproman.2004.06.003 Martilla, J., James, J.: Importance-performance analysis: an easily applied technique for measuring attribute importance and performance can further the development of effective marketing programs. J. Mark. 41, 77–79 (1977)

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Montalbán-Domingo, L., García-Segura, T., Sanz, M.A., Pellicer, E.: Social sustainability criteria in public-work procurement: an international perspective. J. Clean. Prod. 198, 1355–1371 (2018). https://doi.org/10.1016/j.jclepro.2018.07.083 Rezaei, J.: Best-worst multi-criteria decision-making method. Omega (U. K.) 53, 49–57 (2015). https://doi.org/10.1016/j.omega.2014.11.009 Rezaei, J.: The balancing role of best and worst in best-worst method. In: Rezaei, J., Brunelli, M., Mohammadi, M. (eds.) BWM 2021. LNOR, pp. 1–15. Springer, Cham (2022). https://doi.org/ 10.1007/978-3-030-89795-6_1 Kheybari, S., Rezaei, F.M.: Selection of biogas, solar, and wind power plants’ locations: an MCDA approach. J. Supply Chain Manage. Sci. 1(1–2), 45–71 (2020) Kheybari, S., Davoodi Monfared, M., Farazmand, H., Rezaei, J.: Sustainable location selection of data centers: developing a multi-criteria set-covering decision-making methodology. Int. J. Inf. Technol. Decis. Making 19(3), 741–773 (2020) Salimi, N.: Opportunity recognition for entrepreneurs based on a business model for sustainability: a systematic approach and its application in the dutch, pp. 1–17 (2021) Silvius, A.J.G., Schipper, R.: Developing a maturity model for assessing sustainable project management. J. Mod. Proj. Manag. 3(1), 16–27 (2015). https://doi.org/10.3963/jmpm.v3i1.112 Silvius, G.: Sustainability as a new school of thought in project management. J. Clean. Prod. 166, 1479–1493 (2017). https://doi.org/10.1016/j.jclepro.2017.08.121 Slack, N.: The importance-performance matrix as a determinant of improvement priority. Int. J. Oper. Prod. Manag. 14(5), 59–75 (1994). https://doi.org/10.1108/01443579410056803 Talbot, J., Venkataraman, R.: Integration of sustainability principles into project baselines using a comprehensive indicator set. Int. Bus. Econ. Res. J. (IBER) 10(9), 29 (2011). https://doi.org/ 10.19030/iber.v10i9.5624 Waas, T., Hugé, J., Block, T., Wright, T., Benitez-Capistros, F., Verbruggen, A.: Sustainability assessment and indicators: tools in a decision-making strategy for sustainable development. Sustain. (Switz.) 6(9), 5512–5534 (2014). https://doi.org/10.3390/su6095512 Ahmad, W.N.K.W., Rezaei, J., Sadaghiani, S., Tavasszy, L.A.: Evaluation of the external forces affecting the sustainability of oil and gas supply chain using best worst method. J. Clean. Prod. 153, 242–252 (2017)

A GIS-Based BWM Approach for the Location Selection of Solar Power Plant in Tunceli Province (Turkey) Zekeriya Konurhan1(B)

, Melih Yucesan2

, and Muhammet Gul3

1 Department of Geography, Munzur University, Tunceli, Turkey

[email protected] 2 Department of Emergency Aid and Disaster Management, Munzur University, Tunceli, Turkey

[email protected] 3 Department of Transportation and Logistics, Istanbul University, Istanbul, Turkey

[email protected]

Abstract. The world has recently tended to turn to renewable energy sources due to the serious negative impact of fossil fuels on the environment. One of the top priorities for solar energy is the selection of the most suitable location of the solar power plant to be established. In this study, the most suitable solar power plant location selection for Tunceli, a province located in the eastern part of Turkey, is studied with an approach based on Geographic Information System (GIS) and the best-worst method (BWM). A weighting was performed using the BWM model for 16 sub-criteria under four the main criteria of “climatic conditions, geographical conditions, land conditions, and location (distance to crucial points)”. Afterward, maps were created for these criteria, and a 6-point scale in the legends of each map for each sub-criteria was applied. Finally, the most suitable locations were determined with GIS-based calculations. Keywords: Solar power plant · Location selection · GIS · BWM

1 Introduction Increasing industrialization and the emission of harmful gases pose a great threat to the environment. Undoubtedly, it reveals the importance of the need for renewable energy sources to minimize the harmful effects caused by these threats. Resources such as biomass, hydroelectricity, solar, wind, geothermal, and hydrogen are the most important sustainable energy sources. Increasing commodity prices and fluctuations in energy costs in the post-Covid-19 pandemic are problems that can be solved by turning to renewable energy investments for many countries. The costs of solar and wind energy systems have decreased significantly in the last 30 years, and therefore the transition to renewable energy-based systems is gradually increasing [1]. With the new technological tools that have emerged and developed, the costs in renewable energy investments have been reduced somewhat, and solar energy investments have become competitive in terms of usability with traditional energy production [2, 3]. Undoubtedly, the most important © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 87–102, 2023. https://doi.org/10.1007/978-3-031-24816-0_8

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component of such investments is selecting the possible location of the facility. This selection decision is an important decision as it directly concerns the profitability of the power plant. In the scientific literature, the solar power plant location problem has been addressed by many researchers. It is considered a “multi-criteria decision making (MCDM)” problem since it includes many criteria affecting the selection. In addition, revealing the effect of existing criteria with Geographic Information System (GIS)-based models with maps is common in the literature. The current study proposes a GIS-based BWM approach the location selection of a solar power plant. With this hybrid approach, the most suitable location was determined for the Tunceli province which is located in the eastern region of Turkey. In the model, first of all, the weights of 16 different sub-criteria under the main criteria, namely climate, geographical, soil and proximity to important points were obtained by BWM. BWM was developed by Jafar Rezaei [4] in 2015. In principle, this method can be used with any problem whose purpose is to select alternatives with respect to a set of criteria, as in the problem in this study. BWM requires less pairwise comparison data and is capable of more consistent pairwise comparisons than most existing MCDM methods. This means it produces more reliable results. The original BWM was published as two separate articles [4, 5]. Output from BWM (importance weights of criteria) is taken as an input for GIS. GIS is a structure that uses geolocation information to provide a spatial decision support system. The inclusion of GIS and MCDM methods allows policymakers to refine their choices and identify the most appropriate options, considering subjective and contradictory criteria. GIS-based MCDM is widely used in the literature to choose the most suitable site [6, 7]. In this context, in the current study, the scale of each map and the ranges of values were determined, and the most suitable location was determined by weighted overlap. The suitability level for this location is also visualized by a map with a 5-scaled legend. The remaining of this study is organized as follows: The second section includes the literature review of the previous studies on solar power plant location analysis, especially for ones that used BWM and GIS as methodology. The third section shows the framework of the BWM-GIS hybrid methodology and application results. Finally, we provide the concluding remarks, limitations, and future research opportunities.

2 Literature Review While examining the studies in the literature on the subject, two points were evaluated. The first is the analysis of solar power plant site selection models. Here, the studies of the last few years have been brought to the fore and critiqued since there is a lot of work in this field. The second point is to examine the studies in which BWM and GIS are used together in the location selection of renewable energy power plants (such as solar and wind). Regarding the first point, we can mention a number of studies as follows: Sun et al. [8] combined GIS and MCDM to determine the most suitable location for a large-scale solar photovoltaic (PV) and concentrated solar power (CSP) plant in China. Criteria regarding climate, orography, water availability, and location are weighted via the analytic hierarchy process (AHP). Then, the most appropriate location is recommended for the solar

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power plant deployment. Similarly, Hassaan et al. [9] and Ruiz et al. [10] developed a GIS-AHP integration-based tool for site-suitability assessment of solar power plants in Kuwait and Indonesia. Soydan et al. [11] developed a model for sustainable ecological development in Nigde, Turkey, via GIS-AHP. Eleven layers (sunshine duration, solar radiation, slope, aspect, road, water sources, residential areas, earthquake fault line, mine areas, power line, and transformers) weighted by AHP are analyzed in GIS. The optimal location of areas where solar energy could be built is selected based on the obtained results. Habib et al. [12] used remote sensing (RS) technology and GIS and AHP for the optimum site selection of a solar photovoltaic power plant on the northwest coast of Egypt. Techno-economic and environmental criteria are weighted via AHP, and then a land suitability index is created to check the selection of the site. Solangi et al. [13] assessed solar PV power project site selection in Pakistan via AHP and fuzzy VIKOR, a compromise MCDM method widely used in location analysis. Economic, environmental, social, location, climate, and orography criteria are weighted via AHP as in the studies mentioned above, and fuzzy VIKOR is then used to determine optimal location 14 alternatives. Hafeznia et al. [14] studied site selection of utility-scale PV solar farms using GIS and using Boolean and fuzzy logic models for Iran. Sánchez-Lozano et al. [15] used ELECTRE-TRI with GIS in assessing PV solar farm sites in Spain. This is differentiated from the studies by proposing a decision support software IRIS. It is seen from the analyzed studies that the GIS-AHP combination is the most frequently applied method by the researchers. The component that makes the studies different here is the difference in the countries where the application is made and the variability of the criteria considered in the evaluation. In this case, the fact that BWM, which we used in our study, has only recently been used in the field highlights its originality. Considering the case study for Tunceli province (Turkey) and the change in the criteria considered, its integration with GIS can be considered original. Regarding the second point, the literature brings BWM to the fore. A study was carried out on the AHP-GIS integration for the wind farm location selection. Tercan [37], nine evaluation criteria were considered, and BWM was used for their weights. Wind speed was the most prominent evaluation criteria, followed by land cover/use, proximity to certain protected areas, urban settlements, slope, wetlands, and important bird areas. The weighted Sum technique obtained conformity maps in the GIS. In another study by Villacreses et al. [16], a number of MCDM methods with GIS are used to wind farms suitability location in Ecuador. In that paper, AHP is used to calculate the weight of the criteria to install wind farms. The OWA, OCRA, VIKOR, and TOPSIS methods used to select the location. Four MCDM methods were chosen since each potential location can be evaluated with the GIS assessment criteria database. Finally, the Pearson correlation analysis is applied to test the solidity of the methods. BWM-GIS model has been applied to wind turbine, fire station and some other site selection problems for Turkey, it has not yet been applied to solar power plant site selection. Moreover, although the Tunceli province is a suitable region in terms of solar potential, its mountainousness, its backwardness in regional development and the risk of terrorism, etc. could not attract enough investors due to factors In particular, considering the second point as identified above, the use of BWM-GIS integration to select a possible solar power plant location in a city (Tunceli) in Turkey will contribute to the literature in

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terms of both guiding the stakeholders in the practical world and proposing this integrated model from a methodological point of view.

3 Research Methodology and Application Results This section presents details about BWM and GIS used in the research methodology. As mentioned before, BWM was used to determine the weights of the criteria and subcriteria considered for site selection, and GIS was used to determine the suitability index map for the Tunceli province by using these criteria weights. Directly at the parcel level, which areas are suitable were determined by GIS. 3.1 Criteria Used in the Location Selection The criteria used in the study are grouped under 4 main criteria. These are climatic conditions, geographic conditions, land conditions and location. The criteria hierarchy (including main and sub-criteria) is shown in Fig. 1.

Fig. 1. Criteria hierarchy for the solar power plant location selection

Climatic Conditions Solar Radiation, the total amount of short wavelength radiation received from the horizontal surface on the ground, is defined as global horizontal radiation. For solar power plant installation, 4 kWh/m2 of solar radiation per day is considered a moderate value, while 5–6 kWh/m2 per day is considered a good level [12]. In another study, as a result, solar radiation should be between 4–4.5 kWh/m2 at least per day. Annual average temperature: Air temperature directly affects the operation and efficiency of solar panels. According to the literature for solar panels, the average daily temperature should be less than or equal to 25 °C. The high ambient temperature in the area where the solar panels are located prevents the panels from working efficiently. Therefore, high air temperature is not desirable [13, 17, 18]. Annual average precipitation and humidity: Areas with high annual precipitation negatively affect the efficiency of solar power plants as they absorb short-wave radiation [3,

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19]. Likewise, high humidity rates are not desirable in solar power plants [20]. Annual average sunshine duration; In solar power plants, clear weather and sunny days are desirable for solar panels. Clear and sunny weather allows solar panels to receive the necessary energy easily. Geographic Conditions Elevation; As the altitude increases, the efficiency of the solar panels increases because the temperature decreases and the solar radiation is more. In addition, since the increase in altitude will increase the cost of solar panel installation, it is not recommended to be installed in these regions [13, 14]. Slope: The slope value should not be more than 2–3% [14, 21]. It is not recommended to install panels in these areas in solar panel installation since high slope values make it difficult to reach and increase the cost. Orientation: For solar power plants, the sun’s angle of incidence is very important because it affects both temperature and solar radiation [7, 13, 14]. Considering that the study area is in the northern hemisphere, the aspect should be south for the most suitable solar panel installation. Land Conditions Land Use: A large land cover is required for solar power plants. Agricultural lands, forests, wetlands and urban residential areas are unsuitable for solar farms. Bare areas are suitable areas for solar panels. In addition, areas where solar panels will be installed should not be used for any activity [9, 36]. The land use map of the study area was taken from the CORINE (Coordination of Information on the Environment) system, which contains land use and cover data, and reclassified according to the relevant suitability areas. Construction Cost: It expresses the effect of the construction of solar farms on the project cost. Criteria such as distance to urban areas, distance to highways, distance to power lines, slope and terrain affect the construction cost [7]. In this study, conformity analysis was carried out in line with the mentioned criteria in order to determine the construction cost in the study area. Thus, suitable areas can be found in terms of construction cost within the boundaries of the study area. Land Cost: For the cost of land in the study area, the land sales prices at the scale of the districts in the study area were obtained from the relevant internet sources. These prices were evaluated within themselves, averaged and transferred to GIS. Thus, an average cost was determined for each district in the study area and used in the analysis phase. Location Location in solar power plants; It is important because it will be determined according to risks such as cost, security situation and natural disasters. Distance to Main Roads; The proximity of solar power plants to transportation routes is considered as an economic factor. The proximity of solar power plants to the main road is important because activities such as transportation infrastructures, energy transmission,

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personnel transportation, unit support are accessible and it reduces the additional costs of such activities [7, 15, 19]. In this study, a distance greater than 1000 m was considered as a restriction. Distance to Power Lines: It is economically efficient to install solar power plants in areas close to power lines. The proximity of solar power plants to power centers such as direct current substations, high-voltage wireless power transmission, ultra-high-voltage direct current and ultra-high-voltage alternating current is very important in terms of cost. From a technical point of view, the proximity of the solar power plant to the power lines reduces the losses of the transmission lines and increases the reliability of the electricity supply [3, 14]. Accordingly, in the study, distances greater than 1000 m were classified as areas of low suitability and unsuitability. Distance to Fault Lines: Solar power plants should not be installed close to fault lines as they may cause disasters such as earthquakes and landslides [3, 19]. Therefore, areas far from fault lines were determined as suitable areas in the study. Distance to Settlement Centers: Urban areas are important as population centers near the solar power plant can reduce electricity transmission and distribution costs. Thanks to the cost savings, the return on investment and profitability of the solar power plant is realized in a shorter time. In addition, the proximity of renewable energy plants to urban areas can reduce the environmental pollution caused by the traditional electricity generation process around the settlements [3, 14, 35]. On the other hand, the establishment of solar power plants near settlements may have a negative impact on the population growth rate and distribution in these regions [19]. Accordingly, in the study, areas close to settlement centers more than 1000 m away were determined as restricted areas. Distance to Dams: Proximity to water sources is important especially for cleaning and cooling in solar power plants [6]. In this study, areas close to water resources were determined as suitable areas, while dams and lakes were determined as areas excluding water surfaces. 3.2 Weighting Criteria with the Best-Worst Method BWM is MCDM method proposed by Rezaei [4]. It is a pairwise comparison-based weighting tool. It needs less pairwise comparisons than full comparisons (2n − 3, where n refers to the number of criteria). Initially, the “best” and “worst” criteria are determined. Then, these are compared pair wisely with other criteria. A scale of 1–9 is used for the comparisons. One is used if the two criteria have the same importance. If there is an extremely important difference between the two criteria, nine is used. It makes a consistency check by two special vectors of “best to others” and “other to worst” [22, 23]. It has also applied to many engineering and management problems [24–27]. Its application steps are as follows: Step 1. The criteria to be evaluated are determined. The criteria to be used in decision making are shown with (c1 , c2 . . . , cn ). Step 2. Best (most significant, most desired) and worst (least significant, least desired) criteria are determined among the determined criteria. Pairwise comparison is not performed at this stage.

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Step 3. Using the numbers 1–9 determines how the best criterion differs from other criteria. Step 4. Using the numbers 1–9 determines how the worst criterion differs from other criteria. Others-to-Worst vector is created as: AB = (a1W , a2W , . . . , anW ) where ajW show the preference of the criterion j over the worst criterion W. Step 5. Determination of weight (w1∗ , w2∗ , . . . , w∗n ). With the necessary conversion done, the problem is: min ξ    wB     w − aBj  ≤ ξ for all j j    wj    − a jW  ≤ ξ for all j w W  wj = 1, wj ≥ 0, for all j Solving problem, the optimum weights (w1∗ , w2∗ , . . . , w∗n ) and ξ∗ are calculated. Following the procedure in Rezaei [4], the Consistency Ratio (CR) is calculated. The higher the ξ∗ , higher CR and less reliable results will be obtained. As a result of the solution of the problem, the variable weights (w1∗ , w2∗ , . . . , w∗n ) and ξ∗ are calculated. Then the consistency ratio is calculated. When the number of variables exceeds three, CR can never be equal to zero. It can be said that the lower the CR, the more consistent the evaluation is made. Since solar power site selection is an interdisciplinary problem, a team of four experts was formed to evaluate the criteria. The expert team consists of a mechanical engineer, an industrial engineer, a geological engineer and a geography science expert. Based on the hierarchy determined in Sect. 3.5, global weights were calculated with BWM and presented in Table 1. Here, the preferences of four experts on the and sub-criteria are not provided due to space limitations. The consistency of each assessment was examined in terms of input-based approach of Liang [34]. All calculated CR’s were below the corresponding threshold value (Table 2). Table 1. Criterion weights Code

Criteria

Global weights

A1

Solar radiation

0.1822

A2

Annual average temperature

0.0499

A3

Annual average precipitation

0.0280

A4

Sunshine Duration

0.0872

A5

Relative humidity

0.0331

B1

Elevation

0.0242 (continued)

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Code

Criteria

Global weights

B2

Slope

0.0563

B3

Orientation

0.0314

C1

Land use

0.0663

C2

Land cost

0.0566

C3

Construction cost

0.0340

D1

Distance to roads

0.0914

D2

Distance to power lines

0.1409

D3

Distance to fault lines

0.0271

D4

Distance to city centers

0.0512

D5

Distance to dams

0.0404

Table 2. Input-based CR results CR values (input based) Expert ID

A–D

A1–A5

B1–B3

C1–C3

D1–D5

Expert-1

0.1429

0.2857

0.1250

0.0667

0.2619

Expert-2

0.1667

0.2222

0.0417

0.0417

0.1667

Expert-3

0.0667

0.1905

0.0500

0.1500

0.0667

Expert-4

0.1500

0.0714

0.0000

0.0000

0.1190

3.3 Data Preparation for GIS Environment GIS is a tool that provides solutions for spatial decision-making problems by utilizing geographic information [7]. It improves the selection process by integrating with MCDM methods for various site selection problems such as solar power plant location selection and helps to present the optimum option. GIS processes spatial data with a software and offers a map-based result to the decision-maker [3]. ArcGIS, one of the GIS tools, was used in this study. ArcGIS’s Weighted Sum tool is utilized in our analysis. Each criterion is multiplied by a certain weight, and the results are aggregated using map algebra to create the final suitability index. For each sub-criterion, Analytic Hierarchy Process (AHP) was used to determine the priority values corresponding to the six legend values in the GIS. [9, 12, 13, 28, 37]. Therefore, a land suitability map for the solar power plant is obtained with the WO tool in the GIS environment. Global Horizontal Radiation (GHI) and temperature data were obtained from the Global Solar Atlas prepared by the World Bank and the International Finance Corporation [29]. Meteorological data such as precipitation, relative humidity and sunshine duration were obtained from the General Directorate of State Meteorology [30]. Elevation, slope

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and aspect data were produced using the Digital Elevation Model (DEM) data from the USGS (United States Geological Survey) [31]. Road, city centers and dam data were obtained from the Open Street Map (OSM) open access database [32]. Fault line data were obtained from the General Directorate of Mineral Research and Exploration, while power line data were obtained from the Aykaç [33]. 3.4 Study Province Tunceli is a small city located in eastern Turkey, mostly mountainous, with a total population of more than 80,000 (Fig. 2).

Fig. 2. Tunceli province

It is adjacent to the cities of Elazig, Bingol, and Erzincan. It has a harsh and continental climate in winters and a hot and dry climate in summers. Its altitude increases towards the north. As the altitude increases, the time the snow stays on the ground increases. Although the industry is not developed much in Tunceli, the agriculture and livestock industries are partially in good condition. Its natural resources are quite rich and diverse. In addition to being quite good in terms of solar radiation, Tunceli province also has many rivers. The Munzur river passes through the city and empties into the Keban dam lake. It has one of the must-see geographies of Turkey with its historical and geographical beauties.

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The solar radiation in Tunceli, the study area, is between 2–5 kWh/m2 on average per day. While the solar radiation decreases to 2–3 kWh/m2 per day in the northern regions where the altitude is 2500–3000 m in the region, it is 4.5–5 kWh/m2 in the southern regions where the altitude is lower (Fig. 3, a1). The annual average temperature in the study area is around −1 to 15 °C. The average daily temperature exceeds 25 °C only in summer. Especially in the south of the study area, the annual average temperature of 13–14 °C corresponds to suitable values for solar panels (Fig. 3, a2). In Tunceli, the study area, precipitation and humidity rates are high in the northern regions where the altitude increases. Especially around Munzur Mountains, precipitation and humidity rates are high (Fig. 3, a3–a5). The average monthly sunshine duration is between 7–8 h. Especially in the southern regions of the study area, the average sunshine duration reaches 9–9.5 h (Fig. 3, a4).

Fig. 3. Solar radiation (a1), Temperature (a2), Precipitation (a3), Sunshine time (a4), Relative humidity (a5).

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The elevation levels around the Munzur and Mercan Mountains, located north of the study area, reach 3000 m (Fig. 4, b1). These areas are not suitable for solar power plant installation. Considering that Tunceli is in the northern hemisphere, the facing direction should be south for the most suitable solar panel installation (Fig. 4, b2–b3). However, this does not mean that other aspects are not suitable for solar panel installation; panels can be installed in other directions with the angle adjustable solar panels. The land use map of the Tunceli province was taken from the CORINE (Coordination of Information on the Environment) system, which contains the land use and cover data, and reclassified according to the suitability areas (Fig. 4), c1).

Fig. 4. Elevation (b1), Slope (b2), Orientation (b3), Land Use (c1), Land Cost (c2), Construction Cost (c3).

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Parameters such as city centers, roads, power lines, fault line and dams for the study area were evaluated by performing the necessary distance analyses and shown in detail (Fig. 5, d1–5).

Fig. 5. Distance from roads (d1), Distance from power network (d2), Distance from fault line (d3), Distance from setlements (d4), Distance from dams (d5).

3.5 Integration of Criterion Weights to GIS Environment After the relevant data are obtained, these data should be made ready for analysis. In this context, climatological data (GHI, temperature, precipitation, etc.) were entered in the study area-specific data and reclassified using the Inverse Distance Weighting (IDW) interpolation method and made ready for analysis. Elevation, slope and aspect data were prepared for analysis by making the necessary reclassification. Location data is related to the location of solar power plants and with these data, the proximity or distance of the solar power plant is determined according to the determined criteria. For this reason, Buffer distance analysis was applied according to the distances determined on these data. Land use data was taken from the CORINE (Coordination of Information on the

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Environment) system and reclassified for the study. Finally, many factors affect the cost of solar panels, such as elevation, slope, distance to roads. By determining these factors, conformity analysis was made in construction cost, and the data was reclassified and made ready for analysis. A 6-point scale in the legends of each map for each sub-criteria was applied. Weighted Sum analysis was applied using the global weight values found with the Best-Worst method on the entire dataset prepared for analysis, and suitable locations for solar power plants were found. Areas suitable for solar power plant are shown in Fig. 6.

Fig. 6. Suitability map for solar power plant installation for Tunceli province

The most suitable areas on the map are shown in black; suitable areas are shown in green, low suitable areas in yellow, moderately suitable areas in orange and unsuitable areas in red. It is seen that the most suitable areas are in the district of Pertek. Pertek has less elevation than other districts, and its sunshine duration is higher than other districts. A large part of Ovacık and Pülümür districts were determined as unsuitable regions. The altitude of these two regions is high. The sunshine duration is very short.

4 Conclusion The importance of renewable energy sources is increasing day by day due to the increase in environmental awareness and the unregulated prices of fossil energy sources. The use of renewable energy resources is vital for countries such as Turkey that cannot meet their own needs in terms of fossil resources. Solar power plants are relatively medium and long-term investments. The determination of the plant location is closely related to the return on investment. For this reason, many different approaches have been applied in the literature for site selection.

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In this study, the factors affecting the solar plant location selection were weighted with BWM by an interdisciplinary team of experts. Then, these obtained weights were injected into the GIS maps created using the exact data. Thus, suitable areas for location selection on the map have been determined precisely and in a way that is possible to access their coordinates. In the study, the southern parts of the Pertek district and the border region of the center of Tunceli with the Pertek district were determined as the most suitable areas. Most of the solar power plants established in the Tunceli province are in the Pertek district. In this respect, it can be said that the suggested regions are suitable. Since solar panel location selection is an engineering problem that needs to be examined from perspectives such as economy, environmental awareness, and energy security. This study will be a guide for decision makers in many ways. Thanks to the GIS integration with the criterion weights, besides showing the suitable places in coordinate precision, it will also enable the potential suitable places to be updated in case the criterion weights change due to the future dynamic conditions. In addition, by determining the appropriate location with coordinate precision, it will allow decision makers to choose the most appropriate location by considering other external factors such as incentives, electricity unit purchase prices, environmental compliance reports determined by state authorities. Although this study contributes to the literature with BWM-GIS integration. The study has some limitations. In this study, solar panel types were not considered, and a general evaluation was made for solar panels. The criteria weights will inevitably change in the evaluations made according to the solar panel types. Due to private information, public lands could not be reached and could not be excluded from the study. Regulations and region-based government incentives were not taken into account in site selection. We think a more effective site selection can be made by considering these issues in future studies.

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A Fuzzy Best Worst Method Based Prioritization of Solar Panel Selection Criteria Kevser Arman(B)

and Nilsen Kundakcı

Pamukkale University, Denizli, Turkey {karman,nilsenk}@pau.edu.tr

Abstract. Solar energy is a renewable energy source and is known as one of the primary clean energy sources all over the world. One of the most important decisions to be taken to make optimum use of solar energy is the selection of the best solar panel. Both quantitative and qualitative criteria affect the best solar panel selection. For this reason, this problem can be considered as a Multi-Criteria Decision Making (MCDM) problem. The aim of this study is to the prioritization of solar panel selection criteria using Fuzzy Best Worst Method (F-BWM). The contributions of this study are to propose a set of criteria for solar panel selection and to present a new application area for F-BWM. Keywords: Fuzzy multi-criteria decision making · Fuzzy best worst method · Solar panel selection criteria

1 Introduction Energy is very important for societies and energy resources affect the economic and social development of countries. With the growing economy and population, the energy demand is increasing and this situation forces to seek alternative energy resources [1]. A large part of the energy needed in the world is met from fossil resources such as coal, oil, and natural gas. The energy requirement in Turkey is mostly based on fossil resources [2]. However, fossil fuels are finite and depleted day by day therefore focusing on renewable energy sources gains importance [3]. Fossil resources will not meet all needs and cause environmental and health impacts, so it is seen as a significant problem. On the other hand, social and economic development, sustainability, and energy security are opportunities for renewable energy sources [4]. A renewable energy source can be defined as an inexhaustible resource that can be used continuously and replaced naturally. Turkey has significant potential in terms of renewable energy resources such as hydraulic, wind, solar, geothermal, and biomass energy. Solar energy is a renewable energy source and is known as one of the primary clean energy sources all over the world. While solar energy systems progressed technologically day by day, they decreased in terms of cost. Turkey imports a large part of the energy it consumes. This situation reflects negatively on the energy import bills of the country and renewable energy sources are seen as one of the most effective solution [5]. Increasing investments in renewable resources instead of imported resources are very valuable for countries’ development. Turkey has a very © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 103–116, 2023. https://doi.org/10.1007/978-3-031-24816-0_9

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convenient location in terms of solar energy. Therefore, solar energy is one of the most widely used renewable energy sources in Turkey. The use of solar energy can be classified into two categories: electricity and heating. Businesses generally use solar energy for electricity, heating and cooling, and water heating. Thanks to this diversity and advantages, businesses in Turkey have focused on solar energy technologies and they try to improve efficiency while saving money. One of the most important decisions to be taken to make optimum use of solar energy is the selection of the best solar panel. Both quantitative and qualitative criteria affect the best solar panel selection. For this reason, this problem can be considered as a MultiCriteria Decision Making (MCDM) problem. This study aims the prioritization of solar panel selection criteria by using Fuzzy Best Worst Method (F-BWM). Differently from previous academic studies, this study presents a new and significant application area for F-BWM so it can contribute to the literature. Moreover, the results of the study can contribute to the prioritization of the criteria in the selection of solar panel. The remainder of this study is structured as follows. Section 2 presents the literature review. Section 3 explains the methodology. Section 4 computes the weights of the criteria and presents their prioritization. Section 5 presents the conclusions of the study and concludes the study with advices for future work.

2 Literature Review A detailed literature review was carried out and it has been classified into two categories as solar panel, which is the application area of this study, and BWM, which is the method used in this study. Accordingly, Table 1 shows the studies using different MCDM methods within solar panel selection topic and recent studies using BWM and extended BWM. There are many current studies on the solar panel selection topic using MCDM methods. Earlier studies generally have used classic and popular MCDM methods such as AHP, F-AHP, TOPSIS, DEA, VIKOR, CRITIC, Entropy, etc. However, some studies have used relatively current methods such as FUCOM, COMET, SPOTIS, etc. Moreover, BWM and extended BWM have been applied worldwide in various areas. However, BWM in a fuzzy environment has not yet been handled to the prioritization of solar panel selection criteria. This paper aims the prioritization of solar panel selection criteria by using F-BWM. For this reason, this paper presents a new application area for F-BWM.

3 Methodology Best-Worst Method (BWM) introduced by Rezaei [15] is one of the innovative and robust MCDM methods to determine the subjective weights of criteria. In this method, the best (the most important) and worst (the least important) criteria are specified by the decision-makers and the best criterion is compared with all the criteria and all the criteria are compared with the worst criterion and two vectors are obtained: best-toothers and others-to-worst [15]. Finally, a nonlinear min-max model which minimizes the maximum absolute difference between the weight ratios of criteria and their pairwise comparisons is generated to obtain the weights of criteria [34].

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Table 1. Summary of applications Year

Authors

Decision problem

Method

2016

[6]

Solar panel selection

AHP

2018

[7]

Solar panel supplier selection

Fuzzy AHP, DEA

2019

[8]

Solar panel selection

Fuzzy AHP, Fuzzy TOPSIS

2019

[9]

Solar panel energy system installation

Grey SWARA, FUCOM

2019

[10]

Literature review of MCDM methods for solar panel selection

MCDM methods

2020

[11]

Performance evaluation of solar panel selection

Pythagorean Fuzzy SWARA, VIKOR

2021

[12]

Solar panel selection

COMET, SPOTIS

2022

[13]

Solar plants site selection

DEA, G-MCDM

2022

[14]

Selection of cleaning method of solar photovoltaic panels

CRITIC, Entropy, SD, TOPSIS, SAW, MEW

2015

[15]

Mobile phone selection

BWM

2015

[16]

Suppliers evaluation

BWM

2016

[17]

Supplier selection

BWM

2017

[18]

Identification of the best configuration for the selected outstations

BWM

2017

[19]

Three case studies are optimal transportation mode selection, car purchase decision, and supplier performance evaluation

F-BWM

2017

[20]

Determining the weights of DMs in group decisions based process

F-BWM

2018

[21]

Evaluate the importance of logistics performance indicators

BWM

2018

[22]

Identifying and prioritizing the key F-BWM, COPRAS indicators of the environmental sustainability

2018

[23]

Evaluation of the criteria for product deletion of fast-moving consumer goods

F-BWM, MACBETH

2018

[24]

Supplier development problem

Z- BWM

2019

[25]

Selecting a suitable multiclass classification model for acute leukaemia

BWM, VIKOR

(continued)

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K. Arman and N. Kundakcı Table 1. (continued)

Year

Authors

Decision problem

Method

2020

[26]

Sustainable supplier selection

F-BWM, F-CoCoSo with Bonferroni

2020

[27]

Evaluating and selecting a sustainable supplier

F-BWM

2021

[28]

Environmental performance evaluation

D-BWM

2021

[29]

Determination of the importance F-BWM level of the digital supply chain on sustainability

2021

[30]

Criteria assessment for Covid-19 vaccine selection

BWM

2022

[31]

Measuring the destination management performance

F-BWM

2022

[32]

Selection of best business practice BWM from bio-medical waste

2022

[33]

Modeling the factors that affect unsafe behaviors

F-BWM

Fuzzy set theory was introduced by Zadeh [35] to solve various problems under complex and uncertain environments and fuzzy sets have been used in many academic studies utilizing MCDM methods. One of them is the Fuzzy Best-Worst Method (FBWM) developed by Guo and Zhao [19]. Hafezalkotob and Hafezalkotob have stated that BWM can be extended into a triangular fuzzy number (TFN) in uncertain environments [20]. The procedure of F-BWM is similar to BWM developed by Rezaei [15] but differs in that it uses the fuzzy comparisons regarding the best and worst criteria and fuzzy best-to-others and fuzzy others-to-worst vectors have been obtained. In this study, the FBWM based on TFNs is used. The triangular membership function of the fuzzy number M is defined as: ⎧ 0, x < l ⎪ ⎪ ⎪ ⎨ (x−l) , l ≤ x < m (m−l) (1) µM  (x) = (u−x) ⎪ ⎪ (u−m) , m ≤ x ≤ u ⎪ ⎩ 0, x > u  1 = (l1 , m1 , u1 ), and Basic approximate operations of the two positive TFNs M  2 = (l2 , m2 , u2 ), where l1 ≤ m1 ≤ u1 , l2 ≤ m2 ≤ u2 , and l1 , l2 > 0, are obtained as M below [36]: Addition: 1 ⊕ M  2 = (l1 + l2 , m1 + m2 , u1 + u2 ) M

(2)

1  M  2 = (l1 − u2 , m1 − m2 , u1 − l2 ) M

(3)

Subtraction:

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107

Multiplication: 1 ⊗ M  2 = (l1 · l2 , m1 · m2 , u1 · u2 ) M

(4)

 2 = (l1 /u2 , m1 /m2 , u1 /l2 ) 1  M M

(5)

Division:

Addition and subtraction of piecewise linear fuzzy numbers, preserve linear membership function while multiplication and division operations do not preserve linear membership function [36]. It should be noted that Eq. (4)–(5) are the approximate operations. Brunelli and Mezei [36] have analyzed the difference between using approximate and exact arithmetic operations for multiplication and division on TFNs and studied how the choice of the type of arithmetic operation affects the ranking of the fuzzy numbers. For more detailed information about approximate operations readers can refer to [36]. Graded mean integration representation (GMIR) is the method that transforms triangular fuzzy numbers into a crisp number.  1 is calculated by Eq. 6 [37].  1 ) of TFN M  1 = (l1 , m1 , u1 ), and the GMIR R(M Let M   1  1 = (l1 + 4m1 + u1 ) R M 6

(6)

The six-step-procedure of F-BWM is given below [19]: Step 1. Build the decision criteria system: ({C1 , C2 , C3 ….Cn }). Step 2. Select the best and worst criteria: best and worst criteria are determined by DMs/experts. Step 3. Determine the priority of the best criterion over all the criteria by using the linguistic terms in Table 2 then the fuzzy best-to-others vector is obtained as:  AB = aB2 , ..., aBn ), where  aB1 , aBj denoted priority of the best criterion over the jth criterion ( (j = 1,2, …., n) and it should be noted that  aBB = (1, 1, 1). Step 4. Determine the priority of all the criteria over the worst criterion by using the linguistic terms in Table 2 and the fuzzy others-to-worst vector is obtained as:  AW = a2W , ..., anW ), where a1W , ajW denoted priority of the jth criterion (j = 1,2, …., n) over ( the worst criterion and it should be noted that  aWW = (1, 1, 1).

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K. Arman and N. Kundakcı Table 2. Definition and membership function of TFNs

Definition

Abbreviation

TFNs

Equally Importance

EI

(1, 1, 1)

Weakly Important

WI

(1, 1, 3/2)

Fairly Important

FI

(3/2, 2, 5/2)

Very Important

VI

(5/2, 3, 7/2)

Absolutely Important

AI

(7/2, 4, 9/2)

Step 5. Calculate the optimal fuzzy weights (w˜ ∗ = w˜ 1∗ , w˜ 2∗ , ....w˜ n∗ ) of the criteria: the optimal fuzzy weights for the criteria that is the one where, for each fuzzy pair w˜ B /w˜ j and conditions w˜ j /w˜ W , we have w˜ B /w˜ j = a˜ Bj and w˜ j /w˜ W = a˜ jW . To satisfy these for all j, a w˜ w˜ B solution should be obtained where the maximum absolute gap w˜ j − a˜ Bj and w˜ wj − a˜ jw for all j are minimized [15, 19]. Where w˜ B is the fuzzy weight of the best criterion, w˜ j is the fuzzy weights of all the other criteria and w˜ W is the fuzzy weight of the worst ˜ j, w ˜ W are TFNs as per Table 2. Therefore, the fuzzy weights of criteria criterion and w ˜ B, w     w w , uw , w are denoted as w˜ B = lBw , mBw , uBw , w˜ w = lW ˜ j = ljw , mjw , ujw and , mW W w ljw , mw j , uj respectively denotes the lower, medium, and upper limit of the fuzzy numbers. To obtain the optimal fuzzy weights, constrained non-linear optimization problem in Model 7 is solved [26]. mink ∗ ⎧ lw ,mw ,uw   ⎪ ⎪ Bw Bw Bw − lBj , mBj , uBj ≤ (k ∗ , k ∗ , k ∗ ) ⎪ ⎪ lj ,mj ,uj ⎪ ⎪ w w w ⎪ ⎪   l ,m ,u ⎪ ⎪ wj wj jw − ljW , mjW , ujW ≤ (k ∗ , k ∗ , k ∗ ) ⎪ ⎪ ⎨ lW ,mW ,u W  ∼ n s.t. j=1 R wj = 1 ⎪ ⎪ ⎪ w ⎪ ⎪ lj ≤ mjw ≤ ujw ⎪ ⎪ ⎪ w ⎪ ⎪ ⎪ lj ≥ 0 ⎪ ⎩ j = 1, 2, ....., n

(7)

Step 6. Check the consistency degree of the pairwise comparison: if a˜ Bj × a˜ jW = a˜ BW , fuzzy comparison will be fully consistent. Consistency Ratio (CR) is a significant indicator and in practice, inconsistency of fuzzy pairwise comparison may exist. The CR is used to check consistency of a fuzzy pairwise comparison. CR is obtained with Eq. 8 and the study performed by Guo and Zhao [19] presents consistency index (CI) that is the maximum possible value of F-BWM. In addition, CR’s interval is [0,1] and values close to zero denote more consistency. It is accepted when CR < 0.10 in this study. CR =

k∗ CI

(8)

A Fuzzy Best Worst Method Based Prioritization

109

4 Application Turkey has high solar energy potential thanks to its geographical location. According to the data prepared by Republic of Turkey Ministry of Energy and Natural Resource, sun can be used efficiently approximately 110 days a year and average sunshine time is 7.2 h /daily and average total sun energy is 3.6 kWh/m2 - daily in Turkey [38]. Nowadays, sustainability is essential for business success and using solar energy helps to improve sustainability. For instance, solar energy offers both efficiency and cost savings for business and helps also to be “green”. Therefore, all businesses are eyeing this opportunity and invest in the solar energy. For this reason, solar energy among the renewable energy source has been selected in this study. Selection of the best solar panel is quite important decision for business. The aim of this study is to contribute to the prioritization of solar panel selection criteria by using F-BWM. For this purpose, 4 main and 16 sub criteria were collected from the literature and experts’ opinion. Figure 1 depicts the hierarchy model of the solar panel selection.

Fig. 1. Hierarchy model of the solar panel selection criteria

It was interviewed 3 Decision Makers (DMs) to evaluate the solar panel selection hierarchy model. This interview aimed to understand the DMs’ opinions in various aspects such as their suggestions, advisements, and evaluation of the criteria. DMs completed a questionnaire to evaluate the priority of the best criterion over all the criteria and the priority of all the criteria over the worst criterion via the linguistic terms in Table 2. Table 3 presents linguistic evaluations of the main criteria by 3 DMs.

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K. Arman and N. Kundakcı Table 3. Linguistic evaluations of the main criteria C2

C3

C4

EI

AI

FI

WI

DM 1

Best Worst

C2

AI

EI

WI

FI

DM 2

Best

C1

EI

WI

FI

VI

Worst

C4

VI

FI

WI

EI

Best

C3

WI

FI

EI

VI

Worst

C4

FI

WI

VI

EI

DM 3

C1

C1

Table 4 presents linguistic evaluations of the sub-criteria by 3 DMs. To show how the F-BWM can be used in practice, the calculations of main criteria weights from the perspective of DM 1 are as follows: Table 5 shows the fuzzy best-to-others and fuzzy others-to-worst vectors of main criteria with respect to DM1. Model 9 has been obtained based on Model 7. Model 9 is as follows: Mink ∗ s.t. l1 − 3.5*u2 ≤ k*u2 ; l1 − 3.5*u2 ≥ − k*u2 ; m1 − 4*m2 ≤ k*m2 ; m1 − 4*m2 ≥ − k*m2 ; u1 − 4.5*l2 ≤ k*l2 ; u1 − 4.5*l2 ≥ − k*l2 ; l1 − 1.5*u3 ≤ k*u3 ; l1 − 1.5*u3 ≥ − k*u3 ; m1 − 2*m3 ≤ k*m3 ; m1 − 2*m3 ≥ − k*m3 ; u1 − 2.5*l3 ≤ k*l3 ; u1 − 2.5*l3 ≥ − k*l3 ; l1 − 1*u4 ≤ k*u4 ; l1 − 1*u4 ≥ − k*u4 ; m1 − 1*m4 ≤ k*m4 ; m1 − 1*m4 ≥ − k*m4 ; u1 − 1.5*l4 ≤ k*l4 ; u1 − 1.5*l4 ≥ − k*l4 ; l3 − 1*u2 ≤ k*u2 ; l3 − 1*u2 ≥ − k*u2 ; m3 − 1*m2 ≤ k*m2 ; m3 − 1*m2 ≥ − k*m2 ; u3 − 1.5*l2 ≤ k*l2 ; u3 − 1.5*l2 ≥ − k*l2 ; l4 − 1.5*u2 ≤ k*u2 ; l4 − 1.5*u2 ≥ − k*u2 ; m4 − 2*m2 ≤ k*m2 ; m4 − 2*m2 ≥ − k*m2 ; u4 − 2.5*l2 ≤ k*l2 ; u4 − 2.5*l2 ≥ − k*l2 ; 1/6*l1 + 4/6*m1 + 1/6*u1 + 1/6*l2 + 4/6*m2 + 1/6*u2 + 1/6*l3 + 4/6*m3 + 1/6*u3 + 1/6*l4 + 4/6*m4 + 1/6*u4 = 1; l1 ≤ m1 ≤ u1 ; l2 ≤ m2 ≤ u2 ; l3 ≤ m3 ≤ u3 ; l4 ≤ m4 ≤ u4 ; l1 ≥ 0, l2 ≥ 0, l3 ≥ 0, l4 ≥ 0, k ≥ 0 (9)

A Fuzzy Best Worst Method Based Prioritization

111

Table 4. Linguistic evaluations of the sub-criteria C12

C13

C14

C15

C16

EI

VI

VI

AI

AI

WI

DM 1

Best Worst

C15

AI

WI

WI

EI

EI

VI

DM 2

Best

C12

FI

EI

EI

VI

VI

WI

Worst

C14

WI

VI

VI

EI

EI

FI

Best

C11

EI

FI

FI

VI

VI

WI

Worst

C15

VI

WI

WI

EI

EI

FI

C21

C22

C23

DM 3

DM 1

C11

C11

Best

C23

FI

WI

EI

Worst

C21

EI

WI

FI

DM 2

Best

C21

EI

FI

WI

Worst

C22

FI

EI

WI

DM 3

Best

C21

EI

WI

FI

Worst

C23

FI

WI

EI

C31

C32

C33

EI

FI

VI

DM 1

Best Worst

C33

VI

WI

EI

DM 2

Best

C31

EI

VI

FI

Worst

C32

VI

EI

WI

Best

C31

EI

FI

WI

Worst

C32

FI

EI

WI

C41

C42

C43

C44

DM 3

DM 1

C31

Best

C41

EI

FI

FI

WI

Worst

C43

FI

EI

EI

WI

DM 2

Best

C41

EI

WI

AI

FI

Worst

C43

AI

FI

EI

WI

DM 3

Best

C41

EI

VI

EI

WI

Worst

C42

FI

EI

VI

WI

By solving Model 9 using Maple 2020 software, the optimal fuzzy weights of main criteria from the perspective of DM 1 are calculated as: k∗ = (0.4494, 0.4494, 0.4494) w ˜ ∗1 = (0.3714, 0.4323, 0.4323) w ˜ ∗2 = (0.1022,0.1217, 0.1217)

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K. Arman and N. Kundakcı Table 5. The fuzzy best-to-others and fuzzy others-to-worst vectors

Best: C1

Worst: C2

C2

(3.5, 4, 4.5)

C1

(3.5, 4, 4.5)

C3

(1.5, 2, 2.5)

C3

(1, 1, 1.5)

C4

(1, 1, 1.5)

C4

(1.5, 2, 2.5)

w ˜ ∗3 = (0.1465, 0.1764, 0.1905) w ˜ ∗4 = (0.2217, 0.2982, 0.2982). Then the crisp weights are obtained for 4 main criteria, C1: electrical properties, C2: mechanical properties, C3: financial properties and C4: customer satisfaction, which are w∗1 = 0.4221; w∗2 = 0.1185; w∗3 = 0.1738; w∗4 = 0.2854. CR = 0.0559 which shows a very high consistency. Same steps are followed for all the criteria. Table 6 shows local and global weights of all the criteria. The results show that the highest priority main criterion is C1: electrical properties. The ranking of importance according to the weights of all the other main criteria is as follows: C3: financial properties, C2: mechanical properties, and C4: customer satisfaction, respectively. For the sub-criteria, C11: maximum power has the highest priority among the electrical properties. Under the mechanical properties, C21: dimension is the criterion with the highest priority. Under the financial properties, C31: cost per watt has the highest priority. And under the customer satisfaction, C41: brand reliability is the criterion with the highest priority. In addition, the least priority criteria are C14: optimum operating voltage, C15: optimum operating current, and C24: service availability. For this reason, these criteria can be ignored for future studies.

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Table 6. The weights of solar panel selection criteria DM 1

DM 2

DM 3

Local Weights

C1

0.4221

0.3814

0.3028

0.3688

C2

0.1185

0.3029

0.1770

0.1995

C3

0.1738

0.1769

0.3814

0.2440 0.1875

Global Weights

C4

0.2854

0.1386

0.1386

k* and CR

0.4494; 0.0559

0.2360; 0.0352

0.2360; 0.0352

C11

0.3390

0.1151

0.2965

0.2502

0.0923

C12

0.1066

0.2550

0.1338

0.1651

0.0609

C13

0.1066

0.2550

0.1338

0.1651

0.0609

C14

0.0812

0.0922

0.0932

0.0889

0.0328

C15

0.0889

0.0800

0.1071

0.0920

0.0339

C16

0.2773

0.2025

0.2354

0.2384

0.0879

k* and CR

0.1925; 0.0239

0.2360; 0.0352

0.2360; 0.0352

C21

0.2447

0.4288

0.4288

0.3674

0.0733

C22

0.3263

0.2447

0.3263

0.2991

0.0597

C23

0.4288

0.3263

0.2447

0.3333

0.0665

k* and CR

0.3027; 0.0572

0.3027; 0.0572

0.3027; 0.0572

C31

0.5535

0.5535

0.4288

0.5119

0.1249

C32

0.2494

0.1970

0.2447

0.2304

0.0562

C33

0.1970

0.2494

0.3263

0.2576

0.0629

k* and CR

0.2360; 0.0352

0.236; 0.0352

0.3027; 0.0572

C41

0.3574

0.4220

0.3274

0.3689

0.0692

C42

0.1619

0.2859

0.1307

0.1928

0.0362

C43

0.2073

0.1182

0.3344

0.2200

0.0413

0.2181

0.0409

C44

0.2732

0.1737

0.2073

k* and CR

0.3027; 0.0572

0.4494; 0.0559

0.5615; 0.0698

5 Conclusion In this study, solar panel selection criteria have been evaluated using F-BWM. The solar panel selection problem has both quantitative and qualitative criteria. Therefore, F-BWM was used in this study due to its capability in defining uncertainties in a better way. Literature review reveals that no study is available on prioritizing of solar panel selection criteria by using F-BWM. This study will benefit the prioritization of solar panel selection criteria, which is one of the significant issues related to the renewable energy investment. This study makes two main contributions. A set of criteria for solar

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panel selection has been put forward and a new application area for F-BWM has been presented. The limitation of this study is that the alternatives have not been evaluated. For future studies, different alternatives can be handled within the solar panel selection topic. Moreover, researchers can integrate objective and subjective criteria weight information by combining the F-BWM and objective methods such as Entropi, CRITIC, Standard Deviation etc.

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Prioritizing Competitive Capabilities in Additive Manufacturing Systems Using Best-Worst Method Vishwas Dohale(B)

, Milind Akarte , and Priyanka Verma

Operations and Supply Chain Management, National Institute of Industrial Engineering, Mumbai, India {Vishwas.Dohale.2017,milind,priyankaverma}@nitie.ac.in

Abstract. Additive manufacturing systems (AMS) have been realized as one of the cutting-edge technologies that can revolutionize the traditional way of producing goods. It is expected that by deploying AMS, the manufacturing firms can effectively manage the trade-off between volume-variety and cost-flexibility. This study is developed at the outset to explore the level of competitive capabilities, namely cost, quality, delivery speed and reliability, flexibility, performance, and innovativeness, achieved by deploying AMS through an operations management lens. In this work, the Best-Worst method (BWM) is used to compute the weights of the competitive capabilities within AMS using the opinions of five informed respondents from AM domain. The competitive capabilities are further prioritized based on their aggregated weights. The results demonstrated that flexibility and innovativeness are the most critical competitive capabilities that can be retained through AMS implementation. Contrary, when employing AMS, delivery speed and cost are the least achieved capabilities over which firms need to make a possible compromise. This study will benefit academicians and readers in understanding the core competencies of AMS. Based on the desired competitive capabilities, a particular firm can align its production facilities in line with AMS. Keywords: Additive manufacturing system · Manufacturing strategy · Competitive capabilities · Best-Worst Method (BWM) · Prioritization

1 Introduction The world is witnessing the technological transition from analog to digital technology. Additive manufacturing (AM), previously known as rapid manufacturing, is one of the disruptive technologies that has gained popularity from practitioners over conventional manufacturing. Additive manufacturing, or 3D printing as known nowadays, is “the process of joining materials to make objects from 3D model data, usually layer upon layer, instead of subtractive manufacturing methodologies, such as traditional machining” [1, 2]. Charles Hull in 1984, successfully built the first working 3D printer, which was named as Stereo Lithography apparatus [3]. Additive manufacturing is also identified

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 117–128, 2023. https://doi.org/10.1007/978-3-031-24816-0_10

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by the other names such as – additive processes, layer manufacturing, additive fabrication, direct digital manufacturing, rapid manufacturing, rapid tooling, and solid freeform fabrication [4]. Producing complex geometries and unique structures of high variety in comparatively moderate volume is the forte of additive manufacturing systems (AMS) [2, 5, 6]. AM can offer a global competitive advantage to the firms. Dublin (2020) reported that “the global AM market revenue is accounted for USD 12 Billion in 2020, which can reach to around USD 78 Billion by the year 2028” [7]. AMS offers significant advantages over traditional manufacturing systems (TMS), such as - minimal raw material consumption, less wastage of material, and reduced lead time and cost. These advantages draw a tremendous research interest in AM domain for its possible industrial applications in the manufacturing sector [8]. It is claimed that the strategic AM adoption transforms manufacturers to become more sustainable, flexible, and innovative [9]. The traditional trade-offs between the market need in terms of volume and variety or competitive capabilities, viz. cost and flexibility, may stand invalid for AM. Further, AM integration has redefined the manufacturing performance dimensions and the competitive priorities, viz. cost, quality, delivery, and flexibility [8, 10, 11]. Indeed, the potential benefits of AMS in the manufacturing sector are well-addressed in academic and industrial reports; however, very little is discussed about the capabilities achieved by AMS to compete in the market. Thus, more light needs to be thrown on exploring the role of AMS in achieving the competitive capabilities within operations management, such as cost, quality, delivery speed and reliability, flexibility, performance, and innovativeness. This paper is developed to understand the competitive capabilities achieved by the manufacturing firms, if they shift to AMS-enabled production operations. To the best of the author’s knowledge, no study in the extant literature has computed and reported the fit between competitive capabilities and AMS [12]. We have utilized the best-worst method (BWM) to evaluate and prioritize the competitive capabilities in regard to AMS. This helps in understanding the critical capabilities that AMS can achieve. The rest of the paper is arranged as follows - Sect. 2 discusses the literature on AMS and competitive capabilities. The research methodology is highlighted in Sect. 3. Results and discussions are provided in Sect. 4. Finally, the concluding remarks and implications are provided in Sect. 5.

2 Literature Review This section provides an overview of the extant literature on AMS and the critical competitive capabilities within the manufacturing strategy domain. 2.1 Additive Manufacturing Systems AMS is on the cusp of becoming an “obvious choice” in different sectors. AM has a successful application in manufacturing prototypes, trinkets, machine tools, healthcare items, toys, 3D printed houses, intricate aerospace, defense and aircraft components, and durable prosthetic limbs for humans and animals. AM is seen as the future of

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manufacturing and a leap towards industry 4.0 transformation to change business and innovation capabilities [13]. AMS provides flexible and on-demand production whenever required, thereby effectively responding to the uncertain and turbulent environment during a disruptive event. The existing body of knowledge on AM domain predicted that the strategic adoption of AMS can help firms gain a competitive advantage in the marketplace by outperforming in terms of competitive capabilities by offering flexible production at a low cost compared to traditional manufacturing [4, 10, 14]. Further, Niaki et al. [15] have highlighted the benefits of adopting AM in different sectors, including – automotive, aerospace, medical, etc., by evaluating and prioritizing the AM performance determinants. Thus, it is crucial to understand the capabilities achieved by AMS that led to gaining a competitive advantage for the firm. 2.2 Competitive Capabilities Competitive capabilities or priorities are the “dimensions that a firm’s production system must possess to support the demands of the markets in which the firm wishes to compete” [16–19]. Competitive priority identification is considered a key element in manufacturing strategy [17, 20]. The competitive capabilities are expressed as – cost, quality, delivery speed, delivery reliability, flexibility, performance, and innovativeness [18, 21–24]. The type of manufacturing system is majorly responsible for achieving competitive capabilities at a specific level [23]. A lot has been discussed in the literature to understand the level of competitive capabilities achieved through traditional manufacturing systems, viz. job-shop, batch-shop, or continuous flow manufacturing system [21, 25, 26]. It is the need of the hour to understand the level of achievement of competitive capabilities through AMS. Table 1 provides the description of competitive capabilities within manufacturing. Table 1. Competitive capabilities in manufacturing [18, 22, 24]. #

Competitive Capabilities

Description

C1 Cost

This involves the cost associated with labor, material, overhead, and resources for producing a tangible product

C2 Quality

It is the ability to offer materials and activities that conforms to the specifications and expectations of customers

C3 Performance

It is the extent to which the features allow the product to outperform well than other products

C4 Delivery Speed

The total lead time between order taking and delivery to the customer

C5 Delivery Reliability The rate that measures how often an order is late or delivered at the wrong place? (continued)

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#

Competitive Capabilities

Description

C6 Flexibility

It is the ability through which firms can increase or decrease the volumes of existing to respond quickly to customers’ changing needs

C7 Innovativeness

It is an ability to quickly introduce new products or make design changes to existing products

3 Methodology We have utilized the Best-Worst method (BWM) in this study to evaluate the relative weights of the competitive capabilities in AMS. The complete flow to conduct the BWM approach for the current study is illustrated in Fig. 1. The rationale for choosing BWM is due to its additive advantage over the other MCDM methods highlighted in the literature [27–29], such as – • BWM is a vector-based method and consists of lesser attributes comparisons which makes it easy for experts to interpret, • BWM has an integer scale, while in some MCDM methods like AHP, ANP, etc. fractional scales (1/9, 1/4) are also used, which makes judgment complex • BWM mitigates equalizing bias, making it more efficient to calculate the weights of attributes and rank them.

Identifying the competitive capabilities through existing literature Consult the experts from AMS domain to determine the best (most critical) and worst (least critical) capabilities according to their perception Determine the preference of "Best" capability over others by creating "Best-toOthers" vector Determine the preference of other capabilities over the "Worst" capability by creating the "Others-to-Worst" vector Calculate consistency ratio Compute global weights of each capability Prioritize the competitive capabilities based on the relative weights

Fig. 1. Structure of proposed research methodology.

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The reliability of the output relies on the judgment of the selected experts. Thus, critical attention must be given while selecting the experts [30]. The experts are selected based on three critical criteria – 1) experience in the domain; 2) working position in the organization; and 3) interest in providing their feedback and participating in the study. Following these criteria, we consulted five informed experts working in the renowned AM firms with more than 10+ years of experience in AM and strategy field for conducting the BWM process. Out of five, two experts are operations managers, while the rest are manufacturing heads. We have collected the data for BWM by interviewing the experts onsite at their firm to get more detailed insight through the discussion. Further, using the BWM procedure, we evaluated the weights of competitive capabilities. Based on the relative weights, the competitive capabilities are prioritized. 3.1 The Best-Worst Method The Best-Worst Method (BWM) is a popular multi-criteria decision making (MCDM) method [27] that computes the weights of attributes by comparing the best attribute over others and others over the worst attribute [31]. Using less information, BWM conducts consistent comparisons. BWM is based on mathematical modeling with an objective function to gain the optimal weights and consistency ratio (CR). BWM is of two types – nonlinear and linear. Typically, the nonlinear BWM model generates multiple optimal solutions [27]. However, in certain systems, one optimal solution is preferred. This is why Rezaei [32] developed a linear BWM method to compute the single optimal value of an objective function. As our study tries to prioritize the competitive capabilities for manufacturing firms, experts want to have single optimality within the solution. Thus, we have used the linear BWM model. The detailed procedure to conduct linear BWM is explained next. 3.1.1 BWM Procedure BWM comprises five steps to compute the weights of attributes as follows [27, 32]. Step 1: Identify the relevant decision attributes. In this step, we identify the relevant n attributes (c1 , c2 , ...., cn ) those are crucial for the problem under study. In our study, the attributes to be evaluated are competitive capabilities. A total of seven capabilities (c1 , c2 , ...., c7 ) are identified from the literature and enlisted in Table 1. Step 2: Determine the best and the worst attribute. In this step, the “best attribute” (most critical or most desired) and “worst attribute” (least critical or least desired) are identified. Step 3: Develop the Best-to-Others vector by determining the preference of the best attribute over other attributes using a 1–9 scale. AB = (aB1 , aB2 , ..., aBn ) where, aBj denotes the preference of the “best” attribute “B” over attribute “j” Step 4: Develop the Others-to-Worst vector by determining preference for all other attributes over the worst attribute, using a 1–9 scale. AW = (a1W , a2W , ..., anW )T

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where, ajW signifies the preference of attribute “j” with the “W” worst attribute. Step 5: Compute the optimal weights of attributes. To find the criteria’s optimal   weight, we minimize the maximum among the set of  wB − aBj wj , wj − ajW wW  . The problem can be represented as     min max wB − aBj wj , wj − ajW wW  j

s.t.



(1)

wj = 1

j

wj ≥ 0, for all j Model 1 can be transferred as: minξ L s.t.   wB − aBj wj  ≤ ξ L , for all j   wj − ajW wW  ≤ ξ L , for all j  wj = 1

(2)

wj ≥ 0, for all j ξ L∗ represents the consistency ratio (CR) for the comparison vectors under study. Solving model 2, the optimal weights (w1∗ , w2∗ , ..., wn∗ ) and optimal ξ L∗ value are computed. ξ L∗ (CR) ∈ [0, 1]. The value of ξ L∗ closer to 0 shows a high consistency [27]. The optimal weights for the competitive capabilities are computed using BWM. 3.1.2 Evaluating Consistency Ratio A comparison vectors are fully consistent if aBj × ajW = aBW , for all j, where aBj , ajW and aBW are respectively the preference of the best attribute over the jth attribute, the preference of attribute j over the worst attribute, and the preference of the best over the worst attribute. However, some of the j in the calculation may not be fully consistent due to certain vagueness in judgment. Thus, a consistency ratio (CR) is calculated to determine how much a comparison is consistent. The input-based consistency ratio CRI method proposed by Liang et al. [33] is used to calculate the consistency ratio. The Input-based Consistency Ratio CRI can be computed by following equations. CRI = max CRIj j

where,  CRIj

=

|aBj ×(ajW −aBW | aBW ×aBW −aBW

0,

, aBW > 1 aBW = 1

(3)

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The local consistency level corresponds to a specific criterion Cj is given as CRIj . While CRI is the global or overall input-based consistency ratio for all the criteria under study, which can be the maximum value of CRIj . The reason for computing CR through input-based consistency measurement is due to its advantages [33] as – 1) provision of immediate feedback on the input preference, whether they are consistent or not; 2) easy interpretations; 3) can be effectively deployed in different BWM forms, e.g. a linear or nonlinear; 4) immediately determining the most inconsistent pairwise comparison. Liang et al. [33] further provided threshold values for input-based consistency ratio to check whether the judgment is consistent or not. Table 2 enlists the threshold values for input-based consistency ratio. Table 2. Threshold values for input-based consistency ratio [33] Scales

Criteria 3

4

5

6

7

8

9

3

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

4

0.1121

0.1529

0.1898

0.2206

0.2527

0.2577

0.2683

5

0.1354

0.1994

0.2306

0.2546

0.2716

0.2844

0.2960

6

0.1330

0.1990

0.2643

0.3044

0.3144

0.3221

0.3262

7

0.1294

0.2457

0.2819

0.3029

0.3144

0.3251

0.3403

8

0.1309

0.2521

0.2958

0.3154

0.3408

0.3620

0.3657

9

0.1359

0.2681

0.3062

0.3337

0.3517

0.3620

0.3662

4 Results and Discussion The five-step BWM approach is followed to evaluate the criteria weights. As discussed earlier, seven competitive capabilities are identified using a literature review, as shown in Table 1. Five experts from the manufacturing domain provided their opinions on the best and the worst competitive capabilities. Further, preferences on capabilities are received from all the experts as instructed in steps 3 and 4 using a 1–9 scale to formulate best-to-others and others-to-worst vectors. Each expert’s opinions on the best and worst capabilities are enlisted in Table 3 and 4, respectively. After collecting all the judgments from the five experts over best and worst criteria pairwise comparisons, as shown in Table 3 and 4, we evaluated the input-based consistency ratio. Take an example of expert 1. The best criterion is C6, and the worst criterion is C1 (See Table 3 and 5). For simplicity, refer to Table 5. It is evident that the value of aBW is 7. Now using Eq. 3, we computed the value of CRIj as shown in Table 5. The global or overall CRI is 0.1905. From Table 2, the threshold value for 7 criteria (in this study, 7 capabilities) and for the 7-scale is found as 0.3144. Thus the CRI = 0.1905 < 0.3144. This depicts the judgment is consistent. Similarly, we performed the same

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# Experts

Best Capability

Other Competitive Capabilities C1

C2

C3

C4

C5

C6

C7

Expert 1

C6

7

3

4

3

2

1

1

Expert 2

C7

8

3

5

4

3

2

1

Expert 3

C7

4

2

3

7

5

2

1

Expert 4

C6

4

3

3

7

5

1

2

Expert 5

C6

8

2

3

4

2

1

2

Table 4. Experts’ opinions on Others-to-worst vector. Other Competitive Capabilities

Worst Capability Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

C1

C1

C4

C4

C1

C1

1

1

2

3

1

C2

5

6

5

5

4

C3

3

2

4

4

2

C4

4

3

1

1

1

C5

5

4

3

3

2

C6

7

6

5

7

8

C7

6

8

7

7

6

procedure to check the consistency for other experts. It is observed that all the judgments from every expert are consistent. Table 5. Input-based consistency ratio of each capability – Expert 1. Expert 1

C1

C2

C3

C4

C5

C6

C7

Best - C6

7

3

4

3

2

1

1

Worst - C1

1

5

3

4

5

7

6

CRIj

0.0000

0.1905

0.1190

0.1190

0.0714

0.0000

0.0238

After computing the consistency, the weights of competitive capabilities are evaluated using a BWM model for each of the five different participants. This results in obtaining five weight vectors. Finally, the five weight vectors are aggregated using a geometric mean method followed by the normalization. Table 6 provides the five respondents’ weight vectors and the aggregated weight of each capability. Based on the aggregated

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weights, the competitive capabilities are prioritized, as shown in Table 6. The weight of each capability is computed using the BWM method and shown in Fig. 2. Table 6. Weights of Competitive Capabilities.

Aggregated Weights 0.3000 0.2578

0.2527

Priority weights

0.2500 0.2000 0.1476 0.1500 0.1125

0.1070 0.1000

0.0695 0.0529

0.0500 0.0000

Competitive Capabilities

Fig. 2. Aggregated weights of competitive capabilities.

It is evident from Fig. 2 and Table 6 that cost and delivery speed are the worst (least significant) capabilities corresponding to the AMS. As the raw material, processing, and post-processing costs are higher in AMS [4], the cost capability is prioritized the least. However, AMS can retain the cost advantage by producing strategic and specific

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parts (unique components required for a specific purpose), as such parts cost huge when produced through TMS [14]. At the same time, the time for printing a part is considerably more, which results in a higher delivery time. This can be the reason for the low delivery speed capability. Contrary, it is highlighted in the literature that AMS is highly flexible in producing complex geometries and quickly adopts any design changes. Also, it is said that anything which one can design, can be 3D printed using AMS, i.e. design-to-print [2]. Thus, flexibility and innovativeness are the most critical capabilities firms can retain if they transform their manufacturing operations into AMS.

5 Conclusion and Implications In the present era of digitization, AMS has been accepted widely to overcome the inefficacy of traditional manufacturing systems. AMS handles the ever-changing market demands effectively to retain global competitiveness. AMS provides required manufacturing competencies to meet the business goals [4]. Some studies mentioned that AMS could help firms achieve competitive capabilities, viz. Cost, quality, delivery speed and reliability, flexibility, and innovativeness at the highest levels. However, literature scants in underpinning the prominent priorities that can be achieved through AMS adoption. This study is developed to determine the critical capabilities that can be retained by deploying AMS at manufacturing firms. We utilized the Best-Worst Method (BWM) to address this purpose. Using BWM, we determine the weights of each competitive capability corresponding to AMS and thereafter prioritize them. It is seen that flexibility and innovations are the most critical, while cost and delivery speed are the least critical capabilities a manufacturing firm can achieve by employing AMS. Although this study offers novel insights in terms of the strategic fit between AMS and competitive capabilities, we recommend prospective researchers to conduct a study highlighting the comparative analysis of AMS and TMS in terms of competitive capabilities. Further, the level of manufacturing capability through AMS implementation can be computed in future studies. As the AMS adoption is growing globally, we encourage researchers to conduct more case-based research and understand the actual level of capabilities achieved by the firms through AM adoption.

References 1. ASTM: Standard Terminology for Additive Manufacturing Technologies., http://enterprise. astm.org/filtrexx40.cgi?+REDLINE_PAGES/F2792.htm 2. D’Aveni, R.: The 3-D printing revolution. Harv. Bus. Rev. 93, 40–48 (2015) 3. Bogue, R.: 3D printing: the dawn of a new era in manufacturing? Assem. Autom. 33, 307–311 (2013). https://doi.org/10.1108/AA-06-2013-055 4. Khorram Niaki, M., Nonino, F.: The Management of Additive Manufacturing. Springer, Cham (2018) 5. Khorram Niaki, M., Nonino, F.: Additive manufacturing management: a review and future research agenda. Int. J. Prod. Res. 55, 1419–1439 (2017). https://doi.org/10.1080/00207543. 2016.1229064

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Identifying Impact of the Entrepreneurship Ecosystem on the Success of Entrepreneurial Start-Up Firms Georgios Boutris1 and Negin Salimi2(B) 1 Wageningen University and Research, 6709 RZ Wageningen, The Netherlands 2 Wageningen University and Research, 6706 KN Wageningen, The Netherlands

[email protected]

Abstract. The entrepreneurship ecosystem is a widely used approach that facilitates start-ups’ growth. To date, there is a research gap concerning the influence of the entrepreneurship ecosystem on start-ups’ success during different lifecycle stages (bootstrapping, seed, and creation stage). Using Bayesian Best-Worst Method, the importance of various entrepreneurship ecosystem attributes was examined on the entrepreneurial success of start-ups during their lifecycle in the Dutch agri-food sector. To measure success, five indicators were considered: profitability, sales growth, employment growth, market share, and return on investment. The results suggest that the ecosystem attributes of Leadership, Network Density, Talent, and Capital are critical for the success of start-up in each life stages. Furthermore, the study highlights that the ecosystem attributes of Talent and Companies present differences in the creation stage compared to the previous stages. More specifically, Talent becomes even more important, in addition to programs for cooperation between larger companies and start-ups requiring more attention. Finally, using Importance-Performance analysis, the findings indicate that the Dutch entrepreneurship ecosystem seems to be efficient and supportive for the creation and success of entrepreneurial start-up firms. Keywords: Entrepreneurship · Entrepreneurship ecosystem · Start-ups · Dutch agri-food sector · Bayesian Best-Worst Method · Importance-Performance analysis

1 Introduction In recent years, companies have been forced to adapt to more and more challenges such as market changes, sustainability, and entrepreneurship [1]. The entrepreneur is responsible for identifying, acquiring, and pooling resources to maximize a firm’s revenues under conditions of risk and uncertainty [2, 3]. For start-ups, companies in the initial stages of a business that an entrepreneur undertakes to create products or services, these challenges are observed differently based on the stage of their life cycle [4]. To successfully address these challenges, the use of resources and capabilities is crucial and transcends business © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 129–145, 2023. https://doi.org/10.1007/978-3-031-24816-0_11

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boundaries. In practice, this highlights the importance of a thriving entrepreneurship ecosystem that will help start-ups to address uncertainty and risk [5]. More specifically, Sternberg [6] mentioned that entrepreneurship takes place in a community of interdependent actors that form an entrepreneurial ecosystem. As claimed by Mason and Brown [7], these actors can be potential or existing entrepreneurs, organizations that support entrepreneurship, venture capitalists, business angels, and banks, along with institutions such as universities and public sector agencies. This interactive network can lead to higher productivity, employment, and innovation [7–9]. Feld [10] introduced nine attributes of a successful start-up ecosystem. Their functionality is to underline the connection of ecosystem players (e.g., start-ups, investors, mentors, etc.) with an active role of government. As Carayannis et al. [11] emphasized, co-operation, co-evolution and co-specialization are processes that managers and policy makers should consider for the ecosystem improvement. Furthermore, achieving a flourishing entrepreneurial ecosystem is expected to create new jobs and generate innovation. Productive entrepreneurship boosts the efficiency of the market, creates competition, and improves the quality of life [12–14]. Generally, studies have already investigated the efficiency of entrepreneurial startups during their life cycle [5], while earlier Katila et al. [4] went through the strategies a start-up can process to achieve better performance in an industry than its competitors. Moreover, Stam [8] explored how public and private stakeholders perceive the entrepreneurship ecosystem. Although there are indications on how a start-up is affected by the entrepreneurship ecosystem in its lifecycle, there are no data for assessing the impact of different attributes of entrepreneurship ecosystem on the success of a start-up in different life stages There is therefore a gap in the literature on how the entrepreneurship ecosystem affects start-ups at each stage of their lifecycle. Salamzadeh [15] identified three life stages of start-ups (bootstrapping, seed, and creation stage). A thriving entrepreneurship ecosystem consists of various attributes, and different models can be found in the literature. In this research we aim to use the nine attributes which are introduced by Feld [10] for successful entrepreneurship ecosystem and study their importance on five success measures (profitability, sales growth, employment growth, market share, and return on investment) in three different life stages of start-ups in the Agri-food sector in the Netherlands. This industry is very crucial for the Dutch economy [16]. To study this part of the research the Bayesian Best-Worst method (BWM) is used. At this point it is important to note that BWM has been used effectively in previous research on entrepreneurship issues [17–19]. To identify the entrepreneurship attributes which have high importance while their current performance in the ecosystem is low the Importance-Performance analysis is done. In Sect. 2, a literature review is conducted to introduce the concept of the entrepreneurship ecosystem as well as the life stages of start-ups and ways for measuring success. In Sect. 3 the methodology of the research is described, including the collection of archival and empirical data and the methods that will be used for the analysis. In Sect. 4, the study’s findings are presented in combination with the empirical analysis and discussion. Finally, in Sect. 5, the article ends with the conclusions, limitations, and recommendations for future research.

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2 Theoretical Background 2.1 Entrepreneurship Ecosystem Entrepreneurship influences every market and industry all over the world [10], and its improvement depends on ‘entrepreneurship ecosystems’, a system-based approach that policy makers have widely acknowledged [7, 10, 20–22]. In previous studies, the approach of entrepreneurship ecosystem has been analysed based on the importance of geographical location, while some authors emphasised other factors such as the relationship between actors [17, 23]. According to studies for which location is not critical factor for the entrepreneurship ecosystem, interconnections and interactions are included between different networks to find and succeed in innovation [17, 24]. The entrepreneurship ecosystem includes different attributes that make it successful. Still, there is a disagreement on which are the most important [12]. For this research, ten theoretical models were studied along with their suggested entrepreneurship ecosystem attributes: 1) the Entrepreneurial Personality Model, 2) the Entrepreneurial Process Model, 3) the University-based Model, 4) the Pillars of Entrepreneurial Ecosystem Model, 5) the GEM Model, 6) Spigel’s Model, 7) Koltai’s Model, 8) Mason’s & Brown’s Model, Isenberg’s Model, and 10) Feld’s Model. Although there are different models, the model by Feld [10] seems to fit better in this research due to his in-depth investigation of the entrepreneurship ecosystem, such as the key actors, the significant recourses, and the government’s contribution. Furthermore, this model has also been used in recent similar research [17] and it would be interesting to cross-check the results. However, in the recent research which is done by [16] the importance of different attributes is identified on the success of start-ups only in the early stage of life cycle. The list of Feld’s [10] attributes includes: 1) Leadership, 2) Intermediaries, 3) Network density, 4) Government, 5) Talent, 6) Support Services, 7) Engagement, 8) Companies, and 9) Capital. More information about the entrepreneurship ecosystem attributes can be found in the Appendix. 2.2 The Lifecycle of Entrepreneurial Start-Up Firms Start-ups aim first to survive and then to grow during their life cycle. Salamzadeh [15] asserted that the life cycle of start-ups consists of three stages: bootstrapping, seed, and creation stage. Bootstrapping Stage: the first life stage where risk is higher due to absence of funds. Most of the time, funds are provided by the family and friends that seek to support the entrepreneur. In addition, angel investors might provide financial backing in exchange for ownership and earnings. According to Freear et al. [25], bootstrapping is the stage that includes all the processes to build a company from nothing without borrowing, while Brush et al. [26] contended that the purpose of this stage is to get into customers’ minds and promote the feasibility of the service or the product. Seed Stage: the second stage where several start-ups fail due to the high uncertainty [15]. The characteristics of this stage are the teamwork that will evolve the start-up, the valuation of the start-up, the average investment that comes from early investors, and

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the support from accelerators and incubators. As a rule, accelerators contribute to startups’ growth while incubators focus on innovation, demonstrating an attractive business model. In case start-ups get support, the possibility to survive and get through the next stage is higher. Creation Stage: the final stage of the start-up lifecycle that includes the organizational arrangements for the success of start-ups [15]. Corporate finance is the primary choice and manages the finance and its sources. At the same time, high investment is also provided by venture capital firms that evaluate the start-up’s potential. 2.3 Success Measures of Start-Ups Regarding the definition of success, it was reported that different terms are used based on the state of evolution of each start-up [27, 28]. Hormiga et al. [29] believed that start-ups should pay attention to the return of investment and how sales increase annually, while Gelderen et al. [30] highlighted the level of profit, turnover, and personal earnings the entrepreneur has from the beginning of the start-up. In agreement with Coad [31], this growth is subdivided into four groups: labour, level of sales and profit, and the number of employments. Each of these indicators impacts start-ups’ success and seem more beneficial than one-dimensional measurement. In this research five success measures are included: profitability, sales growth, employment growth, market share, and return on investment.

3 Methodology Identifying the importance of different entrepreneurship ecosystem on the success of start-ups in different stages of life cycle can be formulated as an MCDM (Multi-CriteriaDecision Making) problem that needs an MCDM method. In this research, Bayesian Best-Worst Method, a new method which is developed by Mohammadi & Rezaei [32] will be applied. The principle of this method is based on two opposite reference points (the selection of the Best and Worst criteria) and therefore it mitigates cognitive biases like anchoring bias and equalizing bias [33]. Moreover, the small number of comparisons (2n − 3) is necessary for overcoming inconsistency problems and gives a structure to the problem. Bayesian BWM consists of 5 steps which are briefly described here: 1. Determine a set of decision criteria {c1 , c2 , . . . , cn }. These decision criteria may be presented at different levels. 2. Identify the best (B) and the worst (W) criteria based on the expert(s) opinions. The best can be for instance the most desirable or important while the worst can be least desirable or important decision criteria. 3. Estimate the preference of the best over all the other criteria by using a number from 1 to 9 (where 1 is ‘equally important’ and 9 is ‘extremely more important’).  The result of best-to-others comparisons is vector AB= aB1 , aB2 , . . . , aBj , . . . ., aBn , where aBj indicates the preference of criterion B over criterion j.

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4. Estimate the preference of all  the criteria over the worst. The result of others-to-worst comparisons is vector AW = a1W , a2W , . . . , ajW , . . . ., anW , where ajW refers to the preference of criterion j over criterion w. 5. Calculate each individual optimal weight w1:K and the overall optimal weight wagg 1:K given the A1:K B and AW , where k represents the decision maker and k = 1, ..., K. This step distinguishes Bayesian Best Worst Method from the original BWM, since it simultaneously estimates the combined distribution and every individual preference. Using the credal ranking, a credal ordering of every single pair of criteria, it can be numerically estimated the probability or confidence that an attribute is more important than another [32]. 3.1 Data Collection The data collection of this research was based on archival and empirical data. First, qualitative, and quantitative data were comprised from scientific reports, websites, academic and journal articles. Second, by conducting online 45-min interviews, empirical data were collected online, quickly, and without cost. More specifically, 20 experts from the Dutch agri-food sector (managers, founders, entrepreneurs, and directors that have experience in this field for at least five years) were asked to evaluate the importance and performance of the entrepreneurship ecosystem attributes regarding five success measures in three life stages. To reduce bias, an e-mail was initially sent to experts, explaining the interview process, and describing each ecosystem attribute. Finally, all questions were answered to ensure that the data were reliable during the interview, while the consistency ratio was also checked. More details about the experts can be found in the Appendix, Table 3.

4 Results and Discussion 4.1 Bayesian Best-Worst Method To ensure that all the pairwise comparisons are acceptable, two procedures were first carried out: the calculation of the Input-based Consistency Ratio (CR) and its comparison with the related thresholds from Liang et al. (2020). Success measure: Profitability Based on Fig. 1, in the bootstrapping stage, Network Density (w = 0.159) is the most crucial ecosystem attribute, followed by Leadership (w = 0.150) while Support Services (w = 0.072) is perceived as the least important ecosystem attributes. In the seed stage, Network Density (w = 0.139) remains in the first place in terms of importance while in the creation stage, Talent (w = 0.154) shows a remarkable increase in importance compared to the previous stages, thus taking the first place. In the light of previous research, Brown et al. [23] noted the importance of a strong Network Density in the early stage of a start-up’s life while Carayannis et al. [11] asserted that with the creation of a strong Network Density, new start-ups obtain knowledge and gain a competitive advantage. Moreover, Feld [10] correlated highly skilled and qualified entrepreneurs with effective decision-making.

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Profitability 0.2 0.15 0.1

Weights in Bootstrapping stage

0.05

Weights in Seed stage Weights in Creation stage

0

Fig. 1. Weights of ecosystem attributes for profitability

Success measure: Sales growth As can be seen in Fig. 2, in the bootstrapping stage, Network Density (w = 0.144) and Leadership (w = 0.142) are the most dominant ecosystem attributes. The Government (w = 0.071) is at the end of the relevant ranking. In the seed stage, the importance of Capital (w = 0.148) increases dramatically and thus takes the first place. In the creation stage, Capital (w = 0.162) reaches the peak of importance, followed by the upward in weight Talent (w = 0.150).

Sales Growth 0.2 0.15 0.1

Weights in Bootstrapping stage

0.05

Weights in Seed stage Weights in Creation stage

0

Fig. 2. Weights of ecosystem attributes for sales growth

In the early stage, a dense network has been found constructive for start-ups since entrepreneurs access essential information of new opportunities [34] and increase their sales. Additionally, a strong relationship between Capital and sales growth has been reported in the literature. According to Paglia and Harjoto [35], less access to Capital can lead to start-ups’ failure while Salimi [17] identified the importance of Capital to increase a start-up’s sales rates. Success measure: Employment growth

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Based on Fig. 3, in the bootstrapping stage, Talent (w = 0.156) is the most major ecosystem attribute, followed by Network Density (w = 0.142). In the seed stage, Talent (w = 0.152) remains first noting a negligible drop. In the creation stage, Talent (w = 0.164) and Leadership (w = 0.147) show considerable growth and are perceived by the experts as the most vital attributes for employment growth.

Employment Growth 0.2 0.15 0.1 0.05 0

Weights in Bootstrapping stage Weights in Seed stage Weights in Creation stage

Fig. 3. Weights of ecosystem attributes for employment growth

As Salimi [17] demonstrated, Talent is important for increasing the number of employees in a start-up firm. As the start-up passes to the next stage, the cooperation of talented employees from different fields and their efficient communication can open new spots for future talented workforce. Furthermore, Baizid [36] reported that different leadership styles affect employment growth differently, highlighting the influence of Leadership. Success measure: Market share In the bootstrapping stage, Leadership (w = 0.141) is in the first place of importance as opposed to Government (w = 0.074) at the other end. In the seed stage, Capital (w = 0.153) increases significantly, and stands out even more (w = 0.158) than the other attributes in the creation stage. See more information in Fig. 4. According to Rooke and Torbert [37], leaders who can expand the market share and increase profit rates are necessary for every business. Moreover, Coeurderoy and Durand [38] underlined the influence of cost leadership strategy on increasing market share. Similar to sales growth, Capital is critical to obtain a better market position [39] by investing on advertisements, equipment and better workforce. Success measure: Return on Investment As it is shown in Fig. 5, Leadership (w = 0.159) is identified as the most critical ecosystem attribute in the bootstrapping stage. In the seed stage, the significance of Capital (w = 0.149) increases dramatically, taking the top spot in the ranking. In the creation stage, Talent (w = 0.163) presents an all-time high in importance, followed by the increased Capital (w = 0.157) and the stable Leadership (w = 0.140). Government (w = 0.073) shows fluctuation in its weight while Support Services remains at the lowest ranking levels.

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Market Share 0.2 0.15 0.1

Weights in Bootstrapping stage

0.05

Weights in Seed stage Weights in Creation stage

0

Fig. 4. Weights of ecosystem attributes for market share

Return On Investment 0.2 0.15 0.1 0.05 0

Weights in Bootstrapping stage Weights in Seed stage Weights in Creation stage

Fig. 5. Weights of ecosystem attributes for return on investment

Archer [40] claimed that enriched leadership skills could increase sales trends and thus increase the ROI. However, the return on investment is not feasible in the very early stage of a start-up’s life. As mentioned in the literature review, many start-ups fail in the seed stage due to high uncertainty [15]. Not having access to Capital could lead to the failure of the business and as it has been observed, it becomes critical after the bootstrapping stage. Finally, talented, and robust entrepreneurs are undoubtedly needed to achieve success. Credal ranking Figure 6 illustrates the credal ranking for profitability in the bootstrapping stage. The nodes are the ecosystem attributes, while the weights above the arrow represent the confidence level of one powerful ecosystem attribute over another. Any confidence level close to 1 indicates greater confidence in the relationship’s validity [32]. One credal ranking is described, while the rest ranking schemes also can be calculated in the same way.

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Fig. 6. Credal ranking for profitability in bootstrapping stage

As shown in Fig. 6, Network Density is perceived as the most critical ecosystem attribute based on expert responses. At the other extreme, Companies and Support Services are the least essential ecosystem attributes for the respondents. The degree of certainty above the arrow shows that Network Density is the most critical ecosystem attribute with a confidence level of approximately 1. However, there is a confidence level of 0.65 that Network Density overrides Leadership while the latter is in absolute terms more significant than Government and Engagement with a confidence level of 1. 4.2 Importance-Performance Analysis A way to provide information on the Dutch entrepreneurship ecosystem current performance to policy makers, government, decision makers, investors, and mentors is by conducting an Importance-Performance analysis. Identifying the importance level of the ecosystem attributes using the Bayesian BWM is not enough since it does not indicate anything more than what is essential for start-ups. More specifically, only a group of attributes is vital, which presents high importance but low performance. Thus, this analysis technique identifies the ecosystem attributes that need the most improvement. Using a scale from 1 (very low) to 5 (very high), the same 20 experts were asked to rate these ecosystem attributes regarding their current performance on each one of the stages of start-ups in the Dutch agri-food sector. Even if there are diverse methods in the academic literature, the model of Martilla and James [41] seems more suitable for this research. Table 1 presents the evaluation of the entrepreneurship ecosystem attributes based on the way they perform in the Dutch agri-food sector in every life stage. In all three stages, the ecosystem attributes that are crucial to the success of start-ups in the Dutch agri-food sector also have a high level of performance from the perspective of the experts. The attributes Talent, Leadership, Network Density, and Capital belong to this list. Although attributes such as Government and Support Services are considered less important, their current level of performance is more than satisfactory. It is interesting to note that the attribute Companies has medium significance for the success of startups. As it can be seen in Fig. 7 (Importance-performance analysis in the Creation stage), its performance is low, showing however a medium importance. Therefore, it could be

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G. Boutris and N. Salimi Table 1. Importance-performance analysis for the Dutch entrepreneurship ecosystem

Attributes

Bootstrapping performance

Bootstrapping Importance

Seed performance

Seed importance

Creation performance

Creation importance

Leadership

3.90

0.15

3.80

0.14

3.70

0.14

Intermediaries

3.85

0.11

3.65

0.10

3.55

0.09

Network density

3.60

0.14

3.75

0.13

3.55

0.12

Government

2.75

0.08

3.20

0.08

3.20

0.08

Talent

3.80

0.14

3.90

0.14

4.00

0.16

Support services

3.15

0.12

3.20

0.08

3.20

0.08

Engagement

3.60

0.10

3.60

0.10

3.50

0.09

Companies

2.55

0.08

2.70

0.08

2.75

0.10

Capital

3.30

0.12

3.40

0.14

3.60

0.15

considered as an opportunity for experts to invest in programs related to cooperation with large Companies. In the Appendix, the graphs regarding the Importance-Performance analysis in two stages of Bootstrapping and Seed can be found.

A

B

C

D

Fig. 7. Importance-performance chart for creation stage

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5 Conclusions This research aimed to investigate the importance of various entrepreneurship ecosystem attributes for start-ups’ success in the Dutch agri-food sector. Since the research problem includes many areas to be analysed, the authors chose an innovative MCDM analysis method called Bayesian Best-Worst Method by Mohammadi & Rezaei [32]. Furthermore, using the Importance-performance analysis method of Martilla & James [41], the authors proposed a framework that experts (managers, founders, entrepreneurs, and directors) should consider to succeed in each of these stages. In the literature, success can be measured in different ways (profitability, sales growth, employment growth, market share, and return on investment). The results indicate that Leadership, Network Density, Talent, and Capital are vital for each one of the start-ups’ life stages. Based on experts’ perception, the performance level of the most critical ecosystem attributes is high. Thus, it demonstrates that the Dutch agri-food entrepreneurship ecosystem operates efficiently and supports the development and success of start-ups. Moreover, even if Government and Support Services have less importance for the success of start-ups, their performance level is more than satisfactory. It is also interesting to note some differences between the creation and other stages regarding the ecosystem attributes of Talent and Companies. As the start-ups evolve, the need for Talent in all sectors and areas of expertise becomes even more remarkable, while establishing specific departments and programs for cooperation between larger companies and start-ups is becoming more critical. Every research has weak points and limitations, and identifying them is essential for future research. First, the Covid-19 pandemic was a communication barrier, as the interviews were conducted online. Second, the research sample size was relatively small due to the limited time available for data collection. Third, only the entrepreneurship perspective is presented. Fourth, using the same sample for both analysis methods (BBWM & Importance-performance analysis) could be a source of bias. These limitations provide the following insights for future research: Collecting data through face-to-face interviews is likely to provide more valid results. In addition, possible researchers should aim to increase the sample size for the best representation of experts in the Dutch agri-food entrepreneurship ecosystem. At the same time, the participation of key stakeholders like banks and government would be ideal for examining their perspectives as well. More extended periods of collected data can benefit future research, although they hide obstacles regarding validity and reliability. Finally, future researchers can compare the Dutch entrepreneurship ecosystem with the one of a different country in the agri-food sector and present the differences.

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Appendix Table 1 presents the most important entrepreneurship ecosystem attributes along with their description, according to Feld [10]. Table 1. Nine attributes that are key elements for the entrepreneurship ecosystem [10] Attribute

Description

Leadership

Strong group of entrepreneurs who are visible, accessible, and committed to the region being a great place to start and grow a company

Intermediaries

Many well-respected mentors and advisors giving back across all stages, sectors, demographics, and geographies as well as a solid presence of effective, visible, well-integrated accelerators and incubators

Network density Deep, well-connected community of start-ups and entrepreneurs along with engaged and visible investors, advisors, mentors, and supporters. Optimally, these people and organizations cut across sectors, demographics, and culture engagement. Everyone must be willing to give back to his community Government

Strong government support for and understanding the importance of start-ups to economic growth. Additionally, supportive policies should be in place covering economic development, tax, and investment vehicles

Talent

Broad, deep talent pool for all levels of employees in all sectors and areas of expertise. Universities are an excellent resource for start-up talent and should be well-connected to community

Support services Professional services (legal, accounting, real estate, insurance, and consulting) are integrated, accessible, effective, and appropriately priced Engagement

Large number of events for entrepreneurs and community to connect, with highly visible and authentic participants (e.g., meet-ups, pitch days, start-up weekends, boot camps, hackathons, and competitions)

Companies

Large companies that are the anchor of a city should create specific departments and programs to encourage cooperation with high-growth start-ups

Capital

Strong, dense, and supportive community of venture capitalists, angels, seed investors and other forms of financing should be available, visible, and accessible across sectors, demographics, and geography

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Table 2 presents the socio-demographic characteristics of 20 respondents that participated in this research. Table 2. Socio-demographic characteristics Respondents

Gender

Current age

Current education level

1

Male

37

MSc

2

Male

36

Ph.D

3

Male

27

MSc

4

Male

29

BSc

5

Male

46

MSc

6

Male

30

MSc

7

Male

27

MSc

8

Female

30

Ph.D

9

Male

35

Ph.D

10

Male

63

MSc

11

Male

40

MSc

12

Male

34

MSc

13

Male

47

MSc

14

Male

52

MSc

15

Male

57

Ph.D

16

Male

53

MSc

17

Male

32

MSc

18

Male

47

BSc

19

Male

30

BSc

20

Female

40

BSc

Importance-Performance Chart As shown in Fig. 8, the ecosystem attributes that experts perceive as vital for the Dutch entrepreneurship ecosystem in the bootstrapping stage also show a high-performance level. This is relevant to attributes like Talent, Leadership, Network Density and Capital. Other ecosystem attributes like Intermediaries and Engagement perform highly even with a low priority regarding their significance. Finally, attributes like Companies combine low performance and importance in contrast to the rest of the ecosystem attributes.

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Bootstrapping Stage 5

Performance

Network density Intermediaries Engagement Government Support services

3

Talent Leadership

Capital

Companies

1 0

0.1

0.2

Importance Fig. 8. Importance-performance chart for bootstrapping stage

As Fig. 9 illustrates, according to the respondents, the ecosystem attributes that are critical in the seed stage show a high-performance level. Similar to the bootstrapping stage, these attributes are Talent, Leadership, Network Density and Capital. Furthermore, attributes with low importance and poor performance are Government and Support Services.

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Seed Stage 5

Performance

Talent Leadership Intermediaries Network density Engagement Capital Support services Government

3 Companies

1 0

0.1

0.2

Importance Fig. 9. Importance-performance chart for seed stage

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Prioritizing the Distributor’s Key Performance Indicators and Constraints to Implement TOC-Based Solution for Outbound Supply Chain Network Chandrashekhar Chaudhari1,2(B) , Vivek Khanzode1 and Vishwas Dohale1

, Rauf Iqbal1 ,

1 National Institute of Industrial Engineering, Mumbai, India

{vkhanzode,raufiqbal,Vishwas.Dohale.2017}@nitie.ac.in 2 Goldratt Consulting, Tel Aviv, Israel [email protected]

Abstract. The concept of Theory of Constraints (TOC) was introduced by Eliyahu Goldratt, an Israeli Physicist, in his book THE GOAL in 1984. TOC is a management philosophy that focuses on the management of the constraint that limits the performance of a system. Although TOC has benefited organizations within many domains, namely – manufacturing, supply chain, project management, sales, and finance, TOC implementation in the outbound supply chain remains the topic of investigation. Thus, it is crucial to determine the constraints to implement TOC in the outbound supply chain. Further, there is a set of certain Key Performance Indicators (KPI) of the distributors that gets enhanced by implementing TOC’s solution in the outbound supply chain. This study proposes multi-criteria decisionmaking based Best-Worst method to prioritize the most important constraint to implement TOC’s solution in the outbound supply chain. Further, we prioritize the KPIs for the distributors in the outbound supply chain. This study is expected to aid researchers and practitioners in determining the critical constraints and KPIs to focus on and improve the outbound supply chain performance. Keywords: Theory of Constraints · Constraint identification · Distributors’ KPIs · Outbound supply chain · Best-Worst Method (BWM)

1 Introduction Roots of the Theory of Constraints (TOC) were found in the late 70s when Dr. Goldratt presented the concept of Optimized Production Timetable (OPT) [1]. The concept of TOC was published by Goldratt in THE GOAL book in 1984 [2]. TOC is a management philosophy that focuses on the management of the constraint that limits the performance of an organization [3]. Initially, the TOC concept was developed for the production environment; however, over the years, solutions were developed for project management, supply chain management, sales, finance and measurements, and retail [2, 4]. TOC concept advises focusing on one constraint at a time, which significantly impacts the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 146–160, 2023. https://doi.org/10.1007/978-3-031-24816-0_12

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system’s performance. TOC has several tools to improve the system’s performance, i.e., Five Focusing Steps (FFS), Drum-Buffer-Rope Scheduling (DBR), Thinking Process, Critical Chain Project Management (CCPM), etc. Amongst these techniques, FFS is widely used. The concept of FFS is as follows [5]. Step 1: Identify the systems’ constraint(s) Step 2: Decide how to exploit the constraint(s) Step 3: Subordinate everything else to the above decision Step 4: Elevate the constraint Step 5: Warning! Do not allow inertia to be a constraint – go back to step 1 It is crucial to explore the system’s most critical constraint and improve the performance impacted by the critical constraint. However, organizations may identify a wrong constraint in the outbound supply chain. Focusing on the wrong constraint can prevent organizations from achieving desired improvements using the TOC concept [6]. TOC has proved to be a successful solution in the supply chain domain to improvise the overall performance of the supply chain and, in turn, the business performance by exploiting and elevating different constraints throughout an entire value chain [2]. As discussed earlier, TOC works on the principle of identification of a critical constraint of the supply chain and overcoming it by using its popular tools. Although despite having the proven benefits of TOC solutions in the supply chain, the literature is at a nascent stage in demonstrating the application of TOC in the outbound supply chain. TOC’s solution for the outbound supply chain involves creating business offers called ‘mafia offers’ or ‘unrefusable offers’ for distributors and dealers. Such offers result in increased sales and profit for producers and resellers [7]. These offers involve an extension of the TOC’s replenishment mechanism to distributors and dealers as explained below [8]: • Setting buffers for each SKU at each distributor. • Collecting daily consumption and inventory data from the distributors • Frequent replenishment from producer to distributors according to TOC’s colourbased priority mechanism. This paper aims to prioritize the constraints that are preventing firms from successfully implementing the TOC’s solution for the outbound supply chain. Further, this paper attempts to determine and rank the critical KPIs of distributors that can be enhanced through the TOC solution. To the author’s best knowledge, no work focuses on identifying and prioritizing the constraints to implement TOC’s solution in the outbound supply chain. Further, the paper is structured in the following sections as – Sect. 2 provides the review of literature on TOC, the constraints to TOC implementation in the outbound supply chain, and the KPIs of distributors. Section 3 details the BWM used to conduct the present research. Results and discussion are summarized in Sect. 4. Concluding remarks are highlighted in Sect. 5.

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2 Literature Review TOC concept is widely implemented in different areas like operations, supply chain, project management, finance, and measurements. However, there is a lack of literature on TOC’s application in the outbound supply chain with respect to the distribution environment. Considering this research gap, TOC application in the outbound supply chain area has been selected for further investigation. An extensive literature review and experts’ opinions have been collected to identify the critical constraints in implementing TOC’s solution for the outbound supply chain and the KPIs of the distributors that can be impacted through the TOC solution. 2.1 TOC in Supply Chain Several organizations that sell products through a network of distributors and dealers have implemented TOC solutions in their supply chain. Figure 1 illustrates the TOC based supply chain structure for such environments. The key principles of TOC’s solution for the supply chain involve: (a) Holding most of the inventory at the central warehouse level where variability in demand is least; (b) Setting the buffers at all consumption locations based on consumption rate, replenishment lead time factored by variability in demand and supply lead time; (c) Consumption and inventory data from each consumption node is shared with supplying node on a daily basis; and (d) Supplying node replenishes the inventory to the consumption node frequently [9].

Fig. 1. Structure of the TOC based supply chain.

The colour-based priority mechanism is followed by the entire supply chain providing uniform priority for each node, as shown in Fig. 1. Green colour indicates the availability of inventory 2/3rd or more as compared to buffer and the lowest level of priority in the supply chain, whereas red colour indicates the availability of inventory less than 1/3rd of the buffer carrying the risk of stock out and hence highest priority for the supply. The yellow colour signifies sufficient inventory, i.e. 1/3rd to 2/3rd of the buffer, to meet the immediate demand [10]. The Dynamic Buffer MManagement (DBM) helps to changing the buffers based on changes in consumption rate and supply lead time [11]. This solution

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helps in improving the supply chain performance in terms of availability and inventory turns [8]. Similarly, the extension of the TOC solution in the outbound supply chain is expected to improve inventory turns of distributors by more than three times and sales increase by up to 25% [8]. Thus, it is felt that a TOC’s solution can enrich the overall effectiveness of the outbound supply chain process. Despite such proven results, there is a lack of studies in the area of application of TOC in the outbound supply chain [2]. There are certain constraints that prevent the implementation of TOC’s solution in the outbound supply chain. Hence, we have developed this study to identify and evaluate the critical constraints of TOC implementation in the outbound supply chain and the KPIs of distributors that can be improved by overcoming the critical constraint. The constraints and KPIs are discussed in the following section. 2.2 Constraint to Implement TOC Solution in Outbound Supply Chain A constraint is a resource or policy/rule/practice that limits a system’s ability to attend to its goal [12]. Any improvement in the performance of the constraint results in an improvement in the entire system’s performance [5]. The experts from the firms that implemented TOC in their inbound supply chain but could not implement it in the outbound supply chain were selected for the interview. The following criteria were used to select the experts [13, 14] - 1) Expert has a minimum of 5 years of working experience in the company; 2) Expert has adequate knowledge about the problem under study; 3) Expert is willing to participate and share the insights about the problem under study. The profile of the selected experts is given in Table 1. Based on the extent literature and experts’ interviews, we identified 9 constraints that restrict the implementation of TOC’s solution in the outbound supply chain and enlisted in Table 2. Table 1. Profile of the experts. Sr. no.

Industry

Designation

Years of experience

1

Auto Spare Parts Distribution Head: Supply Chain

15+

2

Auto Spare Parts Distribution Head: Sales

15+

3

Luggage Manufacturing and Distribution

Vice President: Supply Chain

10+

4

Luggage Manufacturing and Distribution

General Manager: Sales

12+

5

Pesticides

CEO

20+

6

Ceramic Products

Manager: Distribution

10+

7

Ceramic Products

Area Sales Manager

8+

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C. Chaudhari et al. Table 2. Constraints to implement TOC solutions in outbound supply chain.

Code

Constraint in implementing TOC Solution in outbound supply chain

Reference

C1

Lack of computerized billing system with distributors

[8]

C2

Diversified software used by the distributors

From Experts

C3

Irregular data sharing by the distributors

From Experts

C4

Price discounts offered by the firm for bulk purchases

[15]

C5

Fear in the mind of the distributor that my data may be misused

From Experts

C6

Fear in mind of the distributor to face stock out after they allow the firm to decide orders

[15]

C7

Distributors feared that the company might misuse the system to push unwanted inventories

From Experts

C8

Company’s salespeople are worried that they will lose the sale if inventories are not pushed to distributors

From Experts

C9

Fear in the mind of the company and salespeople that distributors will divert capital to competition if we reduce inventories

From Experts

2.3 KPIs of Distributors KPIs as the attributes for performance evaluation of the system. KPIs help to clearly establish a standard system for performance evaluation of a business or employees. KPIs help to reveal if the objectives of any system are achieved to the desired extent or not [16]. The appropriate KPIs can aid in implementing several actions to achieve the system’s goal. Application of TOC’s solution into the outbound supply chain results in an improvement in several KPIs of distributors and dealers. Table 3 presents the critical KPIs of distributors identified through a literature review and survey with experts. Table 3. The KPIs of the distributors. Code

KPI

Short description

Reference

K1

Return on investment

Net Profit/Average Investment in inventories and credit to customers

[7, 17, 18]

K2

Sales Revenue

Sales Revenue = Income from sales of the goods

[8]

K3

Inventory Turnover

Inventory Turnover = Sales/Average Inventory

[8, 19]

K4

Working Capital Turns

Working Capital Turns = Sales/Average [8] Working Capital

K5

Gross Profit

Net Profit = Sales Revenue – Cost of Goods Sold

[19] (continued)

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Table 3. (continued) Code

KPI

Short description

Reference

K6

Net Profit

Net Profit = Sales Revenue – Total Cost [19]

K7

Return on Sales

ROS = Stock returns from customers/Sales

K8

Sales Growth

Sales Growth =  Sales (t)/Sales (t − x) [8, 19]

K9

Out-of-stock

Out of stock = SKU wise Days of out of From Experts stock/SKU wise expected days of stock availability

[19]

3 Research Methodology This section introduces the methodology deployed in this study for prioritizing the KPIs of the distributors and constraints to implement TOC solutions in the outbound supply chain to determine the critical ones using the Best-Worst Method (BWM). BWM is a multi-criteria decision-making (MCDM) method that evaluates the best criterion and compares all the other criteria to the worst criterion [20]. BWM requires less information and conducts consistent comparisons. This method creates a comparison system comprised of Best-to-Others and Others-to-Worst vectors. The objective is to get the optimal weights and consistency ratio (CR). This process uses a simple optimization model. The reason for selecting BWM is due to its benefits over the other MCDM methods, as accentuated in the literature [20–22], such as • BWM is a vector-based method and consists of lesser attributes comparisons which makes it easy for experts to interpret, • Calculated weights from BWM are more reliable and consistent than other MCDM methods, viz. AHP • BWM has an integer scale, while in some MCDM methods like AHP, ANP, etc. fractional scales (1/9, 1/4) are also used, which makes judgment complex • BWM comprises equalizing bias that makes it more efficient to calculate the weights of attributes and rank them. A survey using experts was conducted to identify the most critical constraint in implementing TOC solutions in the outbound supply chain and the most important KPIs from the distributors’ perspective. The best-worst method is applied to compute the weights of constraints and KPIs. Figure 2 illustrates the overall methodology for conducting this study. BWM can be nonlinear or linear type. The nonlinear BWM model offers multiple optimal solutions [20]. However, certain systems demand a single optimal solution that enhance their performance. Rezaei [23] developed a linear BWM method to address this issue by computing the single optimal value of an objective function. As our study tries to prioritize the constraints to implementation of TOC solutions and KPIs of distributors in outbound supply chain, experts want to attain single optimality within the solution.

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Thus, we have used the linear BWM model. The detailed procedure to conduct linear BWM is explained next. 3.1 Procedure to Conduct BWM Method The five steps of BWM to derive the criteria weights are as follows [20, 23]: Step 1: Identify the relevant constraints and KPIs. In this step, we identify the relevant n constrains (C1 , C2 , ...., Cn ) those are preventing the implementation of the TOC solution in the outbound supply chain and n KPIs of distributors (K1 , K2 , ...., Kn ). A total of 9 constraints (C1 , C2 , ...., C9 ) and 9 KPIs (K1 , K2 , ...., K9 ) are identified from the literature and experts interview as enlisted in Tables 2 and 3.

Fig. 2. Structure of proposed research methodology

Step 2: Determine the best and the worst constraint and KPI.

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In this step, the “best constraint” and “best KPI” (most critical or most desired) as well as “worst constraint” and “worst KPI” (least critical or least desired) are identified. Step 3: Develop the Best-to-Others vector by determining the preference of the best over others using a 1–9 scale. AB = aB1 , aB2 , ..., aBn where, aBj denotes the preference of the “best” attribute “B” over attribute “j” Step 4: Develop the Others-to-Worst vector by determining preference for all others over the worst, using a 1–9 scale. (AW = a1W , a2W , ..., anW )T where, ajW signifies the preference of attribute “j” with the “W” worst attribute. Step 5: Compute the optimal weights. To find the optimal weight of  constraints and  KPIs, we minimize the maximum  among the set of wB − aBj wj , wj − ajW wW  . The problem can be represented as     min max wB − aBj wj , wj − ajW wW  j

s.t.



wj = 1

j

wj ≥ 0, for all j

(1)

Model 1 can be transferred as: minξ L s.t.  wB − aBj wj  ≤ ξ L , for all j   wj − ajW wW  ≤ ξ L , for all j  wj = 1

(2)

j

wj ≥ 0, for all j Solving model 2, the optimal weights (w1∗ , w2∗ , ..., wn∗ ) and optimal ξ L∗ value are computed. ξ L∗ ∈ [0, 1]. The value of ξ L∗ closer to 0 shows a high consistency [20]. The optimal weights for the constraints and KPIs are computed using BWM. 3.2 Computing Consistency Ratio A comparison vectors are fully consistent if aBj × ajW = aBW , for all j, where aBj , ajW and aBW are respectively the preference of the best attribute over the jth attribute, the preference of attribute j over the worst attribute, and the preference of the best over the worst attribute. However, some of the j in the calculation may not be fully consistent due to certain vagueness in judgment. Thus, a consistency ratio (CR) is calculated to determine how much comparison is consistent.

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The input-based consistency ratio CRI method proposed by Liang et al. [24] is used to calculate the consistency ratio. The Input-based Consistency Ratio CRI can be computed by following equations. CRI = max CRIj j

where,  CRIj

=

|aBj × (ajW − aBW | aBW × aBW − aBW

0

aBW > 1 aBW = 1

(3)

The local consistency level corresponds to a specific criterion Cj is given as CRIj . While CRI is the global or overall input-based consistency ratio for all the criteria under study, which can be the maximum value of CRIj . The reason for computing CR through input-based consistency measurement is due to its advantages [24] as – 1) provision of immediate feedback on the input preference, whether they are consistent or not; 2) easy interpretations; 3) can be effectively deployed in different BWM forms, e.g. a linear or nonlinear; 4) immediately determining the most inconsistent pairwise comparison. Liang et al. [24] further provided threshold values for input-based consistency ratio to check whether the judgment is consistent or not. Table 4 enlists the threshold values for the input-based consistency ratio. Table 4. Threshold values for the input-based consistency ratio [24]. Scales

Criteria 3

4

5

6

7

8

9

3

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

4

0.1121

0.1529

0.1898

0.2206

0.2527

0.2577

0.2683

5

0.1354

0.1994

0.2306

0.2546

0.2716

0.2844

0.2960

6

0.1330

0.1990

0.2643

0.3044

0.3144

0.3221

0.3262

7

0.1294

0.2457

0.2819

0.3029

0.3144

0.3251

0.3403

8

0.1309

0.2521

0.2958

0.3154

0.3408

0.3620

0.3657

9

0.1359

0.2681

0.3062

0.3337

0.3517

0.3620

0.3662

4 Results and Discussion As discussed, 9 constraints are identified to implement TOC’s outbound supply chain solution and the 9 KPIs of distributors that can be improved by overcoming these constraints. Experts provided their preferences on the best and the worst constraints and KPIs as instructed in steps 3 and 4 using a 1–9 scale to formulate best-to-others and

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others-to-worst vectors. We used the consensus method for the development of the pairwise comparison. This helped us gain the experts’ overall preference by conducting brainstorming sessions over the data generation and identifying critical constraints and KPIs within the outbound supply chain. Tables 5 and 6 present experts’ opinions on best-to-other vectors and others-to-worst vectors for constraints, while Tables 7 and 8 represent experts’ opinions corresponding to KPIs. Table 5. Constraints: Experts’ opinions on Best-to-Others. Best constraint

Other constraints

C5

C1

C2

C3

C4

C5

C6

C7

C8

C9

8

3

7

6

1

4

5

4

2

Table 6. Constraints: Experts’ opinions on Others-to-worst. Other constraints

Worst constraint - C1

C1

1

C2

3

C3

2

C4

3

C5

8

C6

4

C7

5

C8

5

C9

7

Table 7. Distributor’s KPI: Experts’ opinions on Best-to-Others. Best KPI K1

Other KPIs K1

K2

K3

K4

K5

K6

K7

K8

K9

1

3

3

4

3

3

8

5

3

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C. Chaudhari et al. Table 8. Distributor’s KPI: Experts’ opinions on Others-to-worst. Other KPIs

Worst KPI - K7

K1

8

K2

6

K3

7

K4

5

K5

6

K6

7

K7

1

K8

4

K9

4

The judgments over best and worst pairwise comparisons for constraints and KPIs, as shown in Tables 5, 6, 7 and 8, are subjected to the input-based consistency ratio to check the consistency of the experts’ opinions. In terms of constraint, the best constraint is C5, while the worst is C1 (See Tables 5 and 6). Refer Table 9 for consistency ratio calculations. The value of aBW is 8. Now using Eq. 3, we evaluated the value of CRIj . Table 9 depicts that the global or overall CRI is 0.304. From Table 4, the threshold value for 9 criteria (in this study, 9 constraints) and for the 8-scale is found as 0.3657. Thus the CRI = 0.304 < 0.3657. This depicts that the judgments are within the threshold and consistent in terms of constraints. A similar procedure is used to check the consistency for KPIs pairwise comparisons given in Tables 7 and 8. The input-based consistency ratio calculations for KPIs are given in Table 10. The best and worst KPIs are K1 and K7. The aBW is 8 for KPIs. The value computed for the global or overall CRI is 0.232 using Eq. 3 as shown in Table 10. The threshold value for 9 KPIs and 8-scale is found as 0.3657. The computed CRI = 0.232 < 0.3657, which signifies the consistency of the judgments of KPIs pairwise comparison vectors. Table 9. Input-based consistency ratio of each constraint. Constraints

C1

C2

C3

C4

C5

C6

C7

C8

C9

Best – C5

8

3

7

6

1

4

5

4

2

Worst - C1

1

3

2

3

8

4

5

5

7

CRIj

0.000

0.018

0.107

0.179

0.000

0.143

0.304

0.214

0.107

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Table 10. Input-based consistency ratio of each KPI. Constraints

K1

K2

K3

K4

K5

K6

K7

K8

K9

Best – K1

1

3

3

4

3

3

8

5

3

Worst – K7

8

6

7

5

6

7

1

4

4

CRIj

0.000

0.179

0.232

0.214

0.179

0.232

0.000

0.214

0.071

After computing the consistency, the weights of constraints and KPIs are computed using a BWM model. Tables 11 and 12 provide the weight vectors for constraints and KPIs, respectively. Based on the weights, the constraints and KPIs are prioritized, as shown in Tables 11 and 12. It is observed that ‘Fear in mind of the distributor that my data may be misused (C5)’ is the most critical constraint to implement TOC’s solution for the outbound supply chain, and ‘Return on investment (C1)’ is the most critical KPI for the distributors. The most important inputs for TOC’s solution for the outbound supply chain are daily inventory and sale’s data from the distributors. Since distributors fear that the organizations may misuse their data, they are not sharing data with the organization on a regular basis. This results in the non-frequent replenishment from the organization to the distributors, which in turn restricts the implementation of TOC’s solution in the outbound supply chain. If the organizations can overcome this most critical constraint, they shall be able to ssuccessfully implement TOC’s solution in the outbound supply chain. If organizations succeed in implementing the TOC solution in the outbound supply chain, they can impact the most critical KPI of the distributor, “Return on Investment” by reducing the investment in inventories and improving the sales due to better availability of the products. This is possible due to frequent replenishment and a colour-based priority Table 11. Weights of constraints to implement TOC solution in the outbound supply chain.

Constraint

Weight

Priority

C1 C2 C3 C4 C5 C6 C7 C8 C9

0.028 0.122 0.052 0.061 0.297 0.092 0.073 0.092 0.183

9 3 8 7 1 5 6 4 2

0.069

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mechanism on the basis of daily inventory and sale data shared by the distributors with the organization. Table 12. Weights of distributors’ KPIs.

KPI

Weight

Priority

K1 K2 K3 K4 K5 K6 K7 K8 K9

0.268 0.111 0.111 0.083 0.111 0.111 0.025 0.067 0.111 0.066

1 3 4 7 6 5 9 8 2

5 Conclusion This study is developed to understand the critical constraints that prevent organizations from implementing TOC solutions in the outbound supply chain. Through an extensive literature review and experts’ interviews, crucial constraints to implement TOC’s solution in the outbound supply chain and KPIs of distributors are identified. This is followed by implementing the Best-Worst method for determining the most critical constraints and KPIs by prioritizing them. From the results of this study, the “Fear in mind of the distributor that my data may be misused” is evaluated as a critical constraint to TOC’s solution in the outbound supply chain. On the other hand, the “Return on investment” is considered as a critical KPI of the distributors that can be improvised through the implementation of TOC’s solution in the outbound supply chain. Resolving the critical constraint, i.e. “Fear in mind of the distributor that my data may be misused”, organizations can receive daily inventory and sales data from their distributors, enabling faster and more frequent replenishment from the organizations’ warehouses to the distributors. This translates to an increase in the sale of distributors due to higher availability of the products and reduced inventories. Thus “Return on Investment”, the critical KPI of the distributor, is improved significantly. This is one of the primitive studies to highlight the application of BWM in improving the effectiveness of the TOC application in the outbound supply chain. Researchers working in the TOC domain across the globe can get unique insights through this study by understanding the highly prioritized constraints and KPIs related to TOC implementation in the outbound supply chain. While practitioners can consider the identified constraints

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priority to overcome them by using suitable TOC solutions, viz., thinking process, unrefusable offers etc., and enhance the critical KPIs for the distributors.

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Evaluating and Ranking the Supplier Selection Criteria for Additive Manufacturing Firms Using Best-Worst Method Priya Ambilkar(B)

, Priyanka Verma , and Debabrata Das

National Institute of Industrial Engineering, Mumbai, India {Priya.Ambilkar.2017,priyankaverma,debabrata.das}@nitie.ac.in

Abstract. Additive manufacturing (AM) is a well-known technology applied in different industrial applications which have gained more attention over the last three decades. The crucial aspect of AM is designing and managing the supply chain for AM parts. The most critical strategic decision in the initial process of supply chain management is selecting and evaluating suppliers. Selecting an appropriate supplier can lead to reducing costs in supply chain management. Therefore, there is a need to choose a reliable supplier to enhance the performance of their supply network. For the first-time, supplier selection criteria evaluation for the AM domain is examined in this study. This study proposes multi-criteria decision-making based on the best-worst methods to prioritize AM firm’s raw material supplier selection criteria. The best-worst method is generally applied to get the criteria weight. The reliability of the comparisons is checked using a consistency ratio. Then the most important and least important criteria are obtained and considered while selecting a supplier in AM based on the result. Finally, the study concluded the importance of supplier selection for AM. This study further provides a promising avenue for future research opportunities. Keywords: Additive manufacturing · Supply chain Management · Supplier evaluation · Best-worst method (BWM)

1 Introduction Over the decades, many technologies transitioned from analog to digital processes. One example of this transitioned technology is additive manufacturing, which recently grabbed much attention over conventional manufacturing. Additive manufacturing is defined as “the process of joining materials to make objects from 3D model data, usually layer upon layer, instead of subtractive manufacturing methodologies, such as traditional machining” [1]. It is also known as 3D printing, additive fabrication, additive processes, layer manufacturing, rapid manufacturing, rapid prototyping, rapid tooling, direct digital manufacturing, and solid freeform fabrication [2]. The first working 3D printing machine was developed by Charles Hull in 1984 and named as Stereo Lithography apparatus [3]. Additive Manufacturing (AM) produces complex geometries and unique structures and manufactures parts layer-by-layer (addition of material). In the AM, the raw material © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, pp. 161–175, 2023. https://doi.org/10.1007/978-3-031-24816-0_13

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consumption is less, and wastage of material is minimal, which reduces lead time and cost [4, 5]. AM is considered one of the powerful tools to gain competitive advantages over worldwide firms. According to a 2020 report by Research and Markets, “the global AM market revenue accounted for USD 12 Billion in 2020, and it is expected to reach around USD 78 Billion by the year 2028” [6]. Therefore, AM has drawn a tremendous interest in industrial applications and academic research worldwide in the recent decade. The disruptive improvisation through AM causes organizations to emerge the new managerial approaches for re-examining and developing the opportunities that aid in shrinking the entire supply chain [7]. This can only be achieved by managing AM effectively and aligning it with the supply chain [8]. Thus, it is essential to effectively design a supply chain according to AM. To do so, the first step is determining the appropriate supplier “who can provide high-quality products, flexible operations, and systems, maintain close relations and contribute to the product design operations” [9]. Therefore, selecting reliable and suitable suppliers becomes the most crucial strategic operation in AM to ensure the smooth functioning of the entire supply chain. The paper aimed to shed light on the supplier evaluation process in the AM to enhance the supply chain performance. To the author’s knowledge, no work focuses on AM supplier selection in the existing body of knowledge [10]. Hereafter, Sect. 2 introduces an overview of the supplier selection and BWM literature. Section 3 explained the applied research methodology. Where Sect. 4 is enlisted with results and discussion. Finally, Sect. 5 contains the concluding remarks.

2 Literature Review The BWM is based on a pairwise comparison between the best and worst criteria with the rest of the criteria [11]. In this method, decision-makers have to determine the best and worst criteria by the pairwise comparison of two vectors. The BWM shows reliable results in many fields such as green practices and innovation, logistics performance measurements, research and development performance measurement, and supplier selection. Some studies on BWM are summarized in Table 1. An extensive literature has been done on the supplier evaluation and selection topic in different domains. Various evaluation criteria (traditional, green, sustainable, and resilient) and methods are applied to supplier evaluation problems. This section provides a literature review to identify several factors considered while selecting the supplier. Steps of BWM. The five steps of BWM to derive the criteria weights are as follows [11, 13]: Step 1: Determine a set of decision criteria. In this step, identifying n criteria (c1 , c2 , ...., cn ) those are considered in making a decision. In this case, the identified criteria are c1 , c2 , ...., c9 for supplier evaluation. Step 2: Determine the best and the worst criteria. In this step, the decision-maker identifies the best criteria (most desired or most significant) and worst criteria (least desired or least significant in general). No comparison is made at this stage.

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Step 3: Determine preference of best criterion over all the other criteria, using 1–9 numbers. The resultant Best-to-Others vector as: AB = (aB1 , aB2 , ..., aBn ) where, aBj signifies the preference of the best criterion B over criterion j. It is clear that aBB = 1. Table 3 summarizes various criteria derived through extensive literature review and expert opinion in supplier evaluation. The hierarchy represents supplier selection criteria for AM and is shown in Fig. 1. 2.1 Gap in the Literature The existing body of knowledge about AM is mainly focused on process, material, and design research. There are very few studies explicitly highlighting the topics like process cost, throughput, repeatability, multi-material AM, raw material range, cost and design, and topological optimization for performance. No study has been reported highlighting the decision-making problem of supplier evaluation in AM. To fill this gap in the research, the current study evaluates and ranks the raw material supplier selection criteria for AM firms. Table 1. Earlier studies on BWM and their contributions Study

Novelty

Industry

Contributions

Rezaei [11]

Method

–

BWM is proposed for the first time through the literature

Wan et al. [12]

Case

Oil and Gas

BWM is applied to sustainable supplier selection

Rezaei [13]

Case

Food

BWM is used in to determine the best suppliers among its competitors

Kheybari et al. [14]

Case

Energy

The BWM method was used to find the most suitable location for the bioethanol plant

Kaviani et al. [15]

Case

Automotive

The BWM method was used to determine the importance of barriers

Seyfi-Shishavan et al. [16]

Case

Banking

FBWM is used to determine the critical factors’ weights and performance index

Dalalah et al. [17]

Case

Wood

BWM is used to identify critical factors that stand as a barrier between manufacturing and environmental sustainability

Hosseini et al. [18]

Case

Technology

BWM is used to evaluate the criteria for implementing blockchain technology in the SC

(continued)

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P. Ambilkar et al. Table 1. (continued)

Study

Novelty

Industry

Contributions

Fallah et al. [19]

Case

Electronic

BWM is used to evaluate the criteria for supplier selection

Wu et al. [20]

Case

Hotel

BWM is used to evaluate the criteria based on online reviews for satisfactory hotel selection

Shang et al. [21]

Case

–

BWM is used to evaluate the criteria to rank alternative suppliers for sustainable supply chains

3 Methodology This section introduces the methodology deployed in this study for solving the supplier selection problem in AM. The BWM approach is used to solve supplier selection problems. The BWM approach structure is shown in Fig. 2, shadowed by the related detailed description. This study employed five experts from AM firms to validate the criteria (See Steps of BWM. The five steps of BWM to derive the criteria weights are as follows [11, 13]: Step 1: Determine a set of decision criteria. In this step, identifying n criteria (c1 , c2 , ...., cn ) those are considered in making a decision. In this case, the identified criteria are c1 , c2 , ...., c9 for supplier evaluation. Step 2: Determine the best and the worst criteria. In this step, the decision-maker identifies the best criteria (most desired or most significant) and worst criteria (least desired or least significant in general). No comparison is made at this stage. Step 3: Determine preference of best criterion over all the other criteria, using 1–9 numbers. The resultant Best-to-Others vector as: AB = (aB1 , aB2 , ..., aBn ) where, aBj signifies the preference of the best criterion B over criterion j. It is clear that aBB = 1. Table 3 3) and conduct the BWM process. The experts were requested to vote on the criteria evaluation for supplier selection. A decision team of 5 experts with in-depth knowledge of the field and more than ten years’ work experience are invited. The details of the experts, along with their designation, are shown in Table 2. 3.1 Best-Worst Method (BWM) Best-worst method is a multi-criteria decision making (MCDM) method [11], which evaluates the best criterion over other criteria. Also, comparing all the other criteria over the worst criterion [22]. This method requires less information and conducts consistent comparisons. This method creates a comparison system comprised of Best-to-Others and

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Others-to-Worst vectors. The objective is to get the optimal weights and consistency ratio (CR). This process uses a simple optimization model. Due to its advantages compared to other weighting methods, this method has recently drawn the attention of researchers and the latest studies concerning the development.

Cost Quality Delivery Service Additive manufacturing supplier evaluation criteria

Trust Lead Time Financial Performance Overall Reputation Technology Capability

Fig. 1. Hierarchical representation for AM raw material supplier selection criteria.

Table 2. Experts profile # Experts Background Affiliation

Years of experience Educational qualification

1

Industry

AM Technology Developer

25

2

Industry

AM Engineer

15

3

Industry

AM Technical Manager

14

4

Industry

Application Specialist Metal AM

14

5

Industry

Product Manager- 12 Plastic & Metal 3D Printing

postgraduate Doctorate ✔ ✔ ✔ ✔

✔

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3.2 Steps of BWM The five steps of BWM to derive the criteria weights are as follows [11, 13]: Step 1: Determine a set of decision criteria. In this step, identifying n criteria (c1 , c2 , ...., cn ) those are considered in making a decision. In this case, the identified criteria are c1 , c2 , ...., c9 for supplier evaluation. Step 2: Determine the best and the worst criteria. In this step, the decision-maker identifies the best criteria (most desired or most significant) and worst criteria (least desired or least significant in general). No comparison is made at this stage. Step 3: Determine preference of best criterion over all the other criteria, using 1–9 numbers. The resultant Best-to-Others vector as: AB = (aB1 , aB2 , ..., aBn ) where, aBj signifies the preference of the best criterion B over criterion j. It is clear that aBB = 1. Table 3. Criteria considered in the supplier selection process for AM firms. Code

Criteria

Short description

Reference

C1

Cost

Cost related to order, logistics, transportation, etc.

[23–30]

C2

Quality

Performance of products to meet the expectations

[23–29, 31]

C3

Delivery

Delivery punctuality capability

[23–25, 27, 28, 31]

C4

Service

Ability to provide capacity, repair services

[24–26, 28, 29]

C5

Trust

Ability to maintain long-term relationship

[23, 26, 27, 31]

C6

Lead time

Time spent from order to delivery

[23, 29–31]

C7

Financial performance

Ability to gain desired collection and allocation of financial measures

[28, 29, 32]

C8

Overall reputation

Reputation among its various stakeholders

[23, 26, 31, 32]

C9

Technology capability

Ability to undertake leading edge innovation and technical changes

[23, 26–29]

Evaluating and Ranking the Supplier Selection Criteria

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Identifying various supplier selection criteria through existing literature and experts

Obtain the best and worst criteria

Compare "Best" criterion over others criteria and creating the "Best-to-Others" vector

Compare "Worst" criterion over others criteria and creating the "Others-to-Worst" vector

Calculate consistency ratio

Calculate global weights of each criterion

Fig. 2. Structure of proposed research methodology.

Step 4: Determine preference for each of the other criteria over the worst criterion, using 1–9 numbers. The resultant Others-to-Worst vector would be: (AW = a1W , a2W , ..., anW )T where, ajW signifies the preference of criterion j with the W worst criterion. It is clear that aWW = 1. Step 5: Determine the optimal weights. The optimal weight for the criteria is the one where, for each pair of wB /wj and wj /wW , we have wj /wW = ajW and w  B /wj= aBj . To find  the criteria’s optimal weight,  Wj  B   and maximum absolute value  W − a − a  WW Bj  jW  differences for all j have to be Wj minimized.      wB   wj  min max  − aBj ,  − ajW  j wj wW s.t.



wj = 1

j

wj ≥ 0, for all j

(1)

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P. Ambilkar et al.

The model 1can be transferred into the linear programming formulation: minξ s.t.    wB     w − aBj  ≤ ξ, for all j j    wj     w − ajW  ≤ ξ, for all j W  wj = 1

(2)

j

wj ≥ 0, for all j Model 2 provides an optimal solution for the linear problem. Computing model 2, the optimal weights (w1∗ , w2∗ , ..., wn∗ ) are evaluated to gain optimal ξ ∗ value. ξ ∗ represents the consistency ratio (CR) of the comparison system. CR ∈ [0, 1], ξ ∗ close to 0 values show high consistency [11]. We are obtaining the criteria’s optimal weights wj∗ using BWM. 3.3 Consistency Measurement The consistency ratio proposed in the original BWM [11, 13] can only be obtained after the entire elicitation process has finished. It cannot provide a decision-maker with instant feedback involving his/her consistency. To overcome this problem and provide a decision-maker with an instant and robust idea of his/her consistency level, we propose an input-based consistency measurement method proposed by Liang et al. [33] for BWM is easy to compute and has clear and simple algebraic meaning and interpretation. Following the original index, the new inconsistency index proposed in the following section only attains value 1 when given aBW , t here exists a Cj such that aBj = ajw = aBW . This is possible because the index considers the maximum violation of local inconsistencies and the value 1 can actually be attained. With the input-based consistency ratio, one can immediately indicate a decisionmaker’s consistency level by using his/her provided input, i.e., his/her preferences, instead of going through the entire optimization process. This study implements this method to measure consistency. The Input-based Consistency Ratio (CRI ) is formulated as follows: CRI = max CRIj j

where,

 CRIj

=

|aBj ×ajw −aBW | aBW ×aBW −aBW 0

aBW > 1 aBW = 1

(3)

(4)

CRI is the global input-based consistency ratio for all criteria, CRIj represents the local consistency level associated with a criterion Cj .

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The input-based consistency measurement has advantages over other consistency measurement methods like – 1) It can provide immediate feedback, 2) It is easy to interpret, 3) It can provide a decision-maker with a clear guideline on the revision of the inconsistent judgement, 4) It is model-independent [33]. The inconsistent judgement can be easily identified by using the consistency measurements. However, the degree to which inconsistency can be accepted has far been lacking in the study of BWM. To bridge this gap, a threshold has to be defined. For the input-based consistency ratio, Liang et al. [33] developed an algorithm to establish the thresholds for BWM. Table 4 obtained the consistency thresholds for combinations which range from 3 to 9 criteria, with the highest evaluation grades from 3 to 9 based on the input-based consistency measurement [33]. Table 4. Thresholds values for input-based consistency measurement Criteria Scales

3

4

5

6

7

8

9

3

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

0.1667

4

0.1121

0.1529

0.1898

0.2206

0.2527

0.2577

0.2683

5

0.1354

0.1994

0.2306

0.2546

0.2716

0.2844

0.2960

6

0.1330

0.1990

0.2643

0.3044

0.3144

0.3221

0.3262

7

0.1294

0.2457

0.2819

0.3029

0.3144

0.3251

0.3403

8

0.1309

0.2521

0.2958

0.3154

0.3408

0.3620

0.3657

9

0.1359

0.2681

0.3062

0.3337

0.3517

0.3620

0.3662

4 Results and Discussion The results are enlisted in this section briefly. We have followed the five-step BWM to get the criteria weights. The decision criteria set (see Steps of BWM. The five steps of BWM to derive the criteria weights are as follows [11, 13]: Step 1: Determine a set of decision criteria. In this step, identifying n criteria (c1 , c2 , ...., cn ) those are considered in making a decision. In this case, the identified criteria are c1 , c2 , ...., c9 for supplier evaluation. Step 2: Determine the best and the worst criteria. In this step, the decision-maker identifies the best criteria (most desired or most significant) and worst criteria (least desired or least significant in general). No comparison is made at this stage. Step 3: Determine preference of best criterion over all the other criteria, using 1–9 numbers. The resultant Best-to-Others vector as: AB = (aB1 , aB2 , ..., aBn )

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where, aBj signifies the preference of the best criterion B over criterion j. It is clear that aBB = 1. Table 3 is determined with the help of existing literature and experts. Then we have determined the best criteria and the worst criteria for supplier selection in the AM domain according to the respondent’s viewpoint. Five respondents from different AMbased companies are requested to share their preferences on criteria. Each respondent’s response to the best and worst criteria is enlisted in Table 5. Table 5. Expert’s response on criteria preference. Criterion

‘Best’ criterion

‘Worst’ criterion

C1 C2

1,2,5

C3

4

C4 C5

3

C6

3

C7

1,4,5

C8

2

C9

While following the third step, we asked experts to give preferences for the best criterion with all the other criteria using 1–9 numbers. Table 6 shows the Best-to-Others vectors. Table 6. Expert’s response on best-to-others vector. Best criterion

C1

C2

C3

C4

C5

C6

C7

C8

C9

Exp. 1

C2

2

1

4

6

7

3

9

8

5

Exp. 2

C2

2

1

3

7

8

5

6

9

4

Exp. 3

C6

5

2

3

6

8

1

9

7

4

Exp. 4

C3

4

2

1

5

7

6

9

8

3

Exp. 5

C2

2

1

3

6

7

5

8

9

4

After this, we also asked experts to prioritize all criteria with the worst criterion, again using 1 to 9 numbers. The Others-to-Worst vector is shown in Table 7. Finally, we determined each criteria’s weights using a non-linear programming model of BWM shown in model 1 and 2 for the five different participants. Then the geometric mean normalization method is used to aggregate the five decision-makers’ responses. Each criterion’s weight and the result are shown in Table 9.

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Table 7. Expert’s response on the others-to-worst vector. Exp. 1

Exp. 2

Exp. 3

Exp. 4

Exp. 5

Worst criterion

C7

C8

C5

C7

C7

C1

8

8

9

9

8

C2

9

9

8

8

9

C3

6

4

4

5

4

C4

4

3

5

4

5

C5

3

5

1

2

3

C6

7

7

6

7

7

C7

1

2

3

1

1

C8

2

1

2

3

2

C9

5

6

7

6

6

Once all the judgements from the five experts are gathered, the input-based consistency ratio is calculated. For the same, an example of expert 1 is explained here. In the case of expert 1’s opinion, the best criterion is quality (C2 ), and the worst criterion is Financial Performance (C7 ) (See Table 6 and Table 7). The value of aBW is 9. Now using model 3, we computed the value of CRIj as mentioned in Table 8. The global or overall CRI is determined 0.2222. The threshold value for 9 criteria and for 9-scale is found as 0.3662. Thus the CRI − 0.2222 < 0.3662. This describes that the judgment given by decision-makers is consistent. Correspondingly, the same procedure has been carried out to check the consistency of other experts. It is observed that all the judgements from every expert is consistent. Table 8. Input-based consistency ratio for Expert 1 Expert 1

C1

C2

C3

C4

C5

C6

C7

C8

C9

Best (C2)

2

1

4

6

7

3

9

8

5

Worst (C7)

8

9

6

4

3

7

1

2

5

0.0972

0

0.2083

0.2083

0.1667

0.1667

0

0.0972

0.2222

After calculating the consistency ratio, the weight of each criterion is evaluated using a BWM model for five decision-makers. This results in obtaining five weight vectors. Lastly, the five weight vectors are aggregated using a geometric mean method followed by the normalization. Table 9 illustrates the five decision-makers’ weight vectors and the aggregated weight, w1∗ = 0.154; w2∗ = 0.265; w3∗ = 0.153, respectively till w9∗ = 0.103 and ξ ∗ = 0.102. Based on the aggregated weights, the supplier selection criteria are

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ranked in Table 9. Quality is ranked at the top. The weight of each criterion is calculated using the BWM and represented in Fig. 3 Table 9. Calculated overall weights from five experts’ responses. # criteria

C1 C2 C3 C4 C5 C6 C7

Criteria Cost Quality Delivery Service Trust Lead Time Financial Performance Overall Reputation Technology Capability ( ∗)

C8 C9

Exp. 1 0.192 0.315 0.096 0.064 0.055 0.128

Exp. 2 0.196 0.303 0.131 0.056 0.049 0.078

Weights Exp. Exp. 3 4 0.082 0.102 0.205 0.204 0.137 0.271 0.068 0.082 0.024 0.058 0.277 0.068

Exp. 5 0.198 0.299 0.132 0.066 0.057 0.079

0.152 0.274 0.151 0.070 0.049 0.114

2 1 3 6 7 4

0.027

0.065

0.046

0.027

0.025

0.037

9

0.048

0.024

0.059

0.051

0.044

0.046

8

0.077

0.098

0.103

0.136

0.099

0.106

5

0.068

0.089

0.133

0.138

0.097

0.102

Agg.

Rank

Supplier selection criteria

Fig. 3. Supplier selection criteria weights

0.103

0.045

0.038

0.126 0.049

0.067

0.153

0.265

0.300 0.250 0.200 0.150 0.100 0.050 0.000

0.154

Weights

Finally, it is observed from Fig. 3 and Table 9 that quality, cost, and delivery are the most important criteria for the AM raw material supplier selection. As complex geometrical components can be produced through AM, the customer’s prerequisite for such components is the highest quality. Thus, the raw material for producing such parts needs to be up to standard to offer such high-quality components. Also, the components can be manufactured faster than the traditional manufacturing way through AM technology. For the same, the required raw material delivery needs to be delivered quickly to the AM firms.

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5 Conclusion AM offers terrific potential for companies to accomplish competitiveness in the market. Supplier selection is the supply chain’s initial task, significantly influencing supply chain performance. A practical approach for evaluating supplier selection criteria in the AM domain is presented in this paper for the first time. In this study, the criteria weights are obtained by applying MCDM based BWM. By applying BWM, we identify the significant criteria and then criteria were ranked based on criteria weights. We identified that quality, cost, and delivery are the best criteria for supplier selection for AM firms, whereas the least significant criterion is Financial Performance. Compared to other MCDM techniques, BWM has numerous advantages, such as very structured pairwise comparison and trustworthy outcomes. Additionally, the pairwise comparison time in BWM is comparatively lesser than other MCDM techniques. Thus, BWM can be effectively used as a subjective evaluation technique for weighting decision factors for MCDM problems. This study focused on the limited supplier evaluation criteria, whereas future studies can consider green, sustainable, and resilient criteria for AM firms using different methodologies.

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Author Index

A Akarte, Milind, 117 Ambilkar, Priya, 161 Arman, Kevser, 103 Athanasiou, Georgios, 74

K Kazemi, Mostafa, 59 Khanzode, Vivek, 146 Konurhan, Zekeriya, 87 Kundakcı, Nilsen, 103

B Boutris, Georgios, 129 Brunelli, Matteo, 33

L Labella, Álvaro, 48

C Chaudhari, Chandrashekhar, 146 D Das, Debabrata, 161 Dohale, Vishwas, 117, 146 E Eligüzel, ˙Ibrahim Miraç, 19

M Martínez, Luis, 48 Mohammadi, Majid, 41 O Özceylan, Eren, 19 R Rezaei, Jafar, 41 Rodríguez, Rosa M., 48

G García-Zamora, Diego, 48 Goldani, Nastaran, 59 Gul, Muhammet, 87 Gulum Tas, Pelin, 1

S Salimi, Negin, 129

I Iqbal, Rauf, 146

Y Yucesan, Melih, 87

V Verma, Priyanka, 117, 161

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Rezaei et al. (Eds.): BWM 2022, LNOR, p. 177, 2023. https://doi.org/10.1007/978-3-031-24816-0