2nd conference on Production and Industrial Engineering - CPIE 2010 9781781903865, 9781781903858

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05/10/2012

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ISSN 1741-038X

Volume 23 Number 7 2012

Journal of

Manufacturing Technology Management Special Issue on the 2nd Conference on Production and Industrial Engineering – CPIE 2010 Guest Editors: Dr Anish Sachdeva, Dr Vishal Sharma and Dr Arvind Bhardwaj

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Journal of Manufacturing Technology Management

ISSN 1741-038X Volume 23 Number 7 2012

Special issue on the 2nd Conference on Production and Industrial Engineering – CPIE 2010 Guest Editors Dr Anish Sachdeva, Dr Vishal Sharma and Dr Arvind Bhardwaj

Access this journal online __________________________ 831

CONTENTS

Editorial review board _____________________________ 832 Guest editorial ____________________________________ 833 SCRIS: a knowledge-based system tool for assisting manufacturing organizations in identifying supply chain risks Berman Kayis and Putu Dana Karningsih ___________________________

834

Three-stage supply chain allocation with fixed cost Vinay V. Panicker, R. Sridharan and B. Ebenezer _____________________

853

An integrated vendor-buyer inventory model with partial backordering Fateh Moshrefi and Mohammad Reza Akbari Jokar ___________________

869

An approach to analyze logistic outsourcing problem in medium-scale organization by CFPR and VIKOR Raman Kumar, Harwinder Singh and J.S. Dureja _____________________

885

Selection of logistic service provider using fuzzy PROMETHEE for a cement industry Rajesh Gupta, Anish Sachdeva and Arvind Bhardwaj __________________

899

Determining the parameters of MSG algorithm for multi period layout problem Berna Ulutas and Tugba Sarac¸ ____________________________________

922 This journal is a member of and subscribes to the principles of the Committee on Publication Ethics

CONTENTS continued

A genetic algorithm-based approach for job shop scheduling Rakesh Kumar Phanden, Ajai Jain and Rajiv Verma __________________

937

Factorial analysis of lifting task to determine the effect of different parameters and interactions Sarbjeet Singh and Sunand Kumar_________________________________

947

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EDITORIAL REVIEW BOARD

Azmawani Abd Rahman University Putra Malaysia, Malaysia

Doug Love Aston University, UK

Lynne Baxter University of York, UK

Douglas Macbeth University of Southampton, UK

Nourredine Boubekri University of North Texas, USA

Bart MacCarthy University of Nottingham, UK

Felix Chan The Hong Kong Polytechnic University, Hong Kong

Shunji Mohri Hokkaido University, Japan

Marly Monteiro de Carvalho Universidade de Sa˜o Paulo, Brazil

Andrew Neely University of Cambridge, UK

Ian Gibson National University of Singapore, Singapore

Adegoke Oke Arizona State University, USA

Angappa Gunasekaran University of Massachusetts Dartmouth, USA Jinsheng He Tianjin University, People’s Republic of China Abdel-Aziz Hegazy Helwan University, Egypt Robert Hollier University of Manchester, UK Tarek Khalil Nile University, Egypt Ashok Kochhar Aston University, UK

Kulwant Pawar University of Nottingham, UK Roy Snaddon Polytechnic of Namibia, Namibia Amrik Sohal Monash University, Australia Harm-Jan Steenhuis Eastern Washington University, USA Mile´ Terziovski University of South Australia, Australia Juite Wang National Chung Hsing University, Taiwan

Siau Ching Lenny Koh University of Sheffield, UK Hermann Ku¨hnle Otto-von-Guericke-Universita¨t Magdeburg, Germany

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 p. 832 # Emerald Group Publishing Limited 1741-038X

Guest editorial This special issue consists of selected papers from the 2nd Conference on Production and Industrial Engineering (CPIE 2010). It is a detailed exposition of emerging operations management techniques that would help in enhancing organizational competitiveness. In the era of globalization and liberalization, there has been a tremendous pressure on the organisations to become competitive for their survival and growth. This endeavour would definitely signify the importance of operations management in making and enhancing organizations’ competitiveness. Today, the supply chain management (SCM) principle has been considered as the most effective operations management strategy to gain organizational competitiveness through the network of close collaboration and integration in terms of demand and supply. For a company to be competitive, its supply chain must be flexible, agile, cost-effective and responsive. Nowadays it is more common for companies to collaborate in a global context where each of them focuses on its core competency and outsource the rest. As a consequence, their success becomes increasingly dependent on how well they orchestrate the different aspects and the way they manage the external parties involved in the supply chain. Equally important for organisations’ to be competitive are their abilities to satisfy the customers’ needs, shorten production lead time and lower cost. However, any of these improvements is impossible without consideration of the employees’ comfort; so this aspect, i.e. human factor engineering has its own importance in making an organisation more productive and thus, more competitive. This special issue includes contributions from industry and academia, on trends and developments in supply chain management, layout planning, production scheduling and human factor engineering. The CPIE conference series, from which this special issue has been derived, was started by the Department of Industrial and Production Engineering, Dr B R Ambedkar National Institute of Technology Jalandhar (India), in March 2007. CPIE 2010 (December 3-5, 2010) is an achievement in terms of attracting renowned academicians/researchers, noted industry representatives and the delegates from countries like Canada, the UK, France, Australia, Iran, Egypt, Algeria, Bangladesh, Israel, Mauritius, Turkey and India. In all, about 200 papers were presented on various aspects of latest issues related to industrial and production engineering. The Editors would like to acknowledge Professor David Bennett, Editor in chief, Journal of Manufacturing Technology Management and Emerald Publishers for their tremendous professional support throughout the preparation of this special issue. Last but not the least we would like to express our gratitude towards all the authors for contributing their valuable articles. Finally, we would like to acknowledge the reviewers for their painstaking and time consuming effort in reviewing manuscripts and providing their thorough evaluations.

Guest editorial

833

Anish Sachdeva, Vishal Sharma and Arvind Bhardwaj Guest Editors Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 p. 833 q Emerald Group Publishing Limited 1741-038X

The current issue and full text archive of this journal is available at www.emeraldinsight.com/1741-038X.htm

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SCRIS A knowledge-based system tool for assisting manufacturing organizations in identifying supply chain risks Berman Kayis and Putu Dana Karningsih

Received 13 March 2011 Revised 16 November 2011 Accepted 23 November 2011

School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, Australia Abstract Purpose – Risk identification is the first and crucial step in supply chain risk management process. Due to the nature and complexity of supply chain networks of manufacturing organizations, risk identification nowadays has become more challenging. The purpose of this paper to present the development of a tool, called Supply Chain Risk Identification System (SCRIS), for assisting decision makers in identifying existing risks, and the interrelationship of risks in supply chain (SC) network, by considering different process strategies, namely make to stock (MTS), make to order (MTO) and engineering to order (ETO). Design/methodology/approach – SCRIS is developed using a knowledge-based system (KBS) approach. The knowledge is represented in ruled based form and written using CLIPS expert system language program. To ensure its feasibility, SCRIS is validated using real case studies in several manufacturing industries. Findings – Feedback gathered from organizations involved in validations processes imply the benefit of using SCRIS as a decision support tool in identifying SC risks. SCRIS also has additional positive role in supply chain risk management (SCRM) by promoting communication and collaboration between SC partners. Originality/value – SCRIS provides an extensive tool using KBS approach which covers hundreds of SC risk sub-factors, risk factors, and risk events, as well as mapping the interactions and considering different process strategies which have not been developed to date. A novel SC risks taxonomy is also proposed which encompasses broader issues in the SC network. Keywords Manufacturing industries, Supply chain management, Risk management, Deductive databases, Risk identification, Supply chain risk management, Knowledge based system Paper type Research paper

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 834-852 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267682

Introduction Supply chain risk management (SCRM) has become a focal attention for academia and practitioners during the last decade. Managing supply chain (SC) risks is essential to ensure proper measures are taken so that adverse consequences of SC disruptions could be avoided or minimized. Many incidents occur in SC and may lead to several financial, operational problems and even businesses discontinuity. For example, in 2000, Ericsson failed to fulfil its customer’s demand due to a blaze occurred in its key supplier. Ericsson suffered a major loss of about US$2.34 billion (Sheffi, 2005). Risks in SC occur due to lack of understanding of potential disturbances in today’s SC which are highly complex, geographically dispersed, and interdependent. Global trading practices, rapid technology development, and heavy focus on cost efficiency are the reasons behind this vastly intertwined network (Norrman and Lindroth, 2004; Waters, 2007; Oehmen et al., 2009; Marucheck et al., 2011).

In general, SCRM consists of identification, assessment, evaluation, and mitigation stages (Li and Hong, 2007; Tuncel and Alpan, 2010; Trkman and McCormack, 2009). Risk identification is not only the first step but also the crucial step in SCRM (Norrman and Lindroth, 2004; Manuj and Mentzer, 2008). Improper risk identification can misguide further steps of risk management. Thus, it is important to have a comprehensive understanding of most (if not all) potential risks in SC network. It could be attained by not only identifying risks but also recognizing interrelationships between several risks in the whole SC network. In addition, risks have several attributes (AS/NZS 4360, 2004) and most if not all of these attributes should also be acknowledged. Moreover, different manufacturing environments (e.g. process strategy) may lead to different activities and triggers different SC risks. Therefore, it should be considered when identifying risk too. Since the nature and characteristics of SC network today is highly complex and uncertain, it makes risk identification a very complicated task for decision makers. Identifying SC risks cannot only depend on personal “instinct” and knowledge (Turban et al., 2011). Therefore, a decision support tool that may assist decision makers in identifying SC risks is both very helpful and crucial. Various tools and techniques are available to assist risk identification. Brainstorming, flow chart, fish bone diagram, and fault tree are few examples of them. In spite of this, most of these tools are not specifically for identifying risks in SC network (Shi, 2004; Waters, 2007). Utilizing past experiences and lessons is a common approach for assisting risk management and identification (Kumar and Viswanadham, 2007). Knowledge based system (KBS) has the capability to assist decision makers by utilizing knowledge gathered through publications and lessons learned (Udin et al., 2006; Abdullah et al., 2006). It is a very well known approach for developing decision making tools in many areas including supply chain management (SCM). Despite a wide use of KBS, its application for supporting risk identification in SC network has not been developed in depth. There are vast numbers of studies available in area of SCRM and risk management. This invaluable knowledge need to be utilized to develop a KBS tool for supporting risk identification in SC networks. This research contributes in at least two areas to advance research in SCRM. First, it presents a development of a unique tool to support SC risk identification utilizing KBS approach. This tool is called supply chain risk identification system (SCRIS). Second, SCRIS covers the whole SC network and external SC environment whilst considering characteristics of product(s) they deliver. Additionally, SCRIS does not only provide the list of potential SC risks but also present the interrelationships between these risks. Next, SCRIS also incorporate identification of different SC risks due to different process strategies. It considers three common process strategies, namely: make to stock (MTS), make to order (MTO) and engineer to order (ETO). This paper is organized as follows. In the next three sections selected publications related to SCRM and KBS are presented. Then, it is followed by elaboration of SCRIS development and its validation using case studies in manufacturing industries. Supply chain risk management Today’s SC network operates in an ever more complex environment facing a greater challenge. Rapid technology development in information/communication technology and transportation allows more geographically dispersed suppliers, sub-contractors (offshore manufacturing/outsourcing) and marketplace. Reducing number of suppliers

Identifying supply chain risks 835

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and inventory levels are also becoming a popular practice to achieve more efficient operations. As a result, nowadays SC is a vastly intertwined network with high interdependency between its members and heavy reliance on communication and transportation system for synchronizing its supply and demand flow (Russell and Taylor III, 2009). Combination of this circumstance with uncertain external conditions (e.g. natural disasters, political instability, etc.) makes SC network becomes more susceptible to risks (Hauser, 2003; Gaonkar and Viswanadham, 2007; Khan and Burnes, 2007; Harland et al., 2003). Improper response to any scale of SC disruptions has proved to be fatal in term of financial loss or even business continuity. For example: Toyota suffers huge losses up to $5 billion, from global recall due to gas pedal and floor mat problems (Takahashi and Kachi, 2010). Moreover, SC disruption does not only affect to one individual organization but also the whole member of SC network. Thus, it is important to manage SC risks appropriately by following a systematic approach. According to Waters (2007), SCRM can be defined as “process of systematically identifying, analyzing, and dealing with risks to SC”. While, Chapman et al. (2002) incorporate scope of risks which are: internal and external to SC network and importance of SC members collaboration in managing SC risks. Several authors have proposed different steps to manage SC risks (Cucchiella and Gastaldi, 2006; Juttner et al., 2003; Zsidisin et al., 2000; Cranfield School of Management, 2003; Kiser and Cantrell, 2006; Li and Hong, 2007). In general, SCRM consists of four main steps which are: (1) Risk identification. Identifies potential risks and their sources through comprehensive understanding of SC internal and external conditions and all related activities. (2) Risk assessment. Determines the impact of the risks identified from the previous stage. (3) Risk evaluation. Determines the risk priorities according to their impact and predefined criteria (e.g. cost-benefit, resources availability, etc.). (4) Risk mitigation. Determines suitable action of dealing with risks. Risk identification in SC network Risk identification is the first and essential steps in SCRM. It should provide a comprehensive list of potential SC risks to enable decision makers in developing correct mitigation strategy (Waters, 2007; Hallikas et al., 2004). Furthermore, risk in SC should not be only identified as an isolated event since its interrelationships with other risks are important for understanding their impact on the entire SC network. However, there are fewer studies that consider SC risks interrelationships in their works (Table I). Furthermore, understanding of different manufacturing environment in an SC network is essential to identify potential SC risks. Activities in manufacturing organization vary depending on its manufacturing environments. In addition, process strategy is commonly utilized to represent different manufacturing environments. A particular process strategy dictates all activities which different SC risks. MTS, MTO, and ETO process strategies are widely applied by manufacturing organizations (SCOR, 2008; Cohen and Roussel, 2004). However, existing studies of SC risk identification have not considered yet the relations between different process strategies with potential SC risks.

Hauser (2003) Hallikas et al. (2002, 2004) Giunipero and Eltantawy (2004) Sinha et al. (2004) Christopher and Peck (2004), Juttner et al. (2003) Gaudenzi and Borghesi (2006) Brun et al. (2006) Kiser and Cantrell (2006) Wu et al. (2006) Cucchiella and Gastaldi (2006) Gaonkar and Viswanadham (2007) Li and Hong (2007) Pavlou and Manthou (2008) Micheli et al. (2008) Adhitya et al. (2009) Neiger et al. (2009) Luan et al. (2009) Trkman and McCormack (2009) Oke and Gopalakrishnan (2009) Tuncel and Alpan (2010)

Reference

Yes No No No No Yes Yes No No Yes Yes No No No No

Yes Yes No No No

SC risks interrelations

B B

B B

B

B B

B

B B

B

B B

B

B B B B B B B B B B

B B B

B B B B B

B B

B B

B B

B B B

Risk dimensions/attributes covered in the study Location Owner Time Source Consequences

B B

B B B B

B B

B B

B

B

B

B

B B B

B

B

B

B B B

B

B

B B

B B B

B B

B

B B

B

B B

B

B

Application area in the study Scope/focus in the study Specific Supply side Whole industry Generic only network

Identifying supply chain risks 837

Table I. Summary of selected SCRM literature

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Risk has various risk attributes, namely: source of risks, consequences of risks, time, location, and person/factor/activity that may involved (AS/NZS 4360, 2004). To ensure the comprehensiveness of risk identification process, this research takes into account all of these risk attributes. Table I presents summary of several selected studies in SCRM. As can be seen from this table, most of existing studies only consider some of risk attributes.

838 Knowledge based system KBS or expert system (ES) is a branch of artificial intelligent (AI). It is defined as a computer program combining of knowledge base and inference engine to provide problem-solving features which is designed to imitate expert capability (Leung et al., 1998; Akerkar and Sajja, 2010). KBS is mainly comprised of several components (Giarratano and Riley, 2005; Dym and Levitt, 1991; Metaxiotis, 2004), they are as follows: . Knowledge base is the main part of KBS and consists of factual knowledge (facts) and rules (heuristics). Knowledge could be represented in different forms, such as: rule based (production system), fuzzy logic, induction, case based reasoning, neural network and object oriented systems (Jackson, 1999; Leondes, 2002). . Inference engine makes decision/suggestion based on current facts in knowledge base by applying appropriate rules. There are two reasoning procedures that are commonly used. Forward reasoning/chaining and backward reasoning/chaining. Forward chaining is a data driven reasoning as it conclude “then” part when “if” part is given, while backward chaining is a goal driven method as it prove “then” part by confirming the presence of “if” part. . Working memory contains problem specific facts from consultation session with users and also stores the new facts by incorporating updated data generated by inference engine. . User interface is a means of communication (dialog) between KBS with user. There are three types of programming languages available to develop a KBS/ES, namely: conventional language, AI language and ES shell. ES shell provides an empty knowledge base. It also has built in inference capabilities and a user interface, while these are not provided by conventional and AI language. Moreover, a high skill programming is required to develop KBS using conventional and AI language (Turban et al., 2011). For that reason, ES shell is more popular programming language (Kaetzel and Clifton, 1995; Metaxiotis, 2004). KBS offers several advantages such as: improving decision accuracy in less time, preserving and storing tacit knowledge from experts/experienced staff, allowing easy access and sharing of knowledge (Abraham, 2005; Ramamoorthy et al., 1993). Due to these attractive benefits, KBS has been applied in many domains such as finance, manufacturing, management, construction, biotechnology, and military (Turban et al., 2011; Giarratano and Riley, 2005). In the SCM context, KBS approach was applied by Piramuthu (2005) to develop automated supply chain configurer (ASCC). ASCC suggests the appropriate SC configuration according to customer order specifications. Next, a knowledge-based simulation platform (KBSP) was suggested by Chan et al. (2006) which may assist decision makers/trainees in dealing with their suppliers and

retailers whilst applying vendor managed inventory (VMI) strategy. This system could simulate SC (suppliers, manufacturer and retailers) operations, and predict its performance. Another application of KBS is development of suppliers selection in automotive industries based on supplier’s performance evaluation by Yigin et al. (2007). Development of SCRIS SCRIS is developed using KBS approach which consists of five main stages (Figure 1) (Giarratano and Riley, 2005; Akerkar and Sajja, 2010). Next, each stage of SCRIS development is elaborated.

Identifying supply chain risks 839

1. Initial problem assessment At the first stage of SCRIS development, SCRIS task, scope and audience are determined. SCRIS task is to support risk identification of by providing list of potential SC risks and their interrelationships to its user(s). The list of SC risks is categorized following SCRIS structure, which will be explained next, so that all risk attributes can be displayed. SCRIS users are manufacturing companies who want to identify risks in their SC network in relation to one particular product (type) and the process strategy they use. Source of knowledge to develop SCRIS is gathered from extensive documented publications and reports. 2. Establish SCRIS structure The second stage of SCRIS development is comprised of three activities, they are given below. (a) Eliciting and structuring knowledge. Knowledge is gathered from vast literatures ( journals, articles and case studies) on SCM, SCRM, risk management and

Figure 1. The framework of SCRIS utilizing KB approach

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operations management. Then, this knowledge is structured by considering five risk attributes (risk source, consequences, owners, time and location). Combination of two sub structures (Hallikas et al., 2002; Tah and Carr, 2001) is used to develop SCRIS structure, they are: (1) Hierarchical structure, which represents time, location and risk owner attributes. This structure consists of three main levels, which are: . Level 0. To represents risk attribute “time”, five phases of SC operations from manufacturing organization point of view (SCOR, 2008) are adopted. These five phases are: Plan, Source, Make, Deliver and Return. . Level 1. To represents risk attribute “location”, different SC operations location (i.e. manufacturing organization, its SC partners and SC external environment) is adopted (Juttner et al., 2003). Every SC operations stages at level 0 are connected to SC operations locations in level 1. Accordingly, Plan, Source, Make, Deliver and Return stages are linked to focal organization, SC partners, and SC external environment. . Level 2. To represent risk attribute “person” or “factor”, different risk owners at each SC operations locations occurring at level 1 is applied. Risk owner covers six generic functional areas under manufacturing organization, three players under SC partners, and nine factors under SC external environment. The six generic functional areas are: operational, technical, organizational, communication, resource, and financial (Kayis et al., 2007). The three players/partners of SC, they are: suppliers, customers and logistics providers. The nine factors are: governmental, macroeconomic, socio-cultural, product complementary organization, competitor, other related organization, technology development, nature related conditions and accidents (Wu et al., 2006; Deleris et al., 2004; Chopra and Sodhi, 2004; Kara et al., 2008). (2) Causal structure, which represents risk attribute “risk source” and “risk consequence”. This structure is located under level 2 of hierarchical structure. It consists of risk events which represents “risk consequences”, and risk factors and risk sub factors as “risk sources”. There are several steps that should be carried out to organize the elicited knowledge into SCRIS hierarchical and causal structure, they are as follow: . Classify risks gathered from elicited knowledge according the hierarchical structure. . Arrange these risks into risk events, risk factors, and risk sub factors according to causal relations by developing relation to characteristics of manufacturing organization, SC partners, external SC network and considering different process strategies. . Establish interrelations between risk sub factors, risk factors and risk events within and across different levels of hierarchical structure. . Establish newly defined risk events, risk factors, and risk sub factors when required.

This process is carried out in several iterations using trial error. As a result, a SCRIS structure (Figure 2) is developed for representing each process strategies: MTS, MTO and ETO. (b) Selecting and translating to knowledge representation. SCRIS structure consists of causal interrelationships between risk sub factors, risk factors and risk events which are correspond to IF-THEN statements. Accordingly, rule based is selected as the knowledge representation. Forward chaining is then selected as inference method as it corresponds properly to causal interrelationships of SCRIS structure which depicts the occurrence of risk event (THEN part) as the result of the presence of one or more risk factors and risk sub factors (IF part). Moreover, forward chaining is also suitable to convert hierarchical structure of SCRIS as it is able to develop links between lower to higher hierarchy. Knowledge representation are developed starting from the lowest part of SCRIS structure. Example below may clarify this approach by referring to Figure 3. Example: . IF “Characteristics A of SC network” ¼ yes THEN Risk sub factor I.1.1.1.1.1 ¼ yes. . IF Risk sub factor I.1.1.1.1.1 ¼ yes THEN Risk factor I.1.1.1.1 ¼ yes. . IF Risk factor I.1.1.1.1 ¼ yes THEN Risk event I.1.1.1. ¼ yes. . IF Risk event I.1.1.1. ¼ yes THEN Communication I.1.1. ¼ yes. (c) Selecting ES shell. The next step in developing SCRIS is to select a programming language. There are many ES shells in the market with various prices and capabilities. C Language Integrated Production System (CLIPS) is chosen mainly because it supports rule based and forward chaining approach for knowledge representation and inference methods. It was originally developed by NASA and now is independently maintained and distributed as free public domain software at http://clipsrules. sourceforge.net/. Due to its low cost and availability of user’s support, CLIPS is widely utilized by government, industry, and academia (Giarratano and Riley, 2005). 3. Development and testing of SCRIS prototype At this stage, SCRIS prototype is built to ensure feasibility of SCRIS and suitability of CLIPS as the development tool. The architecture of SCRIS consists of knowledge base, inference engine, working memory and user interface (Figure 4). They are elaborated below. (a) SCRIS knowledge base consist of: (1) Facts represent all data/information which is needed in order to provide SCRIS user with recommendation of potential SC risk in their SC network. Values for these facts are inputted by SCRIS users through dialog session. Facts of SCRIS are written using CLIPS language format by using deftemplate. (2) Rules provide a path to develop interrelations between identified SC risks based on the facts which are input by users or stored in fact list and written in CLIPS language using defrule. These rules are classified according to their purposes and follows the nature of SCRIS structure, namely: . rules for eliciting information from the users on existing and possible conditions in their internal SC network, external SC environment and product;

Identifying supply chain risks 841

JMTM 23,7 Return .......

........

842 Deliver .......

........

Make .......

........

Source Hierarchical structure

Manufacturer/focal organization

Sc Partners

External Enviornment

Communication

Customers

Competitors

Risk Event

Causal structure

Risk Factor

Risk Sub Factor

Level 0: Time

Risk Factor

Risk Sub Factor

Plan

Level 1: Location

Manufacturer/focal organization

Sc Partners

External Enviornment

Level 2: Owner

Communication

Customers

Competitors

Risk Event

Risks and sources

Elicited knowledge

Risk Event

Risk Factor

Risk Sub Factor

Figure 2. SCRIS structure

Risk Event

Risk Factor

Risk Sub Factor

Characteristics of SC network Potential SC risks

(Level 0: TIME)

“THEN” part (5th rule) (Level 1: LOCATION)

I. PLAN

“THEN” part (6th rule)

I.1. Focal Organization

“IF” part (6th rule)

I.1.1. Communication

“THEN” part (4th rule)

“IF” part (5th rule) (Level 2: RISK OWNER)

“THEN” part (3rd rule)

“IF” part (3rd rule)

“THEN” part (1st rule)

“IF” part (1st rule)

I.1.1.1. Risk Event

“IF” part (4th rule)

I.1.1.1.1. Risk Factor

“THEN” part (2nd rule)

I.1.1.1.1.1 Risk Sub Factor

I.1.1.1.1.2 Risk Sub Factor

H I E R A R C H I C A L

Identifying supply chain risks 843

C A U S A L

“IF” part (2nd rule)

Figure 3. Forward chaining in ruled based representation for SCRIS structure

SC network characteristic 1 = yes

User input Current Information of Internal SC network • Manufacturer/focal organization • Suppliers • Customers • Logistics provider • Product

Current Information of External SC network • Macro economy • Socio cultural • Political Governmental • Nature conditions • Competitors • Product complimentary organizations • Technology development • Accidents SCRIS structure • Potential SC Risk Sub Factors • Potential SC Risk Factors • Potential SC Risk Events • SC Risk owner • SC operations location • SC operations stages

Working Memory

Risk Source Knowledge Base

SC risks Knowledge Base

List of identified SC risks

Facts Identified Risk Sub Factors

Rules

Output to users Identified Risk Events

Working Memory Facts

Identified Risk Factors

Corresponding SC Risk owner Rules Corresponding SC operations location

Interrelationships of SC risks

Corresponding SC operations stages

Figure 4. SCRIS architecture and its components relations

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. .

.

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.

.

.

rules for linking input from users with risk sub factors; rules for linking risk sub factors with risk factors, within the same and across different risk owners, SC operations locations, or SC operations stages; rules for linking risk factors with risk events, within the same and across different risk owners, SC operations locations, or SC operations stages; rules for linking risk sub factors with risk events across different risk owners, SC operations locations, or SC operations stages; rules for linking risk events with corresponding risk owners, SC operations location, and SC operations stages; and rules for generating recommendations.

(b) SCRIS inference engine. CLIPS provides inference engine SCRIS to control program operation. SCRIS uses the “depth strategy” for conflict resolution, which is CLIPS’s default strategy. It executes newly activated rules in preference to older rules. (c) SCRIS working memory. Similar with inference engine, working memory is also provided by CLIPS to gather all current facts which are inputted by SCRIS users and from new executed rules by inference engine. (d) SCRIS user interface. It is a text based dialog window to support interaction between users with the SCRIS. SCRIS users’ key in inputs via PC keyboard as part of answering a series of questions (dialogs). At the end of the dialog, SCRIS provides a text based output detailing list of potential risks and their interrelations which may occur in relation to user’s SC network. The screenshot of SCRIS user interface can be seen in Figure 5. The validation of SCRI prototype is conducted in an aluminium product manufacturer that applies MTO process strategy. Senior deputy manager of this company provides input for SCRIS regarding to conditions of its SC internal and external environment. SCRIS then recommend potential SC risks based on this information to the respondent. This SCRIS prototype testing has shown that CLIPS is suitable for developing SCRIS. Also, according to the feedback given by the respondent, SCRIS prototype recommendation has successfully identified and estimated 80 percent of potential this company SC risks. Some suggestion is also given about format, terminology and clarity of questions in the SCRIS interfaces. 4. Development and validation of final SCRIS All feedbacks received from SCRIS prototype testing are incorporated to improve knowledge base and user interface friendliness of final SCRIS. The second validation is carried out for final version of SCRIS for MTO, MTS and ETO. Four manufacturing companies participate in this validation, they are: an electronic part manufacturer and a pharmaceutical company which use MTO process strategy, one plastic wares manufacturer which utilizes MTS and one organization which design, develop, assembly and testing which uses ETO. For explanation purpose, some potential SC risks and their interrelationships which are identified from pharmaceutical manufacturer (case study 1) are presented (Figure 6). Three important areas are selected for this example, they are:

Identifying supply chain risks 845

Figure 5. Screenshot of SCRIS user interface (opening page)

(1) perishable raw materials and final product; (2) high amount of raw material and finished product as its inventory approach; and (3) inadequate warehouse’s environment control. Then, potential SC risks and their interrelationships of pharmaceutical manufacturer are identified accordingly which are elaborated next. SC risks are identified starting from “Plan stage” as the first operations stage in SC. “Perishable product type” and “High level of raw material and finished product inventory” may lead to “risk sub factor I.1.3.6.1.1 Unsuitable inventory approach for certain type of product”. As this company utilizes “high level of raw material and finished product inventory” which does not match with MTO operations strategy, therefore it may lead to “risk sub factor I.1.3.6.1.2 Unsuitable inventory approach for MTO organization”. These two risk sub factors may trigger “risk factor I.1.3.6.1 Inappropriate inventory strategy” and “risk event I.1.1.3.6 Inappropriate inventory plan” which is under “operational” (risk owner) of “focal organization”. “Lack of warehouse control environment design” while have “perishable product” may lead to “risk sub factor I.1.6.3.1.1 Inappropriate warehouse environment control design”. This risk sub factor brings about “risk factor I.1.6.3.1 Inappropriate warehouse design” then causes “risk event I.1.6.3 Inappropriate warehouse plan” which is also under “resources” (risk owner) of “focal organization”. At “Source” which is the next SC operations stage, “risk factor II.1.6.1.1. Inappropriate raw material storage/warehouse environment conditions” is may occurred due to “risk event I.1.6.3 Inappropriate warehouse plan” at “Plan stage”.

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V. RETURN stage

V.2. SC Partners V.2.1. Customers V.2.1.1. High volume of product return from customers V.2.1.1.1. High defective product is received by customers

846 IV. DELIVER stage

IV.1. Focal Organization

IV.2. SC Partners

IV.1.6. Resources

IV.2.1. Customers

IV.1.6.1. Inappropriate storage/warehouse for final product before deliver to customer IV.1.6.1.1. Inappropriate final product storage/warehouse environment conditions

IV.2.1.1. Discontinuation of cust order IV.2.1.1.1. Unable to fulfill customer order

III. MAKE stage III.1. Focal Organization III.1.3. Operational III.1.3.1. Unable to manufacture/produce III.1.3.1.1 Unavailability of raw material/component to be manufactured III.1.3.1.1.1 Unsuitable (deteriorating) quality of raw material/components to be manufactured due to storage

II. SOURCE stage

II.1. Focal Organization II.1.6. Resources II.1.6.1. Inappropriate storage/warehouse for incoming product/part from suppliers II.1.6.1.1. Inappropriate raw material storage/warehouse environment conditions

I. PLAN stage (level 0: Time)

I.1. Focal Organization

Level 1: Location

I.1.3. Operational Risk Events

Figure 6. Few SC risks and their relationships from pharmaceutical company case study

Risk factors Risk Sub Factors

I.1.3.6. Inappropriate inventory plan I.1.3.6.1.Inappropriate inventory strategy

I.1.3.6.1.1. Unsuitable inventory approach for certain type of product

Organization’s information

I.1.6. Resources

Perishable product

Level 2: Risk Owner

I.1.6.3. Inappropriate warehouse/storage plan I.1.6.3.1. Inappropriate warehouses/storage design

I.1.3.6.1.2. Unsuitable inventory approach for MTO organization High level of raw material & finished product inventory

I.1.6.3.1.1. Inappropriate warehouse environment control design Lack of warehouse control environment design

Then, it leads to “risk event II.1.6.1 Inappropriate storage/warehouse for incoming product/part from suppliers” which is under “resources” (risk owner) of “focal organization”. “Risk sub factor III.1.3.1.1.1. Unsuitable quality of raw material/components to be manufactured” at “Make stage” is may triggered by “risk event II.1.6.1 Inappropriate storage/warehouse for incoming product/part from suppliers” at “Source stage”. It may prompt “risk factor III.1.3.1.1.Unavailability of raw material/component

to be manufactured” and “risk event III.1.3.1 Unable to manufacture/produce” which is under “operational” (risk owner) of “focal organization”. “Risk factor IV.1.6.1.1 Inappropriate final product storage/warehouse environment conditions” at “Deliver stage” is caused by “risk event I.1.6.3 Inappropriate warehouse/storage plan” at “Plan stage”. It then may instigate “risk event IV.1.6.1 Inappropriate storage/warehouse for final product before deliver to customer “which is under “resources” (risk owner) of “focal organization”. “Risk factor IV.2.1.1.1 Unable to fulfil order” is may occurred due to “risk event III.1.3.1 Unable to manufacture/produce” at “Make stage”. It may trigger “risk event IV.2.1.1 Discontinuation of order from customer” which is under “customers” (risk owner) of “SC partners”. At “Return stage”, “risk factor V.2.1.1.1 High defective product is received by customers” is caused by “risk event IV.1.6.1 Inappropriate storage/warehouse for final product before deliver to customer“ at “Deliver stage”. It is linked with “risk event V.2.1.1 High volume of product return from customers” which is under “customers” (risk owner) of “SC partners”. As can be seen in this case study, SCRIS does not only recommend SC risks which happen in every stage of SC operations at each locations and each risk owners but also recognize interrelationships between these risks across different SC operations stages, locations and risk owners. Figure 7 shows the partial output of SCRIS for pharmaceutical manufacturer case study. Feedbacks from four manufacturing companies participate in this validation suggest that SCRIS is a viable decision support tool in identifying SC risks. Furthermore, SCRIS also can be utilized as a medium for communication and collaboration between the manufacturing organization and its SC partners in order to successfully manage and mitigate SC risks. Conclusion and future research recommendation A tool for assisting risk identification in a SC network is certainly required by decision makers as they are facing a broader range of risks since SC network is getting more complex and interdependent. This paper illustrates the development and validation of a supply chain risk identification supporting tool called SCRIS, which considers MTS, MTO and ETO process strategies. SCRIS is developed using CLIPS ES shell that supports rule based knowledge representation. It has been successfully validated and feedback received is incorporated to improve its capabilities. Even though different operations strategy is utilized by these organizations, they share a number of common potential risks in their SC. Such as, at Plan stage, these organizations may deal with risk event “delay in new product development” due to the presence of risk factor “inappropriate NPD management and policy” and risk factor “inadequate support of facilities/resources”. For organizations that apply MTO and MTS, this risk event leads to “delay in Time to Market” whereas for ETO organizations mean “delay to deliver as promised to their customer”. Some examples of unique SC risks for certain operations strategy are: risk factor “lack of consideration of modularity in product design” to be able to shorten manufacturing time for MTO organization, risk factor “inflexible machinery/equipment” to allow unique demand for ETO organization, and risk factor “inability to handle sudden customer demand changing” since MTS organization usually has special purpose machinery with specific human resources skill.

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**************************************************************************** SUPPLY CHAIN RISK IDENTIFICATION SYSTEM (SCRIS) RECOMMENDATION OF POTENTIAL RISKS AND THEIR INTERRELATIONS ON YOUR SC NETWORKS **************************************************************************** SCRIS recommends potential SC risks by firstly classified them into five stages of SC operation's, which are: 1. Plan 2. Source 3. Make 4. Deliver 5. Return Then, it is further classified according to: • Internal Organization (Communication, Technical, Operations, Organizational, Resources, and Financial), • Supply Chain Partners (Supplier, Customer, & Logistic providers). Finally, they are categorized into risk events and their possible causes (risk factor) Legend: **** = Risk event ***** = Risk factor (the cause) ##### = Similar risk event/factor/subfactor occurs at the same SC operation's stage >>>>> = Similar risk event/factor/subfactor occurs at different SC operation's stage **************************************************************************** Name of your organization : A Name of the product selected for this assessment : Pharmaceutical I.There is potential SC risks in PLAN STAGE of your SC operations I.1. Due to potential SC risks on YOUR ORGANIZATION I.1.1. At COMMUNICATION related function which may trigger by: ***Risk Event: Inadequate Internal Communication System *****Risk Factor: Failure of communication system in internal organization *****Risk Factor: Internal Organization communication system incapability ***Risk Event: Inappropriate environment to allow internal communication *****Risk Factor: Lack of program to encourage internal communication *****Risk Factor: Communication barrier in internal organization

Figure 7. Partial view of SCRIS recommendation for pharmaceutical manufacturer

***Risk Event: Inadequate communication system for SC partners *****Risk Factor: Lack of availability of communication system for SC partners *****Risk Factor: Incompatibility of your organization communication system with SC partners ***Risk Event: Inappropriate environment to allow communication with SC partners *****Risk Factor: Communication barriers with customers

SCRIS has been successfully developed specifically supports decision makers in managing SC risks by providing recommendations of identified potential SC risks and most importantly their interrelationships in order to set an appropriate risk mitigation strategy. Such an extensive tool covering hundreds of SC risk sub factors, risk factors, and risk events as well as mapping the interactions has not been developed to date. A novel SC risks taxonomy which covers SC risks more comprehensively also has been proposed which encompasses broader issues (time, location, risk owner, risk event,

risk factor, and risk sub factor) in SC network as well as considering different process strategies, namely MTS, MTO and ETO. In general, all organizations imply the benefit of using SCRIS as a decision support tool in identifying SC risks. They also suggest that SCRIS can be utilized as a medium for communication and collaboration between manufacturing organization and its SC partners in order to manage and mitigate SC risks. SCRIS risks taxonomy can be utilized as a common and standard risk register across SC partners. Thus, it encourages a better and close communication between SC partners in order to manage SC risks together. Furthermore, SCRIS output can be utilized as documentation for SC partners which can assist them in managing risks in the future. Feedback from industries suggests a need of further advancement of SCRIS to also incorporate support for risk assessment, risk evaluation and risk mitigation processes. Thus, it will provide a comprehensive SCRM tool for industries. References Abdullah, M.S., Kimble, C., Benest, I. and Paige, R. (2006), “Knowledge-based system: a re-evaluation”, Journal of Knowledge Management, Vol. 10 No. 3, pp. 127-42. Abraham, A. (2005), “Rule-based expert systems”, in Sydenham, P.H. and Thorn, R. (Eds), Handbook of Measuring System Design, Wiley, New York, NY, pp. 909-19. Adhitya, A., Srinivasan, R. and Karimi, I.A. (2009), “Supply chain risk identification using a HAZOP-based approach”, American Institute of Chemical Engineers, Vol. 55, pp. 1447-63. Akerkar, R.A. and Sajja, P.S. (2010), Knowledge-Based Systems, Jones and Bartlett Publishers, Sudbury, MA. AS/NZS 4360 (2004), Handbook: Risk Management Guidelines Companion to AS/NZS 4360:2004, Standards Australia International/Standards New Zealand, Sydney and Wellington. Brun, A., Caridi, M., Salama, K.F. and Ravelli, I. (2006), “Value and risk assessment of supply chain management improvement project”, International Journal of Production Economics, Vol. 99, pp. 186-201. Chan, Y.L., Cheung, C.F., Lee, W.B. and Kwok, S.K. (2006), “Knowledge-based simulation and analysis of supply chain performance”, International Journal of Computer Integrated Manufacturing, Vol. 19 No. 1, pp. 14-23. Chapman, P., Christopher, M., Juttner, U., Peck, H. and Wilding, R. (2002), “Identifying and managing supply-chain vulnerability”, Logistics & Transport Focus: The Journal of the Institute of Logistics and Transport, Vol. 4, pp. 59-64. Chopra, S. and Sodhi, S.M.M. (2004), “Managing risk to avoid supply-chain breakdown”, MIT Sloan Management Review, Vol. 46 No. 1, pp. 53-61. Christopher, M. and Peck, H. (2004), “Building the resilient supply chain”, The International Journal of Logistics Management, Vol. 15, pp. 1-13. Cohen, S. and Roussel, J. (2004), Strategic Supply Chain Management: The Five Disciplines for Top Performance, McGraw-Hill, New York, NY. Cranfield School of Management (2003), Creating Resilient Supply Chains: A Practical Guide, Centre for Logistics & Supply Chain Management, Bedford. Cucchiella, F. and Gastaldi, M. (2006), “Risk management in supply chain: a real option approach”, Journal of Manufacturing Technology Management, Vol. 17 No. 6, pp. 700-20.

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Three-stage supply chain allocation with fixed cost

Three-stage supply chain allocation

Vinay V. Panicker, R. Sridharan and B. Ebenezer Department of Mechanical Engineering, National Institute of Technology Calicut, Kozhikode, India Abstract

853 Received 22 March 2011 Revised 16 October 2011 Accepted 23 November 2011

Purpose – The purpose of this paper is of two-fold. First, the authors propose the application of genetic algorithm (GA)-based heuristic for solving a distribution allocation problem for a three-stage supply chain with fixed cost. Second, a methodology for parameter design in GA is discussed which can lead to better performance of the algorithm. Design/methodology/approach – A mathematical model is formulated as an integer-programming problem. The model is solved using GA-based heuristic and illustrated with a numerical example. An investigation is made for determining the best combination of the parameters of GA using factorial design procedure. Findings – The optimum population size for the selected problem size is found to be 100. The mutation probability for a better solution is 0.30. The objective function value at the above mentioned levels is better than that obtained at the other combinations. Research limitations/implications – This work provides a good insight about the fixed cost transportation problem (FCTP) in a three-stage supply chain and design of numerical parameters for GA. The model developed assumes a single product environment in a single period. Hence, the present study can be extended to a multi-product, multi-period, and varying demand environment. In the parameter design, three distinct numerical parameters are considered. The parameters, population size and mutation probability are set at four levels and the parameter, crossover probability is set at three levels. More levels can be selected so that more combinations can be experimented. Originality/value – The paper presents the formulation and solution of a distribution-allocation problem in a three-stage supply chain with fixed cost for a transportation route. Keywords Supply chain management, Distribution management, Genetic algorithms, Fixed cost transportation problem, Factorial design Paper type Research paper

1. Introduction A supply chain is a network of facilities and distribution options that performs the functions of procurement of materials, transformation of these materials into finished products and the distribution of these products to customers. For any supply chain, logistics or distribution plays a key role in its success. Eskigun et al. (2006) observe that logistics costs amount to 30 per cent of the total production costs. Huq et al. (2010) suggest that most of the inefficiencies associated with supply chain management (SCM) costs are due to the wasteful practices such as inefficient, unnecessary, or redundant stocking practices, or inefficient transportation. To gain a competitive edge in the market, supply chains must overcome these inefficiencies. According to Jain and Benyousef (2008), in future, the competition will not be between individual enterprises, The authors express their sincere thanks to the referees and the special issue editor for their constructive comments, which have immensely helped to bring this paper to the present form.

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 853-868 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267691

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but between competing supply chains. The performance of a supply chain depends mostly on the effective and balanced allocation of customers to distribution centres. Hence, designing an effective production-distribution network is of vital importance for firms aiming to reduce their logistics costs and maintain their competitive positions. This paper focuses on a distribution allocation problem in a three-stage supply chain model with fixed cost. Fixed charge problem or fixed cost problem is a practical problem in the industry (Jawahar and Balaji, 2009). The fixed-charge transportation problem (FCTP) is a special case of traditional transportation problem (TP) (Adlakha and Kowalski, 1999). Unlike TP, FCTP considers a fixed cost for a route in addition to the unit cost which depends upon the quantity of goods transported that is constant for a particular route. Fixed costs include the toll fee on the highways, the reward given to the driver, landing fee at the airport, permit fees or property taxes, etc. When fixed cost is also taken into account, the TP is known as FCTP. The objective of any FCTP model is to find that combination of routes, which can transport goods or services minimizing the total cost. The presence of fixed cost causes discontinuity in the objective function which makes FCTP more difficult to solve. The problem cannot be solved by direct application of the transportation algorithm and it has been shown to be non-deterministic polynomial (NP) hard (Clover et al., 1992). Hence, the solution methodologies adopted in the literature are heuristic algorithms and meta-heuristic algorithms such as GA, tabu search, and simulated annealing extensively. Most of the works in the literature consider the allocation problem in a single-stage supply chain. A single-stage supply chain consists of a set of manufacturing plants and a set of distributors (or customers). Adlakha and Kowalski (1998) consider a TP with the more-for-less (MFL) paradox and Adlakha and Kowalski (1999) analyse a FCTP model with MFL. An MFL paradox occurs when it is possible to ship more total goods for less or equal total cost while shipping the same amount or more from each origin to each destination, keeping shipping costs non-negative. Adlakha and Kowalski (2000) discuss the problem in the order of loading when multiple absolute points are present while solving an FCTP. Using Hungarian and Vogel approximation methods, Adlakha and Kowalski (2003) solve a single-stage FCTP as a small FCTP. Kannan et al. (2008b) formulate a TP of a single-stage supply chain with fixed charge and obtain optimum results using a local search heuristic known as Nelder-Mead method. Raj and Rajendran (2009) propose a simple heuristic algorithm for solving a single-stage FCTP wherein the performance of the algorithm is compared with the existing best method by making use of benchmark problem instances. GA is applied for combinatorial optimization problems. GA is found to be a very effective means to solve location-allocation problems in supply chains (Gen et al., 2001). Han and Damrongwongsiri (2005) apply GA to derive optimal solutions for a mathematical model of a stochastic multiple-period, two-echelon inventory with the many-to-many demand-supplier network problem. GA has been widely used by researchers to find optimal solutions for an FCTP. Gottlieb and Paulmann (1998) propose a GA-based permutation representation for the FCTP. Gen and Li (1998) develop spanning tree based-GA (st-GA) for TP using Pru¨fer number encoding. Gen and Li (1999) use the st-GA approach for FCTP. Jo et al. (2007) consider a non-linear FCTP for a single-stage-supply chain consisting of a plant and a customer. This work depicts the transportation graph of a non-linear FCTP as a spanning tree with the use of Pru¨fer numbers. The model is solved using st-GA. Kannan et al. (2008a) have commented

on the work of Jo et al. (2007) stating an error in the total transportation cost. Gen et al. (2005) summarize the recent research work on network design problems that use GA. It is evident from the literature that researchers have mainly focussed on a single-stage FCTP with a set of manufacturing plants and a set of distributors. In the two-stage FCTP, the entities involved are manufacturing plants, distributors, and retailers. To the best knowledge, only Jawahar and Balaji (2009) have developed a two-stage distribution model with fixed cost. GA-based heuristic is proposed for the solving the two-stage model. Hence, there exists a research gap for solving an allocation problem in an FCTP supply chain model with three or more stages. This paper deals with the modelling and analysis of a more general FCTP supply chain model with three-stages comprising of manufacturing plants, distributors, retailers, and customers. In most of the studies pertaining to the area of FCTP, GA is found to perform better. In GA, there are two categories of parameters, namely structural and numerical. The chromosome representation, operator types and termination criterion are some of the structural parameters. The initial population, population size, number of generations, crossover probability, and mutation probability are the numerical parameters. The performance of GA depends on the numerical parameters. With the same structural parameters, if the numerical parameters in GA are not chosen properly, the population may converge prematurely to a local optimum that is hard to escape from. Hence, there is a need to design the parameters to be used in GA. Furthermore, researchers use the most commonly adopted parameter value in the literature or the trial-and-error method to adjust parameter design manually. To the best knowledge, there is no research work reported on the methodology for parameter design for GA in a three-stage FCTP. This research adopts factorial design as a systematic parameter design method to effectively obtain the best combination of the numerical parameters of GA. Considering the above research aspects, this paper deals with an allocation problem in a three-stage FCTP supply chain model. A supply chain comprising of a set of five manufacturing plants, five distributors, five retailers, and five customers is considered for detailed investigation. This supply chain represents a medium sized supply chain encountered in practice. A fixed cost for a distribution route between two entities (manufacturing plant-distributor, distributor-retailer, and retailer-customer) is taken into account. An integer programming model for the three-stage supply chain is formulated. The model is solved using GA-based heuristic. The best combinations of the numerical parameters are determined using the factorial design concept. Thus, the contribution of this work is two-fold: (1) it models and solves a three-stage FCTP supply chain; and (2) it identifies the best combinations of numerical parameters in the GA-based heuristic. The organisation of this paper is as follows. Section 2 describes the problem formulation. Section 3 explains the solution methodology. Section 4 provides the analysis of results. Section 5 discusses the conclusion. 2. Problem description The problem considered is a multi-echelon supply chain allocation. The supply chain includes entities such as manufacturing plants, distributors, retailers, and customers. The product is manufactured in the manufacturing plant, transported to the distribution

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centres, to the retailers, and then to the customers. A random demand for the product occurs at the retailer end. The model assumes that the demand is satisfied from the local inventory at the retailer. The retailer can replenish its inventory from multiple distributors. Similarly, the distributor can replenish its inventory from multiple plants. Figure 1 shows this three-stage supply chain network. The mathematical formulation for this three-stage supply chain with a set of m plants (i ¼ 1, 2, . . . , m), a set of d distributors (k ¼ 1, 2, . . . , d ), a set of r retailers (l ¼ 1, 2, . . . , r), and a set of n customers ( j ¼ 1, 2, . . . , n) taking into account a fixed cost for a distribution route is described in this section. 2.1 Assumptions The following are the assumptions made in the three-stage supply chain FCTP formulation: . The number of plants, their capacities, and customers, their demand are known. . The number of distribution centres and their capacities are known. . The number of retailers and their capacities are known. . A customer can be supplied with products from more than a retailer. . A retailer can replenish the inventory from multiple distribution centres. . A distribution centre can replenish the inventory from multiple manufacturing plants. 2.2 Model formulation The objective of this formulation is to minimize the total cost incurred in supplying the goods from the plant to customer through the intermediaries such as distribution centres and retailers, considering the possible combination of routes. Notations Indices set of plants.

j

set of distribution centres. Manufacturing Plant I

Distributor I

Retailer I

Customer I

Manufacturing Plant II

Distributor II

Retailer II

Customer II

Manufacturing Plant III

Distributor III

Retailer III

Customer III

Distributor d

Retailer r

…

…

Manufacturing Plant p

…

…

Figure 1. Three-stage supply chain

i

Customer n

k

set of retailers.

l

set of customers.

Three-stage supply chain allocation

Decision variables xij

number of quantity transported from plant i to distributor j.

cij

unit cost of transportation between plant i and distributor j.

fij

fixed transportation cost between plant i and distributor j.

xjk

number of quantity transported from distributor j to retailer k.

cjk

unit cost of transportation between distributor j and retailer k.

fjk

fixed transportation cost between distributor j and retailer k.

xkl

number of quantity transported from retailer k to customer l.

ckl

unit cost of transportation between retailer k and customer l.

fkl

fixed transportation cost between retailer k and customer l.

857

CDl demand at customer l. RCk capacity at retailer k. DCj capacity at distributor j. Si

capacity at plant i.

Problem formulation Minimize: Z¼

m X d X

ðcij xij þ f ij yij Þ þ

i¼1 j¼1

d X r X j¼1 k¼1

ðcjk xjk þ f jk yjk Þ þ

r X n X

ðckl xkl þ f lk ykl Þ

ð1Þ

k¼1 l¼1

Subject to: d X

xij ¼ S i ðfor i ¼ 1; 2; . . . ; mÞ

ð2Þ

xij # DC j ðfor j ¼ 1; 2; . . . ; d Þ

ð3Þ

xjk # RC k ðfor k ¼ 1; 2; . . . ; rÞ

ð4Þ

xkl ¼ CDl

ð5Þ

j¼1 m X i¼1 d X j¼1 r X k¼1

ðfor l ¼ 1; 2; . . . ; nÞ

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xij ; xjk ; xkl $ 0 ðfor all i; j; k and l Þ ( 1; if xij . 0 yij ¼ 0; otherwise ( yjk ¼

ykl ¼

ð7Þ

1; if xjk . 0 0; otherwise

(

ð6Þ

1; if xkl . 0

ð8Þ

ð9Þ

0; otherwise

The objective function (1) is to minimise the total cost incurred in supplying the goods from manufacturing plants to customers through distributors and retailers, considering the possible combination of routes. Constraint (2) denotes supply capacity constraint. It implies that the product quantity which is distributed from the manufacturing plant to the distribution centers cannot be more than the current capacity of the plant. Constraint (3) represents distributor capacity constraint. This constraint maintains that the quantity of shipment received in a distribution center from plants must be less than or equal to the storage capacity of the distribution centre. Constraint (4) provides retailer capacity constraint. This constraint maintains that the quantity shipment received in a retailer from various distribution centers must be equal to or less than the retailer capacity. Constraint (5) indicates customer demand constraint. This gives the demand of the customer in the supply chain. The total quantity available at the retailers must be equal to the demand of the customers. Constraint (6) is the non-negative constraint on the decision variables. The quantity shipped from the plant to the distribution centres and from the distribution centre to the retailers and from the retailer to the customers must be non-negative and should be integers. Constraints (7)-(9) denote binary constraints. If the plants/distribution centres/retailers are open, the value should be 1, otherwise the value is 0. 2.3 Reduced TP Balinski (1961) observes that there exists an optimal solution to the relaxed version of FCTP by relaxing the integer restriction on yij, with the property that: xij yij ¼ ; where mij ¼ minðai ; bj Þ ð10Þ mij The FCTP now is simplified and is known as relaxed transportation problem (RTP) of an FCTP. The model is simply a standard TP with the unit transportation costs as: f ij C ij ¼ cij þ ð11Þ mij The optimal value of RTP provides a lower bound on the optimal value of FCTP as shown by Balinski (1961). If Xij is an optimal solution to RTP, then: XX XX ðcij X ij þ f ij yij Þ ð12Þ C ij X ij # Z #

The mathematical model of FCTP developed in this paper is transformed to an RTP, to find the lower bound value for the model. 3. Solution methodology The problem is solved using a permutation based-GA. Generally, GA consists of a string representing the points in the search space, a set of genetic operators for generating new search points and a stochastic assignment to control the genetic operations. It typically consists of four phases described as follows. 3.1 Step 1: coding phase The individuals in a population used in GA for solving FCTP are chromosomes. A chromosome consists of q genes (integers), where q is the product of the number of sources and destinations. Each gene in the chromosome is designated to a cell that corresponds to the combination of a source and a destination. 3.2 Step 2: initialization phase Initialization is the generation of the initial population of chromosomes. This means the selection of the initial search points. In this phase, two parameters, namely population size and chromosome length need to be specified. The population size must effectively represent the search space. This affects the ultimate performance and efficiency of GA. The selection of chromosome length depends on the accuracy requirement of the optimization problem. The higher the chromosome length, the better will be the resolution and accuracy. However, this leads to an enormous increase in computation time and, more importantly, time of convergence could be prolonged. In this work, the chromosome length is defined as the product of the number of source and destination points. The initial population of size N is created with chromosomes randomly without duplication. 3.3 Step 3: evaluation phase In the evaluation phase, a function called “fitness function” is used as a tool to evaluate the fitness of each chromosome in the population. For minimization type problems, fitness function is a function of variables that bear inverse proportionality relationship with the objective function or it is the reciprocal of a function of variables with direct proportionality relationship with the objective function. In this study, the fitness value is calculated as: 1 ð13Þ Fitness value ¼ 1 þ Objective function value 3.4 Step 4: genetic operations phase This step of GA involves generating a new population from the existing population based on the fitness values of chromosomes. The genetic operators are reproduction, crossover, and mutation. 3.4.1 Step 4a: reproduction. There are several methods for generating the new population namely roulette wheel selection, tournament selection, rank based selection, etc. This research adopts roulette wheel method for the selection of chromosomes for reproduction. The roulette wheel selection is easier to implement. Further, in selection, there is a chance that some weaker solutions may survive the selection process; this is an advantage because it may include some component which

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could prove useful following the recombination process. The reproduction is an operation whereby an old chromosome is selected according to its fitness value and stored in a mating pool. More number of copies of highly fit chromosomes will be selected to the mating pool. In roulette wheel selection, the parents which have better fitness value are selected. In this selection method, all the chromosomes are considered to be placed on a roulette wheel. When a marble is thrown on the wheel, the chromosome which has more fitness value will have more chance of selection. Based on this logic, a procedure to simulate this selection is presented as follows: . Compute the sum of the fitness value of all chromosomes in the population and denote it as S. . Generate a uniformly distributed random number, K in the interval 0 to S. . Starting from the first chromosome in the population, obtain the cumulative fitness value of the chromosome until the cumulative fitness value first exceeds K. Then, identify the corresponding chromosome for which the cumulative fitness value up to that chromosome first exceeds K and treat it as one of the parents for cross over. 3.4.2 Step 4b: crossover. This is a recombination operation, wherein the gene information contained in the two selected parents is recombined to generate two children with some characteristics of the parents. In order to control crossover, the parameter called crossover probability (Pc) is used. For each chromosome, a random number between 0 and 1 is generated and compared with Pc. If it is less than Pc, crossover operation is performed on the chromosomes. In this study, partial mapped crossover (PMX) operator is used for crossover where the procedure is explained as follows: . Select two positions along the string uniformly at random (say 4 and 7 as shown in Figure 2). . Exchange two substrings between parents to produce proto-children. . Determine the mapping relationship between two mapping sections. . Legalize offspring with mapping relationship. Thus, crossover results in two children. Parent 1 2

6

4

5

3

7

8

9

Parent 2 2 1

5

6

4

8

9

3

7

Child 1 1

2

5

6

4

8

9

3

7

Child 2 2

1

6

4

5

3

7

8

9

1

Figure 2. Illustration of the PMX crossover operator mutation operator

6

4

4

5

8

9

Mapping relationship 3

7

3.4.3 Step 4c: mutation. This operator is capable of creating new chromosomes in the population to maintain the population diversity. Mutation probability (Pm) is the parameter used to control the mutation. For each string, a random number between 0 and 1 is generated and compared with Pm. If it is less than Pm, mutation is performed on the string. The present study uses heuristic mutation. 3.4.3.1 Heuristic mutation. The procedure involved in heuristic mutation is as follows (Gen and Cheng, 1997): . Pick up l genes at random. In this study, l is assumed as 3. . Generate neighbours according to all possible permutations of the selected genes. . Evaluate all neighbours and select the best one as offspring. The procedure is shown in Figure 3.

Three-stage supply chain allocation 861

4. Results and discussion A supply chain comprising of five plants, five distributors, five retailers, and five customers is considered for the purpose of illustration. This supply chain represents a medium sized supply chain observed in the real-world. As discussed in Section 2.1, the present work also discusses the method for the selection of numerical parameters in GA so as to provide a better solution. A sample problem data is generated according to uniform distribution as follows: . Unit cost of transportation in each stage: U (5, 10). . Fixed cost for a transportation route in each stage: U (10, 100). . Capacity of suppliers: U (100, 300). . Demand of customers: U (100, 300). The data thus generated is shown in Tables I-V. The code for GA-based heuristic is developed in MATLAB 7.8.0. Using the GA code, the distribution allocation problem in the three-stage supply chain with fixed cost is solved. The allocation is given in Tables VI-VIII.

Select three positions at random 1

2 r 3

4

5

6

7

8

9

The selected positions swap with each other and form new combination 1

2

6

4

5

3

7

8

9

1

2

6

4

5

8

7

3

9

1

2

3

4

5

8

7

6

9

1

2

8

4

5

3

7

6

9

1

2

8

4

5

6

7

3

9

Figure 3. Illustration of the heuristic mutation operator

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After the allocation with GA-based heuristic, the TORA software (Taha, 2008) is used to find the lower bound value for the problem. The FCTP model is converted to RTP and is used in TORA. The allocation using TORA is given in Tables IX-XI. A comparison of total cost is made for the following: .

862

. .

RTP model solved using TORA (i.e. considering equivalent cost). FCTP model solved using GA-based heuristic. The allocation obtained for the RTP model using TORA (i.e. considering the fixed cost and variable cost for the allocations).

The results of comparison thus obtained are shown in Table XII. The total cost obtained using GA-based heuristic is the actual total cost since it considers the fixed cost and the variable cost of transportation. In the reduced problem,

Table I. Capacity of suppliers

Table II. Customer demand

Capacity (units)

Demand (units)

Supplier 1

Supplier 2

Supplier 3

Supplier 4

Supplier 5

200

300

300

200

100

Customer 1

Customer 2

Customer 3

Customer 4

Customer 5

300

100

350

250

100

Distributor 1 Fixed Unit costa costa

Table III. Transportation cost matrix between suppliers and distributors

Supplier Supplier Supplier Supplier Supplier

1 2 3 4 5

25 71 66 10 77

5 7 5 8 9

100 21 42 27 75

6 7 5 6 9

Distributor 3 Fixed Unit cost cost 26 99 11 13 83

8 9 8 10 5

Distributor 4 Fixed Unit cost cost 88 61 78 57 63

6 7 9 10 5

Distributor 5 Fixed Unit cost cost 27 55 14 15 40

5 7 9 8 9

Note: aThe costs are in monetary units

Retailer 1 Fixed Unit costa costa

Table IV. Transportation cost matrix between distributors and retailers

Distributor 2 Fixed Unit cost cost

Distributor Distributor Distributor Distributor Distributor

1 2 3 4 5

93 47 76 23 84

7 5 9 7 6

Retailer 2 Fixed Unit cost cost 92 80 78 46 73

Note: aThe costs are in monetary units

7 7 9 5 9

Retailer 3 Fixed Unit cost cost 61 63 41 74 24

10 6 8 6 8

Retailer 4 Fixed Unit cost cost 10 61 59 60 73

5 10 8 7 5

Retailer 5 Fixed Unit cost cost 94 95 92 64 94

10 8 10 8 5

the fixed cost and variable cost are used to derive an equivalent cost and the problem is solved using this equivalent cost. Hence, even though the total cost for the reduced problem is slightly less than that of the total cost (actual cost) for GA-based heuristic as shown in Table XII, it is not the actual cost. Thus, GA-based heuristic provides an attractive solution methodology for solving the FCTP.

Three-stage supply chain allocation 863

Customer 1 Fixed Unit cost a cost a Retailer Retailer Retailer Retailer Retailer

1 2 3 4 5

57 91 46 64 18

Customer 2 Fixed Unit cost cost

8 5 7 8 5

40 23 32 44 34

Customer 3 Fixed Unit cost cost

9 8 7 10 6

29 67 82 28 91

8 6 10 6 10

Customer 4 Fixed Unit cost cost 77 58 98 61 29

Customer 5 Fixed Unit cost cost

8 8 10 9 6

88 88 38 39 86

5 5 9 7 7

Note: aThe costs are in monetary units

Retailer 1 Retailer 2 Retailer 3 Retailer 4 Retailer 5 Demand

Distributor Distributor Distributor Distributor Distributor Demand

Supplier Supplier Supplier Supplier Supplier Demand

1 2 3 4 5

1 2 3 4 5

Customer 1

Customer 2

Customer 3

Customer 4

Customer 5

Capacity

0 300 0 0 0 300

0 0 100 0 0 100

50 0 0 300 0 350

0 0 0 0 250 250

100 0 0 0 0 100

300 300 300 300 300

Retailer 1

Retailer 2

Retailer 3

Retailer 4

Retailer 5

Capacity

0 150 0 0 0 150

0 0 0 300 0 300

0 100 0 0 0 100

300 0 0 0 0 300

0 0 0 0 250 250

300 300 300 300 300

Distributor 1

Distributor 2

Distributor 3

Distributor 4

Distributor 5

Capacity

0 0 300 0 0 300

0 50 0 200 0 250

0 0 0 0 0 0

0 200 0 0 100 300

200 50 0 0 0 250

200 300 300 200 100

Table V. Transportation cost matrix between retailers and customers

Table VI. Final allocated matrix between customer and retailer

Table VII. Final allocated matrix between retailer and distributor

Table VIII. Final allocated matrix between distributor and supplier

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Table IX. Final allocated matrix between customer and retailer

Table X. Final allocated matrix between retailer and distributor

Table XI. Final allocated matrix between distributor and supplier

4.1 Parameter design for GA-based heuristic In this study, three numerical parameters are considered. Factorial design is used. Population size and mutation probability are set at four levels. Crossover probability is set at three levels. These levels are described as follows: (1) Population size: 20, 50, 100, and 150. (2) Crossover probability: 0.7, 0.8, and 0.9. (3) Mutation probability: 0.20, 0.25, 0.30, and 0.35.

Retailer 1 Retailer 2 Retailer 3 Retailer 4 Retailer 5 Demand

Distributor Distributor Distributor Distributor Distributor Demand

Supplier Supplier Supplier Supplier Supplier Demand

1 2 3 4 5

1 2 3 4 5

Customer 1

Customer 2

Customer 3

Customer 4

Customer 5

Capacity

0 250 0 0 50 300

0 0 100 0 0 100

0 50 0 300 0 350

0 0 0 0 250 250

100 0 0 0 0 100

300 300 300 300 300

Retailer 1

Retailer 2

Retailer 3

Retailer 4

Retailer 5

Capacity

0 100 0 0 0 100

0 0 0 300 0 300

0 100 0 0 0 100

300 0 0 0 0 300

0 0 0 0 300 300

300 300 300 300 300

Distributor 1

Distributor 2

Distributor 3

Distributor 4

Distributor 5

Capacity

0 0 300 0 0 300

0 0 0 200 0 200

0 0 0 0 0 0

0 200 0 0 100 300

200 100 0 0 0 300

200 300 300 200 100

Model and solution method Table XII. Comparison of results between TORA and GA-based heuristic

Consideration of fixed and variable cost

RTP model solved using TORA Equivalent cost RTP model solved using TORA Fixed cost and variable cost considered explicitly FCTP model solved using GA- Fixed cost and variable cost considered explicitly based heuristic

Total cost (in monetary units) 18,961.50 19,112.00 19,227.00

For each design, five independent GA runs are taken. Analysis of variance (ANOVA) is used to determine the significance of each factor on the objective function. ANOVA F-test is conducted at 5 per cent level of significance. When crossover probability is selected in the model, the result shows that crossover operation is not significant. Thus, by excluding the crossover probability factor from analysis, the results get improved. The results of ANOVA thus obtained are shown in Table XIII. The F-value for the model is 4.24 which implies that the model is significant. The p-values less than 0.05 (significance level) indicate model terms that are significant. Table XIII shows that population size is significant. The mutation probability is not significant at 5 per cent, since the p-value is 0.0526 which is slightly higher than 0.05. Figure 4 shows the interaction effects of population size at various levels keeping the mutation probability constant. Similarly, Figure 5 shows that the best mutation probability is 0.30 for the constant population size.

Source

Sum of squares

Model A-population size C-mutation probability AC Residual

þ 007

3.602 £ 10 2.043 £ 10þ 007 4.854 £ 10þ 006 1.074 £ 10þ 007 1.814 £ 10þ 007

df

Mean square

Three-stage supply chain allocation 865

F-value p-value, prob . F

15 3

þ 006

2.402 £ 10 6.811 £ 10þ 006

4.24 12.01

0.0003 ,0.0001

3 9 32

1.618 £ 10þ 006 1.193 £ 10þ 006 5.670 £ 10þ 005

2.85 2.10

0.0526 0.0590

Significant

Table XIII. ANOVA results

Interaction C: Mutation prob

25,200

23,925

22,650

C3 C1

C2

C4

21,375

20,100 Level 1 of A

Level 2 of A

Level 3 of A

A: pop size

Level 4 of A

Figure 4. Interaction of population size with objective function value

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25,200

866

23,925

22,650

A1

A2 A3 A4

21,375

Figure 5. Interaction of mutation probability with objective function value

20,100 Level 1 of C

Level 2 of C Level 3 of C C: Mutation prob

Level 4 of C

5. Conclusions Supply chain system is an integrated production system which aims at quick and efficient service towards the customers. In a supply chain system, distribution plays a significant role in maintaining the uninterrupted flow of goods and services between the manufacturer and the customers. The performance of a supply chain depends mostly on the effective and balanced allocation of customers to distribution centres. In this study, supply chain modelling and optimization is perceived as determining the allocation of distribution activity between partners. In today’s world, managers have to cope up with the growing markets and greater customer expectations. The measure of success of any company is in terms of lower costs, shorter lead time, lesser stock, reliable delivery and better customer service. This can be achieved by the effective allocation of customers among the different facilities. The FCTP has been studied extensively because of the considerable merit of practice, even though it is a non-polynomial deterministic problem. The objective of an FCTP is to find the combination of routes that minimizes the total costs while satisfying the supply and demand constraints. This study models a three-stage supply chain allocation problem with fixed cost. The formulated model is solved using GA-based heuristic and a systematic method is carried out for the parameter design of the proposed GA-based heuristic. The parameters are kept at various levels and using the factorial design concept, it is found that the optimum population size for the selected problem is 100. The mutation probability for better solution is found to be 0.30. The objective function value at the above mentioned levels is better than that obtained at the other combinations. Factorial design provides the best combination of levels of the factors that are investigated. Thus, the present study provides a better insight to managers about the FCTP in a three-stage supply chain and design of numerical parameters for GA. This is a significant contribution to the literature.

In the present study, the mathematical model developed for the three-stage supply chain assumes a single product environment in a single period with the consideration of transportation costs. This work can be extended to include costs of production and inventory. Further, a multi-product, multi-period environment can also be investigated. In the parameter design of GA, the levels selected are three or four. More levels can be selected so that more combinations can be experimented and better values can be obtained.

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References Adlakha, V. and Kowalski, K. (1998), “A quick sufficient solution to the more-for-less paradox in the transportation problem”, OMEGA: The International Journal of Management Science, Vol. 26 No. 4, pp. 541-7. Adlakha, V. and Kowalski, K. (1999), “On the fixed-charge transportation problem”, OMEGA: The International Journal of Management Science, Vol. 27 No. 3, pp. 381-8. Adlakha, V. and Kowalski, K. (2000), “A note on the procedure MFL for a more-for-less solution in transportation problems”, OMEGA: The International Journal of Management Science, Vol. 28 No. 4, pp. 481-3. Adlakha, V. and Kowalski, K. (2003), “A simple heuristic for solving small fixed-charge transportation problems”, OMEGA: The International Journal of Management Science, Vol. 31 No. 3, pp. 205-11. Balinski, M.L. (1961), “Fixed cost transportation problems”, Naval Research Logistics Quarterly, Vol. 8 No. 1, pp. 41-54. Clover, F., Klingman, D. and Phillips, N.V. (1992), Network Models in Optimization and Their Applications in Practice, Wiley, New York, NY. Eskigun, E., Uzsoy, R., Preckel, P.V., Beaujon, G., Krishnan, S. and Tew, J.D. (2006), “Outbound supply chain network design with node selection and lead time considerations”, Naval Research Logistics, Vol. 54 No. 3, pp. 282-300. Gen, M. and Cheng, R. (1997), Genetic Algorithms and Engineering Design, Wiley, New York, NY. Gen, M. and Li, Y.-Z. (1998), “Spanning tree-based genetic algorithm for bi-criteria transportation problem”, Computers & Industrial Engineering, Vol. 35 Nos 3/4, pp. 531-4. Gen, M. and Li, Y.-Z. (1999), “Spanning tree-based genetic algorithm for bi-criteria fixed charge transportation problem”, IEEE Proceedings, pp. 2265-71. Gen, M., Cheng, R. and Oren, S.S. (2001), “Network design techniques using adapted genetic algorithms”, Advances in Engineering Software, Vol. 32 No. 14, pp. 731-44. Gen, M., Kumar, A. and Kim, J.R. (2005), “Recent network design techniques using evolutionary algorithms”, International Journal of Production Economics, Vol. 98 No. 2, pp. 251-61. Gottlieb, J. and Paulmann, L. (1998), “Genetic algorithms for the fixed charge transportation problems”, Proc. of the IEEE Conf. on Evolutionary Computation, ICEC, pp. 330-5. Han, C. and Damrongwongsiri, M. (2005), “Stochastic modelling of a two-echelon multiple sourcing supply chain system with genetic algorithm”, Journal of Manufacturing Technology Management, Vol. 16 No. 1, pp. 87-108. Huq, F., Stafford, T.F., Bhutta, M.K.S. and Kanungo, S. (2010), “An examination of the differential effects of transportation in supply chain optimization modelling”, Journal of Manufacturing Technology Management, Vol. 21 No. 2, pp. 269-86. Jain, V. and Benyoucef, L. (2008), “Managing long supply chain networks: some emerging issues and challenges”, Journal of Manufacturing Technology Management, Vol. 19 No. 4, pp. 469-96.

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Jawahar, N. and Balaji, A.N. (2009), “A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge”, European Journal of Operational Research, Vol. 194 No. 2, pp. 496-537. Jo, J.B., Li, Y. and Gen, M. (2007), “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm”, Computers & Industrial Engineering, Vol. 53 No. 2, pp. 290-8. Kannan, G., Sasikumar, P. and Vinay, V.B.P. (2008a), “Comments on the erratum to nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm – by Jung-bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering, (2007)”, Computers & Industrial Engineering, Vol. 55 No. 2, pp. 533-4. Kannan, G., Senthil, P., Sasikumar, P. and Vinay, V.P. (2008b), “A Nelder and Mead methodology for solving small fixed-charge transportation problems”, International Journal of Information Systems and Supply Chain Management, Vol. 1 No. 4, pp. 60-72. Raj, K.A.A.D. and Rajendran, C. (2009), “Fast heuristic algorithms to solve a single-sink fixed-charge transportation problem”, International Journal of Operational Research, Vol. 6 No. 3, pp. 304-29. Taha, H.A. (2008), Operations Research: An Introduction, Pearson Education, New Delhi. About the authors Vinay V. Panicker is an Assistant Professor in the Department of Mechanical Engineering at National Institute of Technology Calicut, Kerala. He received an M.Tech in Industrial Engineering from National Institute of Technology, Tiruchirapalli. His research interests are in the areas of supply chain management, logistics management, and multi-criteria decision making. He has published technical papers in refereed international journals and proceedings of international and national conferences. Currently, he is pursuing research in the area of fixed charge transportation problem. R. Sridharan is Professor of Industrial Engineering in the Department of Mechanical Engineering at the National Institute of Technology Calicut, India. He received his PhD in 1995 from the Department of Mechanical Engineering at the Indian Institute of Technology, Bombay, India. His research interests include modelling and analysis of decision problems in supply chain management, job shop production systems and flexible manufacturing systems. He has published papers in refereed international journals and proceedings of international and national conferences. R. Sridharan is the corresponding author and can be contacted at: [email protected] B. Ebenezer is a Graduate Student in the Department of Mechanical Engineering at National Institute of Technology Calicut, Kerala, where he is pursuing his post graduate studies in Industrial Engineering and Management. His research interests are in the areas of vendor managed inventory and logistics management in supply chains. He has published technical papers in the proceedings of international and national conferences.

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An integrated vendor-buyer inventory model with partial backordering Fateh Moshrefi and Mohammad Reza Akbari Jokar Department of Industrial and System Engineering, Sharif University of Technology, Tehran, Iran

An integrated vendor-buyer inventory model 869 Received 23 March 2011 Revised 1 October 2011 Accepted 23 November 2011

Abstract Purpose – The purpose of this paper is to analyze the effects of supply chain coordination on inventory management while the retailer inventory cycle consists of a shortage period and the backorder rate linearly decreases as a function of shortage duration. It is intended to consider how on-hand inventory and shortage durations are altered when the decisions are centralized. Design/methodology/approach – Mathematical modelling of inventory costs for the retailer and the vendor is used to formulate objective functions. The vendor sets his inventory period as an integer multiple (n) of the retailer inventory cycle in which the integer multiple is a decision variable. Solution spaces of models are analyzed to determine two other decision variables including, on-hand inventory duration and shortage length. Findings – The integrated model consists of a unique pseudo convex area when (n) is fixed and as a result, there is a unique minimum point. Based on numerical examples and sensitivity analysis, in most situations coordinated inventory management reduces total costs of the supply chain and cost reduction rate increase at larger production rates. Originality/value – This paper is a combination between production-inventory models in two-stage supply chains and partial backordering, which has appeared in single inventory models. To the best of the authors’ knowledge, no mathematical model has yet been proposed. Moreover, the benefits of synchronization are analyzed through numerical examples. Keywords Supply chain management, Inventory management, Partial backordering, Stock dependent demand Paper type Research paper

1. Introduction Coordinated management of supply chains is one of the most important issues in competitive markets of the twenty-first century. Many researchers have proposed integrated inventory models with specific assumptions. However, in a few of them shortage period is allowed as a part of buyer’s inventory cycle, especially with a mixture of backorders and lost sales. The former idea is appeared in various papers that investigated a single inventory system. Abad (2001) developed an inventory model with price-dependent demand and partial backlogging in which selling price is computed after obtaining inventory parameters. San Jose et al. (2005, 2006, 2007) proposed some analytical papers with various customer impatient functions. While authors usually engaged in investigating solution spaces, an interesting issue in their researches is direct computing of inventory parameters by specific formulas based on all possible situations. Lodree (2007) surveyed an inventory system in which goodwill cost is explicitly represented as the cost of breaking a supplier-buyer agreement. Moreover, they

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 869-884 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267709

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classified six categories among papers with partial backorder subject. Based on this survey, demand can be constant, stock dependent, time dependent, or price dependent while the deterioration may be considered or not. Although there are several other inventory models with assumptions related to partial backorder, none considers a whole supply chain. Sajadieh et al. (2009) proposed an integrated vendor-buyer model with stochastic lead time, in which shortages are allowed and fully backlogged. They showed that as the fluctuations of lead time increases, integrated policy becomes more cost-efficient. In another paper a mathematical model is developed in a supply chain with stock-dependent demand. The efficiency of centralized decision making on revenue generation versus traditional policy is mentioned (Sajadieh et al., 2010). Ben-Daya et al. (2008) investigated literature in joint economic lot sizing problem and classified five groups based on transfer policy from the vendor to the buyer. However, in none of them shortage was allowed as a part of buyer’s inventory cycle. Tyan et al. (2007) developed a large integrated supply chain model for deteriorating items under inflation. They also assumed that a constant part of demand during shortage period is backlogged. Huang (2004) extended the production-inventory model for a single buyer and a single vendor in a condition that, a random percentage of produced items are defective and each of them incurs the supply chain a constant cost. In a similar paper, Huang et al. (2010) examined the previous structure with order-processing cost reduction and permissible delay in payments. Finally, Yan et al. (2011) developed an integrated vendor-buyer model for perishable products in JIT environment without any shortages. In this paper, a mathematical model is developed for a supply chain consisting of a vendor and a buyer. Besides stock-dependent demand, shortages are allowed and a customer impatient function is applied to generate a mixture of backorders and lost sales. In fact, this research is an extension of common variable partial backorder models in inventory management to a two-stage supply chain, which is analyzed mathematically. The remainder of this paper is organized as follows. In Section 2, notations and assumptions are reviewed and the problem is addressed. In Sections 3 and 4 modeling and analyzing of traditional and centralized supply chains is presented. In Section 5, sensitivity analysis is developed based on a numerical example. Finally, important conclusions besides future research insights are exposed in Section 6. 2. Assumptions and notations Consider a supply chain consisting of one vendor and one retailer. The vendor produces goods at a constant rate and the retailer faces a demand rate which depends on stocked inventory. The inventory cycle for the retailer may consist of a shortage period in which the demand is partially backlogged based on a decreasing function. This production-inventory system with allowable variable partial backorder rate for buyer, is more practical and helps to effectively manage inventories through analyzing different aspects that could be obtained by varying shortage parameters, production rate, demand rate and dependence sensitivity of demand. The purpose of this research is to determine the optimum inventory cycles by balancing inventory, ordering and shortages costs for both parties of the supply chain in two traditional and integrated models.

The following notations are used to illustrate inventory models throughout the paper: D

demand rate.

P

constant production rate for the vendor which is greater than maximum possible demand rate.

n

number of shipped batches from the vendor to the retailer throughout vendor cycle.

H

inventory holding cost per unit per unit of time for vendor.

S

constant production setup cost for the vendor.

R

constant ordering cost for the retailer.

h

inventory holding cost per unit per unit of time for retailer.

V

unit of lost sale cost which is the sum of goodwill cost and benefit lost.

v0

fixed backorder cost per item.

v

backorder cost per unit per unit of time.

Furthermore, assumptions for reflecting the inventory functions in mathematical models are as follows: . Inventory cycle of the retailer is sum of the on-hand inventory length (k) and the shortage length (c). The vendor sets his period as an integer multiple (n) of retailer’s cycle length. k, c, and n are decision variables. . Lead time is assumed to be negligible and the vendor dispatches productions whenever retailer inventory cycle repeats. . Shortages for the retailer is based on the following function as equation (1) (San Jose et al., 2007), in which, as time elapses during the shortage period, fewer customers are willing to wait until replenishment. In this function a is the initial backorder rate and b is the decreasing backorder factor: t BðtÞ ¼ a 2 b ; c .

t # c; b # a

ð1Þ

In none-shortage periods, the demand rate is assumed to be dependent on inventory volume at the retailer’s shelf area. For this reason equation (2) is applied as below in which s is the coefficient of demand dependence rate to inventory volume for the retailer, and D0 is the initial demand value: DðtÞ ¼ D0 þ s · I ðtÞ;

0#s#1

ð2Þ

3. Traditional supply chain At the outset, we develop buyer’s inventory structures. Besides holding cost and ordering cost, there are costs of shortages including backlogged items and lost sales. As shown in Figure 1, the retailer’s inventory cycle consists of an on-hand inventory section and a shortage period which both are decision variables.

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Inventory level

872

Q

Figure 1. Retailer’s inventory system

l1max Time

l2max ψ

We denote inventory level at time t in none-shortage periods with I 1 ðtÞ 0 # t # k and at shortage periods with I 2 ðtÞ 0 # t # c. Having I 1 ð0Þ ¼ I max 1 , I 1 ðkÞ ¼ 0, I 2 ðcÞ ¼ 0 and the relationship between demand and inventory, we can obtain and solve relevant differential equations as illustrated in equations (3) and (4): dI 1 D0 s ðk2tÞ ¼ 2D0 2 s*I 1 ðtÞ 0 # t # k ) I 1 ðtÞ ¼ ½e 2 1
dt s

ð3Þ


 dI 2 t ¼ D0 a 2 b ; dt c

ð4Þ


 bt 2 0 , t , c ) I 2 ðtÞ ¼ D0 t a 2 2c

Thus, we get: I max ¼ 1


 D0 sk b ½e 2 1
and I max ¼ c a 2 : 2 s 2

Now, one can obtain cost structures as follows. Inventory carrying cost per cycle is: HC r ¼ h ·

Z

k

I 1 ðtÞdt ¼ h ·

Z

0

k

0

 D0  sðk2tÞ hD0 e 2 1 dt ¼ s s




1 sk ðe 2 1Þ 2 k s

 ð5Þ

Total shortage cost can be derived as:

SC ¼ v0

Z 0

c

D0 BðtÞdt þ v

Z




c

I 2 ðtÞdt ¼ D0 cv0

0


 b a b 2 2 a2 þ D0 c v 2 2 6

ð6Þ

The cost of lost sales during shortage period is:
 Z c b OC ¼ V D0 ð1 2 BðtÞÞdt ¼ cVD0 1 2 a þ 2 0

ð7Þ

Finally, total cost per unit of time for the retailer will be: TC r ðk; cÞ ¼




 
  D0 h sk h b b R 2 a ð 2 þ ð e 2 1 Þ 2 k c V þ a 2 v 2 VÞ þ vc þ 0 D0 kþc s2 s 2 2 6

ð8Þ

The objective is to minimize TCr while two decision variables k, c are none negative. Using optimal values for k *, and c * the order quantity could be obtained as:

  b e sk 2 1 max max Q ¼ I 1 þ I 2 ¼ D0 c a 2 : þ 2 s

An integrated vendor-buyer inventory model 873

Proposition 1. TCr is a strictly pseudo-convex function in k and c. The proof is represented in Appendix 1. Based on proposition 1 and linearity of constraints, there will be a unique global minimum for TCr and the optimal solutions can be easily obtained using common optimization softwares. Next, we consider vendor’s cost structures. As shown in Figure 2, the vendor sets his inventory period as a multiple integer of retailer’s cycle. Since shortage is not an issue on behalf of the vendor, only inventory holding costs must be calculated. Formulation of inventory holding cost for the vendor is proposed by many researchers like Yang (2010) and Sajadieh et al. (2009). For this purpose, first, cumulative inventory cost is derived and then costs of dispatched batches are subtracted according to their time of shipments. Using the above explanation we get:     
 Q nQ nðn 2 1Þ T 2 nQ 2Q HC v ¼ H nQ ðn 2 1ÞT þ P 2P 2   ð9Þ ðn 2 1ÞT Q nQ ¼ HnQ þ 2 2 P 2P Thus, the total inventory cost per unit of time for the vendor becomes: TC v ¼

S HQ½ððn 2 1ÞT=2Þ þ ðQ=PÞ þ ðnQ=2PÞ
þ nT T

ð10Þ

Now the objective is to determine an optimal number of shipments so that TCv be minimized. By taking first derivative of TCv with respect to n (temporarily assume n is a continuous variable) and setting it to zero, we get the following optimality condition: Inventory level

Time T n.T

Figure 2. Vendor’s inventory system

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n * ðn * 2 1Þ #

2SP # n * ðn * þ 1Þ HQðTP 2 QÞ

ð11Þ

It can be easily shown that TCv is convex in n, resulting a unique value of n for the optimality condition (11). Therefore, in traditional supply chain, retailer computes k * and c * and declares Q and T to the vendor. Then, he determines the optimal number of shipments to locally optimize his costs. 4. Coordinated supply chain In this case, the whole supply chain cost model is obtained by adding equations (8)-(10) and substituting T and Q with k þ c and D0 ðcða 2 ðb=2ÞÞ þ ððe sk 2 1Þ=sÞ, respectively. After factorization we have: (




 h sk h b ðe 2 1Þ 2 k þc Vþ a2 ðv0 2 VÞ s2 s 2


  R þ Sn b b e sk 2 1 2 a þ vc 2 þH c a2 þ þ 2 6 D0 2 s  )


 sk ðn 2 1Þðk þ cÞ b e 21 1 n þ D0 c a 2 2 £ þ 2 p 2p 2 s

D0 TC J ¼ kþc

ð12Þ

The objective is to minimize TCJ subject to none-negativity constraints for k and c and integrality for n. Since new expressions that are added to equation (10) to form equation (12) are independent of n, the optimality condition in Section 2 remains valid. One way to find the optimal solutions is to increment n one by one (from n ¼ 1) and optimize TCJ for the given n to obtain global optimum values for three decision variables. Unfortunately, for a given n TCJ is not a convex function in k, c. However, it can be shown that it has a unique local minimum point. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lemma 1. If n increases to kn (k . 1), QðTP 2 QÞ reduces to 1=qk where 0 , q , 1. Proof. We can write TCJ as TC 1J þ TC 2J where TC 1J is independent of n and originally derived from retailer’s cost function. By taking the first partial derivative of TC 2J with respect to n and equating it to zero, we can get: rffiffiffiffiffiffiffiffi 2SP 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n¼ H QðTP 2 QÞ

ð13Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Therefore, if n increases to kn (k . 1), QðTP 2 QÞ decreases to 1/k. However, fluctuations in n do not affect optimal values ffiof k and c with respect to TC 1J and this pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi part remains unchanged, thus QðTP 2 QÞ remains constant. Therefore, ultimate pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi deviations of QðTP 2 QÞ will be in range of 1 to 1/k that can be declared as A 1=qk; 0 , q , 1.

Corollary 1. If n increases, optimal values for k and c will decrease. Proof. We can rewrite (TP 2 Q) as:
sk 

 e 21 b þ c P 2 D0 a 2 P k 2 D0 s 2

ð14Þ

Based on assumptions, production rate (P) is greater than maximum possible demand rate. The largest possible demand rate based on equation (3) can be derived as D0e sk. Therefore, we have: P $ D0e sk. By taking first derivative of equation (14) with respect to k we have: P 2 D0e sk which is positive. Also, derivative of equation (14) with respect to c is again positive. So if k or c increases, TP 2 Q and Q both increase. From lemma 1, if n increases, Q(TP 2 Q) will decrease. Now if Q increases, at least one of two k and c increase and then TP 2 Q increases too implying that Q(TP 2 Q) must increase which contradicts lemma 1. Therefore, if n increases, Q and TP 2 Q must decrease and as a result, optimal value for k or c or both will decrease. A Based on corollary 1, k*i21 and c*i21 are upper bounds for k*i and c*i . Corollary 2. If optimality condition (11) is satisfied for n1 but is not satisfied for n2 . n1, then for any larger quantity of n than n2, the condition cannot be satisfied. Proof. Consider optimality condition obtained and illustrated in equation (11). According to lemma 1, the middle part in equation (11) has a lower increase rate than first part: n *(n * 2 1). Therefore, if equation (11) is satisfied for n1 and is not satisfied for n2, it can be concluded that ((2SP)/HQ(TP 2 Q)) has became less than n *(n * 2 1). Thus, by increasing n, optimality condition cannot be satisfied again. A Proposition 2. If n ¼ 1, then TCJ will be a strictly pseudo-convex function in k and c. Proof. As proposed in proof of proposition 1, we denote TCJ ¼ (F(k, c)/(k þ c)). If the convexity of F(k, c) can be proved, the rest of the procedure for proof is exactly as proposition 1. For n ¼ 1 TCJ will be: D0

ðh=s 2 Þðe sk 2 1Þ 2 kðh=sÞ þ cðV þ ða 2 ðb=2ÞÞðv0 2 VÞÞ þ vc 2 ðða=2Þ 2 ðb=6ÞÞ þ ðR=D0 Þ kþc þ

D20 H ðcða 2 ðb=2ÞÞ þ ðe sk 2 1Þ=sÞ2 þ ðS=D0 Þ 2P ðk þ cÞ ð15Þ

It is clear that equation (15) is composed of two distinct parts, ðF 1 ðk; cÞÞ=ðk þ cÞ and ðF 2 ðk; cÞÞ=ðk þ cÞ related to the retailer and the vendor, respectively. Convexity of F1(k, c) is proved in proposition 1. For convexity of F2(k, c) we prove that partial derivatives of F2(k, c) with respect to k and c are positive and also the relevant hessian determinant is positive definite (for notational convenience we let g ¼ ðD20 H Þ=ð2PÞ . 0): 

  ›2 F b e sk 2 1 2sk sk ¼ g 2e þ 2 se c a2 .0 þ ›k 2 2 s
 ›2 F b 2 ð16Þ ¼ 2 g a 2 .0 ›c 2 2 Det Hessian ¼

g 2 sk e ð2a 2 bÞ2 ð2ðe sk 2 1Þ þ scð2a 2 bÞÞ . 0 2

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Therefore, F2(k, c) is a strictly convex function in k and c. Since (› 2F)/(›k›c) in F1(k, c) is zero, the hessian for F(k, c) ¼ F1(k, c) þ F2(k, c) remains positive definite and F(k, c) will be strictly convex. Now, we can prove pseudoconvexity of TCJ (for n ¼ 1) similar to Appendix 1. A Proposition 3. For n . 1, if P þ D0(2 2a þ b) $ 0 then TCJ has a unique pseudoconvex space and therefore has a unique local minimum. Proof is shown in Appendix 2. Based on represented propositions and lemmas, we can develop an algorithm to find global optimal values for k, c and n as follows: . Step 1. Set n ¼ 1, j ¼ 0, and an arbitrary large number for optimal total cost. Minimize TC 1J to obtain k*1 and c*1 . . Step 2. Check condition (11) and if it was false, go to step 3. Otherwise set j ¼ 1 and If TC 1J , TC * replace TC * by TC 1J and also let: k * ¼ k*1 , c * ¼ c*1 , and n * ¼ 1. . Step 3. Increase n by one and obtain k1n and k2n (refer to Appendix 2). Position hofunique n local minimum o i hwhile n is i constant, will be located in an area given by: 0; min k1n ; k2n ; k*n21

.

.

, 0; c*n21 . According to Appendix 2, out of these ranges

for k, there is no guarantee for related hessian matrix to be positive definite. Based on this constraints minimize TC nJ to obtain k*n and c*n . Step 4. Check optimality condition in equation (11) and if it was false, go to step 5. Otherwise, set j ¼ 1 and If TC nJ , TC * replace TC * by TC nJ and also let k * ¼ k*n , c * ¼ c*n , and n * ¼ n. Then go to step 3. Step 5. If j ¼ 1, algorithm is terminated. Optimal values for decision variables will be: k * , c * , n * . Else, if j ¼ 0 go back to step 3.

The above algorithm will be terminated in a finite number of iterations. We have developed related codes in Maple 13 software and solved two numerical examples. 5. Numerical example In this section, we optimize the model in two traditional and centralized situations to compare the result of synchronization. In the first example, we use the retailer’s parameters appeared in San Jose et al. (2007) and adopt the vendor’s parameters as in Table I. The optimal quantities for the objective function and decision variables are obtained in about two seconds which are given in Table II. Based on Table II, in centralized model the length of holding inventory for both parties is reduced, while, the shortage period for retailer becomes longer. Moreover, it is

Parameter

Table I. Parameters used in numerical example 1

R S h H D0 s

Value

Parameter

Value

$250/order $2,000/order $0.53/unit/month $0.2/ unit/month 25/month 0.2

V v0 v P A B

$15/unit $0.2/unit $2/unit/month 100/month 0.9 0.1

clear that in centralized model, total cost of supply chain is reduced to 2.24 percent compared to the traditional approach. In another example, we assume the parameters in Table III for retailer and vendor, and solve the model in two traditional and centralized situations. Based on the results in Table IV, it is obvious that applying centralized approach reduces total cost of supply chain by 7.58 percent compared to the traditional approach. But in this case the result of integration is different; both on-hand inventory and shortage length are reduced and the production-inventory cycle for the vendor becomes shorter. For sensitivity analysis based on the example 1, first we investigate the model for different production rates. As reflected in Figure 3, coordinated supply chains will be Management policy

k*

c*

n*

Q

Vendor cycle

Chain monthly costs

Traditional Centralized

4.41 3.82

0.77 1.24

7 6

194 170

36.28 30.35

TCr þ TCv ¼ 228.96 TCJ ¼ 223.84

Parameter R S h H D0 s

Value

Parameter

Value

$200/order $800/order $5/unit/month $3/unit/month 500/month 0.1

V v0 v P A B

$8/unit $0.2/unit $2/unit/month 2000/month 0.9 0.1

Management policy

k*

c*

n*

Q

Vendor cycle

Traditional Centralized

0.36 0.18

0.27 0

2 4

301 92

1.26 0.72

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Table II. Obtained results for numeric example 1

Table III. Parameters used in numerical example 2

Chain monthly costs TCr þ TCv ¼ 2,001.94 TCJ ¼ 1850.22

Table IV. Obtained results for numeric Example 2

3.5 Percent Saving 3 2.5 2 1.5 1 0.5 0

75

100

125 150 175 Production Rate

200

250

Figure 3. Percent-saving in various production rates

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more cost efficient at higher rates of production. Note that production rate must be more than demand rate in any moment and also it must comply with P $ D0(2a 2 b) (refer to Appendix 2). Therefore, we are not allowed to investigate production rates lower than about 70. In addition to Figure 3, effects of changes in production rate on retailer’s cycle is shown in Figures 4 and 5. It is obvious that in the traditional policy, alterations in production rate will not affect k and c. But when decisions are centralized, changing vendor’s parameters such as production rate, production setup cost and unit holding cost will affect retailer’s cycle components. Based on Figures 4 and 5 it can be concluded Months 4.6 4.4 K-coordinated K-traditional

4.2 4 3.8 3.6

25 0

20 0

17 5

15 0

12 5

10 0

3.4 75

Figure 4. Buyer’s on-hand inventory length in different production rates

Production Rate Months 1.8

ψ-coordinated

ψ-traditional

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

Production Rate

25 0

20 0

17 5

15 0

12 5

10 0

0 75

Figure 5. Buyer’s shortage duration in different production rates

that in integrated model, higher rates of production rate results in longer shortage length while on-hand inventory duration becomes shorter. Next, we alter quantities of initial backorder rate, a, and the coefficient of demand sensitivity, s, in three different values of production rates such as, 75, 100, and 200. The results are reflected in Tables V and VI, respectively. a

k*Tr

Production rate ¼ 75 0-0.7 4.5 0.8 4.5 0.9 4.41 1 4.19 Production rate ¼ 100 0-0.7 4.5 0.8 4.5 0.9 4.41 1 4.19 Production rate ¼ 200 0-0.6 4.5 0.7 4.5 0.8 4.5 0.9 4.41 1 4.19

a

k*Tr

Production rate ¼ 75 0 6.07 0.01 5.9 0.05 5.52 0.1 5.08 0.2 4.41 0.3 3.93 Production rate ¼ 100 0 6.07 0.01 5.96 0.05 5.52 0.1 5.08 0.2 4.41 0.3 3.93 0.4 3.55 Production rate ¼ 200 0 6.07 0.01 5.9 0.05 5.52 0.1 5.08 0.2 4.41 0.3 3.93 0.4 3.55

k*J

c*Tr

c*J

n*Tr

n*J

% saving

4.2 4.32 3.91 3.82

0 0 0.77 1.31

0 0.24 0.93 1.56

8 8 7 7

8 7 7 6

0.28 0.32 0.55 1.12

4.13 4.12 3.82 3.54

0 0 0.77 1.32

0 0.7 1.24 1.62

8 7 7 6

7 6 6 6

1.73 1.12 2.24 1.06

4.12 4.06 4.03 3.82 3.58

0 0 0 0.77 1.32

0 0.22 1.13 1.57 1.89

7 7 6 6 6

6 6 5 5 5

2.17 2.26 2.42 2.84 3.02

k*J

c*Tr

c*J

n*Tr

n*J

% saving

6.38 6.22 5.65 4.73 3.91 3.66

0.46 0.48 0.55 0.63 0.77 0.89

0.68 0.73 0.92 0.88 0.93 1

6 6 6 7 7 8

5 5 5 6 7 7

0.62 0.54 0.26 1.24 0.55 0.78

7.08 6.88 5.47 4.91 3.82 3.35 2.84

0.46 0.48 0.55 0.63 0.77 0.89 1

0.92 0.98 0.93 1.14 1.24 1.47 1.45

5 5 6 6 7 7 7

4 4 5 5 6 6 7

0.33 0.23 0.94 0.83 2.24 1.96 1.61

6.9 6.69 5.93 4.64 3.81 3.25 2.61

0.46 0.48 0.55 0.63 0.77 0.89 1

0.9 0.96 1.12 1.18 1.56 1.87 1.87

5 5 5 5 6 6 7

4 4 4 5 5 5 6

0.93 0.85 0.57 0.72 2.84 3.54 6.67

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Table V. Effect of various initial backorder rates

Table VI. Effect of increasing demand sensitivity to stocked volume

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It is clear that if backorder rate (a) is decreased, shortage length becomes shorter while on-hand inventory duration for retailer becomes longer. This is the result of assigning higher costs for the unit of lost sale in comparison to the value of the unit of backlogged demand. Moreover, as ratio of backordered demand increases, coordinated management of supply chain becomes more cost efficient. Based on obtained results, in backorder rates lower than 0.6, shortage period is economically not allowable. For demand sensitivity (s) with quantities larger than 0.4, the production rate becomes less than maximum demand rate, which is inconsistent with assumptions and therefore, sensitivity analysis for these ranges is not considered. Based on Table IV, as the sensitivity of demand to stocked-inventory at retailer’s shelf area increases, duration of on-hand inventory becomes shorter and shortage period becomes longer. However, we cannot get a clear relationship between alterations of this parameter and percent-saving from integrated model. Since the model consists of 12 different parameters (which introduced in notations and equations (1) and (2)), we cannot explore our analyses for other parameters; However, practically production rate, demand rate sensitivity and backorder parameters are more important. 6. Conclusions This paper investigated an integrated production-inventory system in a two-stage supply chain consisting of one retailer and one producer. In addition to stock-dependent demand, we allowed shortage for the buyer. It is assumed that unsatisfied demand in shortage period is partially backlogged and as we approach to the end of the shortage period, customer impatience phenomenon is intensified. In this system two constant and time-dependent penalty costs are paid to awaiting customers. Moreover, a nonlinear model with linear constraints was obtained. It was proven that in the integrated model, for a given number of shipments there is a unique pseudoconvex space. Therefore, there is a unique local minimum. To determine optimal decision variables, a five step algorithm was introduced based on proven mathematical relationships. At last according to numerical examples, coordination of inventory management throughout the supply chain is a cost efficient policy compared to the traditional situation. For further study this model can be extended for perishable items. Moreover, customer impatient function can be exponential which induces more realistic backlogging occurrence. It can be developed for multiple retailers with capacity constraints for display shelf areas. Season patterned demand or stochastic lead time could be investigated too. References Abad, P.L. (2001), “Optimal price and order size for a reseller under partial backordering”, Computers and Operation Research, Vol. 28, pp. 53-65. Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (2006), “Convex functions and generalizations”, Nonlinear Programming: Theory and Algorithms, 3rd ed., Wiley, Hoboken, NJ. Ben-Daya, M., Darwish, M. and Ertogral, K. (2008), “The joint economic lot sizing problem: review and extensions”, European Journal of Operational Research, Vol. 185 No. 2, pp. 726-42.

Huang, C.K. (2004), “An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration”, International Journal of Production Economics, Vol. 91 No. 1, pp. 91-8. Huang, C.K., Tsai, D.M., Wu, J.C. and Chung, K.J. (2010), “An integrated vendor-buyer inventory model with order-processing cost reduction and permissible delay in payments”, European Journal of Operational Research, Vol. 202 No. 2, pp. 473-8. Lodree, E. Jr (2007), “Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract”, European Journal of Operational Research, Vol. 181 No. 1, pp. 168-83. Sajadieh, M.S., Akbari Jokar, M.R. and Modarres, M. (2009), “Developing a coordinated vendor-buyer model in two-stage supply chains with stochastic lead-times”, Computers & Operations Research, Vol. 36 No. 8, pp. 2484-9. Sajadieh, M.S., Akbari Jokar, M.R. and Modarres, M. (2010), “An integrated vendor-buyer model with stock-dependent demand”, Transportation Research Part E: Logistics and Transportation Review, Vol. 46 No. 6, pp. 963-74. San-Jose, L.A., Sicilia, J. and Garcia-Laguna, J. (2005), “The lot size-reorder level inventory system with customers impatience functions”, Computers & Industrial Engineering, Vol. 49 No. 3, pp. 349-62. San Jose, L.A., Sicilia, J. and Garcia-Laguna, J. (2006), “Analysis of an inventory system with exponential partial backordering”, International Journal of Production Economics, Vol. 100 No. 1, pp. 76-86. San Jose, L.A., Sicilia, J. and Garcia-Laguna, J. (2007), “An economic lot-size model with partial backlogging hinging on waiting time and shortage period”, Applied Mathematical Modeling, Vol. 31 No. 10, pp. 2149-59. Tyan, L.S., Ming, W.H. and Chang, H.W. (2007), “An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation”, International Journal of Production Economics, Vol. 106, pp. 248-60. Yan, C., Banerjee, A. and Yang, L. (2011), “An integrated production-distribution model for a deteriorating inventory item”, International Journal of Production Economics, Vol. 133 No. 1, pp. 228-32. Yang, M.F. (2010), “Supply chain integrated inventory model with present value and dependent crashing cost is polynomial”, Mathematical and Computer Modeling, Vol. 51, pp. 802-9. Further reading Chern, M.S., Yang, H.L., Teng, J.T. and Papachristos, S. (2008), “Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation”, European Journal of Operational Research, Vol. 191, pp. 127-41. Appendix 1 Proof of proposition 1. TC r is a strictly pseudoconvex function. If we denote TC r ¼ ðFðk; cÞ=ðk þ cÞÞ, it can be shown that F is convex in k, c:

›2 F ¼ ðhs 2 Þe sk . 0; ›k 2

›2 F v ¼ ð3a 2 2bÞ . 0 ›c 2 3

ðA1Þ

ð›2 F=›k›cÞ ¼ 0, hence hessian is positive definite and F is convex in k, c. Now, we suppose that for two distinct points (k1, c1), (k2, c2) we have TCr(k1, c1) $ TCr(k2, c2). Then, we prove that: DTC rk1 ;c1 ðk2 2 k1 ; c2 2 c1 Þ , 0 (Bazaraa et al., 2006).

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According to above assumption and noting that F(k,c) . 0 we can write: Fðk1 ; c1 Þ Fðk2 ; c2 Þ Fðk2 ; c2 Þ k2 þ c2 Fðk2 2 c2 Þ 2 Fðk1 ; c1 Þ # $ ) ) Fðk1 ; c1 Þ k1 þ c1 Fðk1 ; c1 Þ k1 þ c1 k2 þ c2 k2 2 k1 þ c2 2 c1 # k1 þ c1

ðA2Þ

Since F(k, c) is strictly convex we can write: Fðk2 ; c2 Þ 2 Fðk1 ; c1 Þ .

›F ›F jk ;c ðk2 2 k1 Þ þ jk ;c ðc2 2 c1 Þ ›k 1 1 ›c 1 1

ðA3Þ

Based on equations (A2) and (A3) we can get: ð›F=›kÞjk1 ;c1 ðk2 2 k1 Þ þ ð›F=›cÞjk1 ;c1 ðc2 2 c1 Þ Fðk2 ; c2 Þ 2 Fðk1 ; c1 Þ , Fðk1 ; c1 Þ Fðk1 ; c1 Þ ðk2 2 k1 þ c2 2 c1 Þ # k1 þ c1

ðA4Þ

  ›F ðk2 2 k1 þ c2 2 c1 Þ jk1 ;c1 ðk2 2 k1 Þ þ ›F›cÞjk1 ;c1 ðc2 2 c1 Þ , Fðk1 ; c1 Þ k1 þ c1 ›k

ðA5Þ

or:

By dividing equation (A5) to k1 þ c1 and note that TCr ¼ (F(k,c)/(k þ c)) we conclude that: ð›F=›kÞjk1 ;c1 ðk2 2 k1 Þ þ ð›F=›cÞjk1 ;c1 ðc2 2 c1 Þ TCðk1 ; c1 Þ , ðk2 2 k1 þ c2 2 c1 Þ k1 þ c1 k1 þ c1

ðA6Þ

or: ð›F=›kÞjk1 ;c1 ðk2 2 k1 Þ þ ð›F=›cÞjk1 ;c1 ðc2 2 c1 Þ TCðk1 ; c1 Þ 2 ðk2 2 k1 þ c2 2 c1 Þ , 0 ðA7Þ k1 þ c1 k1 þ c1 The above expression (A7) is equivalent to DTC rk1 ;c1 ðk2 2 k1 ; c2 2 c1 Þ , 0 and thus we completed proof. Appendix 2 Proof of proposition 3. For n . 1, if P þ D0(2 2a þ b) $ 0, then TCJ has a unique pseudoconvex area and therefore has a unique local minimum. For this reason, first we denote TCJ ¼ (F(k, c)/(k þ c)). If we show the hessian matrix for F as: " # ak;k ak;c ; ac;k ac;c we can have following analyses: (1) ac,c . 0 because:





 ›2 F 2v b 1 b 1 n ð3a 2 2bÞ þ 2H a 2 ¼ ðn 2 1Þ þ D0 a 2 12 .0 ›c 2 3 2 2 2 P 2

ðA8Þ

(2) For a given n, ak,k is positive in ½0; kn1
and negative in ½k1n ; 1
. If we expand (› 2F)/(›c 2) we have:

"



 
›2 F n 21 b 1 n sk 2 1 sk h þ H 2 þ e 2 ¼ 4HD ðe Þ s 0:5ðn 2 1Þð k þ c Þ þ D þ c a 2 0 0 p 2P p 2P ›k 2 s 2 #

 
21 b 1 n 2 þ H ðn 2 1Þ þ H þc a2 p 2P s 2

ðA9Þ 2

2

sk 2

Thus, (› F/›c ) is composed of a negative coefficient for (e ) and a coefficient for e call it G(k, c, n). We can show that ak,k(k ¼ 0, c ¼ 0) is positive: ak;k ð0; 0Þ ¼

sk

h þ H ððn 2 1ÞP 2 ðn 2 2ÞD0 Þ .0 P

that we

ðA10Þ

Also we show that if P þ D0(2 2a þ b) $ 0 then G(k, c, n) is positive:

›G H s ›G H s ðn 2 1Þ . 0 ðPðn 2 1Þ þ D0 ðn 2 2Þð22a þ bÞÞ . 0 ¼ ¼ ›k 2 ›c 2P ›G H ð2P þ 2D0 þ sðPðk þ cÞ þ cD0 ð22a þ bÞÞÞ . 0 ¼ ›n 2P Gð0; 0; 2Þ ¼ h þ H . 0

ðA11Þ

From equations (A10) and (A11) we can conclude that for a given c and n, there is unique value for k like k1n that for k . k1n ð›2 F=›c 2 Þ will be negative. Based on corollary 1, optimal value for c cannot be larger than c*n21 . Since ›G/›c . 0, to obtain the largest possible value of k that for which › 2F/›k 2 can be positive, we need to find a quantity for k like k1n which is obtained by solving:  ›2 F

k; c ¼ c*n21 ¼ 0 for k $ 0: 2 ›k Thus, for k . kn1 ; ð›2 F=›c 2 Þ is always negative and hessian is undefined.   (3) For a given n, if we suppose that P þ D0(2 2a þ b) $ 0, then hessian in k2n ; 1 is  undefined and in 0; kn2 is positive definite. If we obtain hessian determinant for TCJ for a given n, we have: (for notational convenience we let q1 ¼ ð22a þ bÞ , 0 and q2 ¼ ð23a þ bÞ , 0. Det Hessian ¼

 

 H ðe sk Þ2 2 2 2 2 2 8D0 P vq2 12H 2P ðn 2 1Þ þ 2D P q ðn 2 1Þðn 2 2Þ þ D q ðn 2 2Þ ðn 2 2Þ 0 1 0 1 48P 2 3  e sk 2 6ð2ð1 þ sðk þ cÞÞP 2 ðn 2 1Þ2 þ D0 Pðn 2 1Þðn 2 2Þð22saðk þ 3cÞ þ 48P 2 þ 4 þ sbðk þ 3cÞÞ þ D20 q1 ðn 2 2Þ2 ðsbc 2 2sca þ 2ÞÞq1 H 2 2 8Pððn 2 1Þ £ ðð23vsðk þ cÞ 2 6v 2 6hÞa þ ðvsðk þ cÞ þ 3h þ 2vÞbÞP þ ðð6scv þ 6hÞa 2 þ ðð25scv 2 6hÞb 2 6vÞa þ ðð1:5h þ scvÞb þ 2vÞbÞðn 2 2ÞD0 ÞH  2 16hP 2 vq2 2 3H 2 P 2 q21 ðn 2 1Þ2 ðA12Þ sk 2

Again DetHessian is composed of a negative coefficient for (e ) which is independent of k and c a coefficient for e sk that we note it as G(k, c, n), and a negative constant that is independent of c and k. It can be shown that if P þ D0(2 2a þ b) $ 0, then G(k, c, n) is positive. Because:

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 ›G 4 ¼ 6HP s ðn 2 1Þ 2q1 ðð22D0 a þ 2P þ bD0 Þn þ 2P þ 2bD0 2 4D0 aÞ 2 q2 P v . 0 3 ›k
 ›G 24q2 P v .0 ¼ 6H s ð2q1 ðn 2 2ÞD0 þ ðn 2 1ÞPÞð2q1 ð2Pðn 2 1Þ þ q1 ðn 2 2ÞD0 ÞÞH þ ›c 3

 ›G ¼ 12Hn 2ð2q1 Þðsk þ 1ÞHP2 þ ð2q1 Þðskb þ 2ska þ 4ÞHD0 P 2 2HD20 ðq1 Þ2 ›n  

2b þ 12H 2ðq1 Þðsk þ 1ÞH þ ð2skv þ 4h þ 4vÞa 2 ð2v þ 3h þ svkÞ P2 3

 3Hq1 4v þ 4HD20 ðq1 Þ2 . 0 ðsbk 2 2ska þ 4Þ 2 4ha2 þ að4v þ 4hbÞ 2 b hb þ þ D0 P 3 2


 

4vb 2q2 4hv 2 2 Hþ .0 £ Gð0; 0; 2Þ ¼ 12P 2q1 H þ 4ha 2 2hb þ 4av 2 3 3 ðA13Þ

It is too hard to find out that DetHessian (0,0,2) is positive or not. However, if it becomes negative we have two possible conditions: by increasing, DetHessian will be always negative, or it becomes positive and then becomes negative and remains negative. So for a given n and c, there is at most one unique value for k like kn2 that for which DetHessian becomes negative. Based on corollary 1, for a given n, the value for c cannot be larger than c*n21 . Since optimal

n ›G/›c . 0, to acquire largest value of k k2 that for which DetHessian remains positive, we have

to find unique value kn2 that is obtained from:

 Det Hessian k; c ¼ c*n21 ¼ 0 for k $ 0: Thus, for k . k2n , DetHessian is always negative and hessian matrix is indefinite and we cannot have any local minimum. Therefore, we can conclude that in TCJ ¼ F(k, c/k þ c), the only interval for k that for which F(k, c) is convex is at [0, min {kn2 ; k2n }]. For larger values of k the hessian of F(k, c) is surely undefined. Moreover, in the above interval the hessian becomes positive just one time and therefore there is only one convex area for F(k, c). As it was shown in proposition 1, TCJ will be pseudoconvex in this area and therefore there is a unique local minimum for TCJ.

Corresponding author Fateh Moshrefi can be contacted at: [email protected]

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An approach to analyze logistic outsourcing problem in medium-scale organization by CFPR and VIKOR Raman Kumar and Harwinder Singh Department of Mechanical Engineering, Guru Nanak Dev Engineering College, Ludhiana, India, and

Logistic outsourcing problem 885 Received 13 March 2011 Revised 7 October 2011 Accepted 23 November 2011

J.S. Dureja Department of Mechanical Engineering, Punjabi University, Patiala, India Abstract Purpose – The purpose of this paper is to make out a complete solution to logistic outsourcing problem in a medium-scale organization by using consistent fuzzy preference relation (CFPR) and vlsekriterijumska optimizacija i kompromisno resenje (VIKOR) method. Design/methodology/approach – The initial approach to this research was to develop a comprehensive framework for logistic outsourcing problem and selection of most appropriate third party logistic (3PL) provider. Findings – It has been found that the organization should outsource logistic activities. The alternatives (3PL providers) have also been ranked and the fifth 3PL provider has been termed as best third party logistic provider. Research limitations/implications – The parameters selected for this study and developed framework are applicable only to a medium-scale organization manufacturing automobile parts in northern India. Originality/value – This is probably the first time that an attempt has been made to apply the two-phase methodology approach, using CFPR and VIKOR, to analyze a multi-criteria logistic outsourcing problem. A case is provided which demonstrates how to solve logistic outsourcing, a multi-criteria decision-making problem. Keywords Manufacturing industries, Outsourcing, Logistic outsourcing, Consistent fuzzy preference relation, VlseKriterijumska Optimizacija I Kompromisno Resenje Paper type Research paper

1. Introduction Since the early 1990s, the worldwide practices of logistic outsourcing have been increasing, resulting in an annual 10 percent increase (Sohail and Sohal, 2003). Logistics is an emerging business area in many countries. Logistics is the management of the flow of goods and services from starting of origin to the consumption to meet the customer satisfaction (CS) and it has been evolved through several stages – planning, implementing and controlling the efficient, cost effective flow and storage of raw materials, in-process inventory, finished goods, and related information from point of origin to point of consumption for the purpose of conforming to customer requirements (Van Goor et al., 2003). By outsourcing logistics activities, firm can do concentrate on

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their core business operations, reduce their asset base and may increase CS. The term logistic outsourcing refers to call third party logistic (3PL) provider to perform logistic activities previously performed in-house. 3PL can be defined as relationships between interfaces in the supply chains and third party logistics providers, where logistics services are offered, from basic to customized ones, in a shorter or longer-term relationship, with the aim of effectiveness and efficiency (Woo and Saghiri, 2011). Bask (2001) insight the relations between supply chain strategies and 3PL provider and also add knowledge to 3PL provider for efficient work. Third party logistic provider typically specialize in integrated operation and offer a wide range of services including; warehousing, transportation, distribution, freight consolidation, value-added services such as packaging, labeling, inventory control, order fulfillment, pick and pack, etc. In logistic outsourcing there is risk factor as 3PL would be able to see confidential information and the study of relationships between logistics performance and customer loyalty are affected by risk characteristics of products and efficiencies (Ramanathan, 2010). The article is organized as follows: Section 2 presents a literature review. Section 3 includes case study and outlines the basis of the consistent fuzzy preference relations (CFPR) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Finally, Section 4 concludes the research and provides suggestions for further research. 2. Literature review A better understanding between existing outsourcing model and outsourcing process in practice was showed and developed a conceptual decision model based on the principles of satisfying (De Boer et al., 2006). A fuzzy TOPSIS decision making approach has been presented to deal with the supplier selection problem in supply chain system (Chen et al., 2006). The AHP procedure has been used in the selection of the right global logistics service for a Turkish automotive company (Gol and Catay, 2007). An attempt has been made to apply a comprehensive methodology consisting of analytical network process (ANP) for the selection of a logistic service provider (Jharkharia and Shankar, 2007). An analytic hierarchical prediction model based on the reciprocal additive CFPR has been used to measure the chance of successful knowledge management implementation (Wang and Chang, 2007). Data envelopment analysis (DEA) has been implemented to evaluate the efficiency of a group of 3PL warehouse logistics operations (Hamdan and Rogers, 2008). A rough set theory and VIKOR algorithm have been used for selection of suppliers and a case example has been examined and validation was proved (Guo and Zhang, 2008). The CFPR has been used to improve decision making consistency and to select merger strategy for financial organizations (Wang and Lin, 2008). The TOPSIS method with interval data has been presented to earmark potential 3PL services providers (Qureshi et al., 2009). A fuzzy preference programming method and fuzzy ANP approach has been applied to get crisp priorities and to solve supplier selection problem (Pang, 2009). A FAHP and a fuzzy multiple goal programming (FMGP) has been used for selection of thin film transistor liquid crystal display supplier (Lee et al., 2009). AHP technique in fuzzy environment (FAHP) has been used for selecting 3PL provider (C¸akir et al., 2009). A new evaluation method with rough set and particle swarm optimization (PSO) neural network has been introduced for selection of 3PLs provider (Zhang, 2009). Analytical hierarchy process has been applied on a vendor selection problem in small scale, medium scale and large-scale industries (Kumar et al., 2009).

A benchmarking has been provided for selecting a suitable 3PL provider by using two-phase methodology consisting of AHP and TOPSIS (Perc¸in, 2010). Two different techniques DEA technique and super-efficiency analysis technique has been applied for selection of most appropriate 3PL provider (Saen, 2010). An analytical hierarchy process based on fuzzy preference programming has been implemented for selection of vendor (Kaur et al., 2010). A case example has been examined by using fuzzy AHP for selection of best 3PL provider (Soh, 2010). An entropy approach and fuzzy VIKOR approach has been used for calculating weight of objectives and supplier selection, respectively, Shemshadi et al. (2011). A novel heuristic approach was adopted as an optimization technique to solve a multi criteria decision making (MCDM) problem, i.e. vendor selection problem (Chakraborty et al., 2011). An extended VIKOR method based on generalized interval-valued trapezoidal fuzzy numbers has been used for weighting the attributes (Liu and Wang, 2011). 3. Research methodology Two separated phases are designed in order to address the research methodology. The first phase consist of a solution approach (CFPR) to logistic outsourcing problem, i.e. should company go for logistic outsourcing or not. Then, the second phase provides a solution approach to selection of 3PL provider by using CFPR and VIKOR method. The stages of research methodology are shown in Figure 1. 3.1 Case study This case study has been conducted at a private limited company manufacturing automobile parts. The case company was incorporated in the year 1985 for the manufacture of automobile products in northern India. Today the group stands tall with an approximate turnover of Rs 162 crore. Group has strength of about 2,500 employees and technocrats. To accomplish this mission, the ownership, staff, and management go to great lengths to treat each customer like a member of the family and provide them with the best choice of products and highest quality of service in the industry. The multi-criteria decision problem is divided into smaller constituent parts in a hierarchy and a multi tier hierarchy diagram of outsourcing objectives is framed out. The alternatives are the lowest levels of the hierarchy. Links are drawn to form the hierarchy and the relationship among objectives and alternatives as shown in Figure 2. 3.2 A solution approach to logistic problem by CFPR method 3.2.1 Consistent fuzzy preference relations. CFPR were proposed for constructing the decision matrixes of pair-wise comparisons based on additive transitivity (Herrera-Viedma et al., 2004). This method reduce the judgment times and avoid checking inconsistency, hence enables decision makers to express their preferences over a set of alternatives with the least judgments (n 2 1). The study of consistency preference relations becomes a very important aspect in order to avoid misleading solutions in decision making. Applying this method it is possible to assure better consistency of the fuzzy preference relations provided by the decision makers, and in such a way, to avoid the inconsistent solutions in the decision making processes. 3.2.2 Steps in CFPR method. Step 1. Degree of preference. The degree of preference or intensity of the decision maker in the choice of each pair-wise comparison used in this model is quantified

Logistic outsourcing problem 887

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Select suitable objective and sub-objectives and Draw hierarchy diagram CFPR Do pair-wise comparison

Calculate normalized matrix and priority weights

Summary of possible outcome with respect to each other

Is success possibility greater than 50% Yes

No Successful outsourcing

Unsuccessful outsourcing Questionnaire

Relative weights of alternatives with respect to each weight of sub-objectives

CFPR Calculate weights of objectives and sub-objectives VIKOR Conduct VIKOR procedure by using weight calculated by CFPR and Determine value of Ei, Fi

Determine value of Pi and rank the alternatives

Figure 1. Flow chart of methodology used

End

Logistic outsourcing problem

Distribution Method Selection

Focus on core competence (FCC)

Order fulfilling (OF)

Total Sales Volume (TSV)

Increase in time to market (TM)

Successful outsourcing

Flexibility

Supplier Profile and relationship

World class technology (WCE)

Reputation (RP)

Operational Flexibility (OF)

Market Knowledge and Experience (MKE)

Range of Services provided (RSP)

Compatibility (CP)

3PL provider (A1)

3PL provider (A2)

Service Quality

On-time Delivery (OTD) Accuracy of Order Fulfillment (AOF) Customer Satisfaction (CS)

3PL provider (A3)

Threat to Security (TS)

Customer location (CL)

Service level requirement (SL)

889

Unsuccessful outsourcing

Risk

Cost effective

Low quality of delivered product (LQDP)

Cost of items (COI)

Production and Delivery delay (PDD)

3PL provider (A4)

3PL provider (A5)

Figure 2. Multi-tier hierarchy diagram

on a scale of 1-9. Even number (2, 4, 6, 8) can be used to represent compromises among the preference above. The suggest numbers used in this model to express degree of preference are shown in Table I. Step 2. Pair-wise comparison of different objectives. In this research work seven objectives such as such as focus on core competence, order fulfilling, total sales volume, increase in time to market, threat to security, customer location and service level has been consider for the solution of logistic outsourcing problem. The pair-wise comparison matrix value based on discussion and questionnaire filled by higher and Definition Equally important Moderately more important Strongly more important Very strongly more important Extremely more important Intermediate values

Intensity of importance 1 3 5 7 9 2, 4, 6, 8

Table I. Nine-point intensity of importance scale

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middle level employees of industry. The pair-wise comparison matrix for the objectives of phase 1 is shown in Table II. Step 3. Establish preference relation pair-wise comparison matrixes. In fact, only six comparisons are required for seven attributes. They are calculated by formula given below. The preference relation matrix for pair-wise comparison of attributes is shown in Table III: Pij ¼ gij ¼ 1=2 £ ð1 þ log9 aijÞ P21 ¼ 1 2 P12 P12 ¼ ð1 þ log9 2Þ=2 ¼ 0:66

P31 ¼ 1:5 2 P12 2 P23

P23 ¼ ð1 þ log9 2Þ=2 ¼ 0:66

P34 ¼ ð1 þ log9 1=2Þ=2 ¼ 0:34

P45 ¼ ð1 þ log9 1=3Þ2 ¼ 0:25

P41 ¼ 2 2 P12 2 P23 2 P34

P56 ¼ ð1 þ log9 2Þ=2 ¼ 0:6

P51 ¼ 2 2 P12 2 P23 2 P34 2 P45

P67 ¼ ð1 þ log9 3Þ=2 ¼ 0:75

P61 ¼ 2:5 2 P12 2 P23 2 P34 2 P45 2 P56 P71 ¼ 3 2 P12 2 P23 2 P34 2 P45 2 P56 2 P67

The other values can be determined by using property Pij þ Pjk þ Pki ¼ 3=2. Step 4. Normalized matrix of different sub-objectives. After a pair-wise comparison matrix is obtained, the next step is to divide each entry in column by the sum of entries in column to get value of normalized matrix. The value of normalized matrix of different sub-objectives is shown in Table IV. The values of normalized matrix rij are calculated as given in the formulae mentioned below:

Table II. Pair-wise comparison of different sub-objectives

Table III. Preference relations pair-wise comparison matrix

FCC OF TSV TM TS CL SL

FCC OF TSV TM TS CL SL Total

FCC

OF

1

2 1

TSV 2 1

TM

5 1

TS

1/3 1

CL

2 1

SL

3 1

FCC

OF

TSV

TM

TS

CL

SL

0.5 0.34 0.18 0.34 0.59 0.43 0.18 2.56

0.66 0.5 0.34 0.5 0.75 0.59 0.34 3.68

0.82 0.66 0.5 0.66 0.91 0.75 0.5 4.8

0.66 0.5 0.34 0.5 0.75 0.59 0.34 3.68

0.41 0.25 0.09 0.25 0.5 0.34 0.09 1.93

0.57 0.41 0.25 0.41 0.66 0.5 0.25 3.05

0.82 0.66 0.5 0.66 0.91 0.75 0.5

aij rij ¼ Pn

i¼1 aij

Thus, the approximate priority weight (W1, W2, . . . , Wj) for each attribute is obtained as shown in Table V: n 1X Wj ¼ aij n i¼1

Logistic outsourcing problem 891

Step 5. Establish pair-wise comparison matrix for rating of alternatives with respect to attributes. The summarize results of evaluating the possible of the implementation with respect to each of the seven objective are shown in Table VI. The graded adequacy of each objective was done on the opinion of experts in the organization, as follows: FCC ¼ 5 (extremely good), OF ¼ 3 (good), TSV ¼ 1/5 (extremely poor), TM ¼ 1 (fair), TS ¼ 3 (good), CL ¼ 5 (very good), SL ¼ 3 (good): Pij ¼ gij ¼ 1=2 £ ð1 þ log5 aij Þ Step 6. Priority weights for alternatives with respect to attributes. The prediction weight is determined by multiplying the priority weights of attributes and the evaluation ratings of alternatives. Chances of successful outsourcing implementation is: 0:833 £ 0:185 þ 0:693 £ 0:135 þ 0:167 £ 0:84 þ 0:5 £ 0:135 þ 0:693 £ 0:213 þ 0:833 £ 0:163 þ 0:693 £ 0:84 ¼ 0:671 The chances of successful outsourcing logistic activities is more less 50 percent so outsourcing of logistic activities are in favour for case company.

FCC OF TSV TM TS CL SL

Objective FCC OF TSV TM TS CL SL

FCC

OF

TSV

TM

TS

CL

SL

0.355 0.178 0.118 0.071 0.118 0.089 0.071

0.414 0.207 0.103 0.052 0.103 0.069 0.052

0.415 0.277 0.138 0.028 0.069 0.046 0.028

0.248 0.198 0.248 0.05 0.149 0.099 0.01

0.332 0.221 0.221 0.037 0.111 0.055 0.022

0.289 0.217 0.217 0.036 0.145 0.072 0.024

0.179 0.143 0.179 0.179 0.179 0.107 0.036

Table IV. Normalized matrix of different sub-objective

Priority weight 0.185 0.135 0.084 0.135 0.213 0.163 0.084

Table V. Priority weight of sub-objective

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Table VI. Summary of possible outcome

Success

Failure

0.5 0

1 0.5

0.833 0.167

0.5 0.16

0.84 0.5

0.693 0.307

0.5 1

0 0.5

0.167 0.833

0.5 0.5

0.5 0.5

0.5 0.5

0.5 0.16

0.84 0.5

0.693 0.307

0.5 0

1 0.5

0.833 0.167

0.5 0.16

0.84 0.5

0.693 0.307

FCC Success Failure OF Success Failure TSV Success Failure TM Success Failure TS Success Failure CL Success Failure SL Success Failure

3.3 Selection of 3PL provider by using CFPR and VIKOR method 3.3.1 Implementation of CFPR Step 1. Data collection. The data was collected through questionnaire on a five-point rating scale (outstanding, good, average, fair, poor). Four experts at different level from organization were selected to fill the questionnaire. Then the scale rating converted into crisp number by using AHP technique as shown in Table VII. Step 2. The importance of sub-objectives in each 3PL provider. In this research work 12 sub-objectives has been included to find out the best 3PL provider among five 3PL provider. The geometric mean of award score given by experts has been calculated by given below formula and values are shown in Table VIII: Geometric mean ¼ ðMultiplication of award given by exportsÞ0:25 Step 3. Relative weights of alternatives with respect to each weights of sub-objectives. The values of relative weights of alternatives with respect to each weight of sub-objectives are shown in Table IX.

Table VII. Pair-wise comparison judgement matrix for five-point rating scale

Outstanding Good Average Fair Poor

Outstanding

Good

Average

Fair

Poor

Weight

1 1/3 1/5 1/7 1/9

3 1 1/3 1/5 1/7

5 3 1 1/5 1/7

7 5 3 1 1/3

9 7 5 3 1

0.503 0.260 0.134 0.068 0.035

Step 4. Preference relation pair-wise comparison of different objectives. In this research work five objectives such as such as flexibility, supplier profile and relationship, service quality, risk and cost effective has been consider for the selection of best 3PL provider. The preference relation values of objective have been computed as shown in Table X. Step 5. Preference relation pair-wise comparison of different sub-objectives. In this research work 12 sub-objectives such as world class technology (WCE), operational flexibility (OF), range of services provided (RSP), reputation (RP), market knowledge and experience (MKE), compatibility (CP), on-time Delivery (OTD), accuracy of order fulfillment (AOF), Customer Satisfaction (CS), low quality of delivered product (LQDP), Production and delivery delay (PDD) and cost of items (COI) has been considered for selection of 3PL provider for case company. The preference relation values of sub-objectives have been computed as shown in Table XI. The overall weight of sub-objectives has been calculated by multiply sub-objective weights to corresponding objectives weights The weights of objective and sub-objectives are summarized and in Table XII. 3.3.2 Implementation of compromise ranking method. The VIKOR (the Serbian name is “VlseKriterijumska Optimizacija I Kompromisno Resenje”, which means multi-criteria optimization (MCO) and compromise solution) method was first established by Zeleny (1982) and later promoted by Opricovic and Tzeng (2002).

A1 A2 A3 A4 A5

A1 A2 A3 A4 A5

WCT

OF

RSP

RP

MKE

CP

OTD

AOF

CS

LQP

PDD

COI

0.307 0.187 0.426 0.221 0.307

0.362 0.426 0.307 0.260 0.187

0.158 0.307 0.158 0.187 0.260

0.307 0.158 0.426 0.26 0.362

0.307 0.187 0.362 0.187 0.187

0.187 0.158 0.095 0.187 0.187

0.158 0.426 0.260 0.362 0.307

0.260 0.426 0.307 0.307 0.362

0.041 0.035 0.035 0.035 0.041

0.049 0.049 0.049 0.095 0.095

0.035 0.057 0.080 0.049 0.041

1.000 0.969 0.974 0.989 0.941

WCT

OF

RSP

RP

MKE

CP

OTD

AOF

CS

LQP

PDD

COI

0.212 0.129 0.295 0.152 0.212

0.235 0.277 0.199 0.169 0.121

0.148 0.286 0.148 0.175 0.243

0.203 0.105 0.282 0.172 0.239

0.249 0.152 0.294 0.152 0.152

0.229 0.194 0.117 0.229 0.229

0.105 0.282 0.172 0.239 0.203

0.157 0.257 0.185 0.185 0.218

0.220 0.186 0.186 0.186 0.220

0.144 0.144 0.144 0.283 0.283

0.133 0.219 0.307 0.185 0.157

0.205 0.199 0.200 0.203 0.193

Supplier profile Flexibility and relationship Flexibility Supplier profile and relationship Service quality Risk Cost effective

0.5 0.34 0.5 0.13 0.573

0.66 0.5 0.66 0.29 0.733

Logistic outsourcing problem 893

Table VIII. Importance of alternatives w.r.t. each sub-objectives

Table IX. Relative weights of alternatives w.r.t. each sub-objectives

Service Cost quality Risk effective Weights 0.5 0.34 0.5 0.13 0.573

0.87 0.71 0.87 0.5 0.943

0.427 0.267 0.427 0.057 0.5

0.24 0.17 0.24 0.078 0.272

Table X. Pair-wise comparison matrix of objective

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Table XI. Pair-wise comparision matrix of sub-objectives

Pair-wise comparison of sub-objectives WCT WCT 0.5 OF 0.185 RSP 0.435 Pair-wise comparison of sub-objectives RP RP 0.5 MKE 0.75 CP 0.342 Pair-wise comparison of sub-objectives OTD OTD 0.5 AOF 0.815 CS 0.657 Pair-wise comparison of sub-objectives LQP LQP 0.5 PDD 0.342

Flexibility 0.24 WCT OF RSP Table XII. Weights of objectives and sub-objectives

0.424 0.102

0.199 0.048

0.377 0.09

of flexibility OF RSP 0.815 0.565 0.5 0.25 0.75 0.5 of supplier profile and relationship MKE CP 0.25 0.658 0.5 0.908 0.092 0.5 of service quality AOF CS 0.185 0.343 0.5 0.658 0.342 0.5 of risk PDD Weights 0.658 0.581 0.5 0.419

Supplier profile 0.17 RP MKE CP 0.31 0.053

0.501 0.085

0.189 0.032

Weights 0.424 0.199 0.377 Weights 0.31 0.501 0.189 Weights 0.221 0.446 0.333

Service quality 0.24 OTD A0 CS

Risk 0.078 LQP PDD

0.221 0.053

0.581 0.046

0.446 0.107

0.333 0.08

0.419 0.033

Cost effective 0.272 COI 1 0.272

It focuses on ranking and selecting the best alternative from a finite set of alternatives with conflicting criteria, and on proposing the compromise solution. The compromise solution is a feasible solution, which is the closest to the ideal solution, and a compromise means an agreement established by mutual concessions made between the alternatives. The following multiple attribute merit for compromise ranking is developed from the Lp-metric used in the compromise programming method. The VIKOR method is an effective MCDM tool, specifically applicable to those situations when the decision maker is not able, or does not know to express preference at the beginning of the decision making process. The compromise solutions can be the base for negotiations, involving the decision maker’s preference on criteria weights: ( Lp;i ¼

 M
X wj ½ðmij Þmax 2 mij
p ½ðmij Þmax 2 ðmij Þmin
j¼1

)1=p ð1Þ

where M is the number of criteria and N is the number of alternatives. The mij values (for i ¼ 1, 2, . . . , N; j ¼ 1, 2, . . . , M) denote the values of criteria for different alternatives. In the VIKOR method, L1,i and L1,i are used to formulate the ranking measures.

Step 1. Determine the value of Ei and Fi. Ei ¼ L1;i ¼

M X wj ½ðmij Þmax 2 mij
½ðmij Þmax 2 ðmij Þmin
j¼1

Fi ¼ L1;I ¼ Maxm of



ð2Þ

 wj ½ðmij Þmax 2 mij
½ðmij Þmax 2 ðmij Þmin


ð3Þ

Logistic outsourcing problem 895

Equation (2) is only applicable to beneficial attributes (whose higher values are desirable). For non-beneficial attributes (whose lower values are preferable), the term ½ðmij Þmax 2 mij
in Equation (2), is to be replaced by ½mij 2 ðmij Þmin . Hence, for non-beneficial attributes, Equation (2) can be rewritten as given below and shown in Table XIII: Ei ¼ L1;i ¼

m X wj ½mij 2 ðmij Þmin
½ðmij Þmax 2 ðmij Þmin
j¼1

ð4Þ

Step 2. Calculate Pi values as follows.

 Ei 2 Ei2min Fi 2 Fi2min Pi ¼ v þ ð1 2 vÞ Ei2max 2 Ei2min Fi2max 2 Fi2min Where Ei2 max and Ei2 min are the maximum and minimum values of Ei, respectively, and Fi2 max and Fi2 min are the maximum and minimum values of Fi, respectively. v is introduced as weight of the strategy of “the majority of attributes” (or “the maximum group utility”). Normally, the value of v is taken as 0.5. The compromise ranking list for a given v can be obtained by ranking with the Pi measure. The best alternative is the one having the minimum Pi value as shown in Table XIV. Values of E E3PL1 E3PL2 E3PL3 E3PL4 E3PL5

Values of F 0.637 0.477 0.513 0.745 0.340

F3PL1 F3PL2 F3PL3 F3PL4 F3PL5

Values of P P3PL1 P3PL2 P3PL3 P3PL4 P3PL5

0.272 0.131 0.151 0.222 0.085

Table XIII. Values of Ei and Fi

Rank 0.867 0.292 0.390 0.866 0

4 2 3 4 1

Table XIV. Values of Pi and rank of attributes

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4. Conclusions In this paper, ranking methods have been employed on a multi-criteria logistic outsourcing problem. The model has been framed and evaluated using two-phase methodology by using CFPR and VIKOR for weighting a hierarchical structure and ranking alternatives, present an accurate description of the TPL provider selection problem. The cost effective is the most appropriate objective on the basis of priority weight in the selection of 3PL provider for case company. The fifth 3PL provider has been placed at first position for case company. The combination of CFPR and VIKOR methodology seem to be beneficial in decision making manufacturing environment as well as to compare the results from other methods. In purposed methodology less pair-wise comparison is needed and there is no need to calculate eigenvalue and consistency ratio as compared to AHP method. Hence presented methodology is easier to implement and free from healthy mathematical calculation. Though a lot of advantages, there are limitation in this methodology as all the possible criteria could not added in this model and ranking of attribute may be change if a new attribute is added. This work can also be extended with the other outranking methods such as Modified TOPSIS and PROMETHEE techniques. The fuzzy multi-criteria evaluation methods in a fuzzy environment such as fuzzy AHP, fuzzy TOPSIS and fuzzy ANP can be implemented. Excel program and MATLAB coding can be developed and be made more user-friendly on the basis of this model. This methodology can combine with mathematical model for improvement. References Bask, A.H. (2001), “Relationships among TPL providers and members of supply chains – a strategic perspective”, Journal of Business & Industrial Marketing, Vol. 16 No. 6, pp. 470-86. C¸akir, E., Tozan, H. and Vayvay, O. (2009), “A method for selecting third party logistic party logistic provider using fuzzy AHP”, Journal of Naval Science and Engineering, Vol. 5 No. 3, pp. 38-54. Chakraborty, T., Ghosh, T. and Dan, P.K. (2011), “Application of analytical hierarchy process and heuristic algorithm in solving vendor selection problem”, Business Intelligence Journal, Vol. 4 No. 1, pp. 167-77. De Boer, L., Gaytan, J. and Arroyo, P. (2006), “A satisficing model of outsourcing”, Supply Chain Management: An International Journal, Vol. 11 No. 5, pp. 444-55. Gol, H. and Catay, B. (2007), “Third-party logistics provider selection: insights from a Turkish automotive company”, Supply Chain Management: An International Journal, Vol. 12 No. 6, pp. 379-84. Guo, J. and Zhang, W. (2008), “Selection of suppliers based on rough set theory and VIKOR algorithm”, Proceedings of the 2008 International Symposium on Intelligent Information Technology Application Workshops, pp. 49-52. Hamdan, A. and Rogers, K.J. (2008), “Evaluating the efficiency of 3PL logistics operations”, International Journal of Production Economics, Vol. 113 No. 1, pp. 235-44. Herrera-Viedma, E., Herrera, F., Chiclana, F. and Luque, M. (2004), “Some issues on consistency of fuzzy preference relations”, European Journal of Operational Research, Vol. 154 No. 1, pp. 98-109. Jharkharia, S. and Shankar, R. (2007), “Selection of logistics service provider: an analytic network process (ANP) approach”, Omega: The International Journal of Management Science, Vol. 35 No. 3, pp. 274-89.

Kaur, P., Verma, R. and Mahanti, N.C. (2010), “Selection of vendor using analytical hierarchy process based on fuzzy preference programming”, OPSEARCH, Vol. 47 No. 1, pp. 16-34. Kumar, S., Parashar, N. and Haleem, A. (2009), “Analytical hierarchy process applied to vendor selection problem: small scale, medium scale and large scale industries”, Business Intelligence Journal, Vol. 2 No. 2, pp. 355-62. Liu, P. and Wang, M. (2011), “An extended VIKOR method for multiple attribute group decision making based on generalized interval-valued trapezoidal fuzzy numbers”, Scientific Research and Essays, Vol. 6 No. 4, pp. 766-76. Opricovic, S. and Tzeng, G.H. (2002), “Multicriteria planning of post-earthquake sustainable reconstruction”, Comput Aid Civ Infrastruct Eng, Vol. 17 No. 3, pp. 211-20. Pang, B. (2009), “A fuzzy ANP approach to supplier selection based on fuzzy preference programming”, International Conference on Management and Service Science, pp. 1-4. Perc¸in, S. (2010), “Evaluation of third-party logistics (3PL) providers by using a two-phase AHP and TOPSIS methodology”, Benchmarking: An International Journal, Vol. 16 No. 5, pp. 588-604. Qureshi, M.N., Kumar, P. and Kumar, D. (2009), “Selection of 3PL services providers: a combined approach of AHP and graph theory”, International Journal of Services Technology and Management, Vol. 12 No. 1, pp. 35-60. Ramanathan, R. (2010), “The moderating roles of risk and efficiency on the relationship between logistics performance and customer loyalty in e-commerce”, Transportation Research Part E: Logistics and Transportation Review, Vol. 46 No. 6, pp. 950-62. Saen, R.F. (2010), “A new model for ranking 3PL providers”, Australian Journal of Basic and Applied Sciences, Vol. 4 No. 8, pp. 3762-9. Shemshadi, A., Shiraji, H., Toreihi, M. and Tarokh, M.J. (2011), “A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting”, Expert Systems with Applications, Vol. 38 No. 10, pp. 12160-7. Soh, S. (2010), “A decision model for evaluating third-party logistics providers using fuzzy analytic hierarchy process”, African Journal of Business Management, Vol. 4 No. 3, pp. 339-49. Sohail, M.S. and Sohal, A.S. (2003), “The use of third party logistics services: a Malaysian perspective”, Technovation, Vol. 23 No. 5, pp. 401-8. Van Goor, A.R., Amstel, M.J.P.V. and Amstel, W.P.V. (2003), European Distribution and Supply Chain Logistics, Wolters-Noordhoff, Groningen. Wang, T.C. and Chang, T.H. (2007), “Application of consistent fuzzy preference relations in predicting the success of knowledge management implementation”, European Journal of Operational Research, Vol. 182 No. 3, pp. 1313-29. Wang, T.C. and Lin, Y.L. (2008), “Applying consistent fuzzy preference relation to select merger strategy for financial organizations”, International Conference on Machine Learning and Cybernetics, pp. 222-7. Woo, H.S. and Saghiri, S. (2011), “Order assignment considering buyer, third-party logistics provider, and suppliers”, International Journal of Production Economics, Vol. 130 No. 2, pp. 144-52. Zeleny, M. (1982), Multiple Criteria Decision Making, McGraw-Hill, New York, NY. Zhang, J. (2009), “The research of 3PLs provider selection based on rough set and PSO”, IITA International Conference on Services Science, Management and Engineering, pp. 165-8.

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About the authors Raman Kumar holds a Bachelor’s degree in Mechanical Engineering from JCD Engineering College, Sirsa. Currently, he is pursuing a Master’s degree in Production Engineering from Guru Nanak Dev Engineering College, Ludhiana, India. He is doing his research work in the field of third party outsourcing. Raman Kumar is the corresponding author and can be contacted at: [email protected] Harwinder Singh holds a Bachelor’s degree in Mechanical Engineering, a Master of Business Administration degree, a Master’s degree in Production Engineering and a PhD in Mechanical Engineering. Currently, he is working as Associate Professor in the Department of Mechanical Engineering at Guru Nanak Dev Engineering College, Ludhiana, India. He has contributed a significant number of research papers at the international level. His present area of interest includes optimization techniques, decision making in manufacturing environment and management of production systems. J.S. Dureja holds a Bachelor’s Degree in Mechanical Engineering, a Master’s degree in Production Engineering and a PhD in Mechanical Engineering. Currently, he is working as Assistant Professor in the Department of Mechanical Engineering at University College of Engineering at Punjabi University, Patiala, India. He has contributed a significant number of research papers at the international /national level and is working the areas of reliability of manufacturing systems, and non-traditional manufacturing systems.

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Selection of logistic service provider using fuzzy PROMETHEE for a cement industry

Selection of LSP

Rajesh Gupta

Received 15 March 2011 Revised 15 November 2011 Accepted 24 November 2011

Department of Mechanical Engineering, Giani Zail Singh College of Engineering and Technology, Bathinda, India, and

899

Anish Sachdeva and Arvind Bhardwaj Department of Industrial and Production Engineering, Dr B.R. Ambedkar National Institute of Technology, Jalandhar, India Abstract Purpose – The purpose of this paper is to develop a method to select the best alternative in a multi-criteria decision making (MCDM) environment when the decision is taken by a group of members in an uncertain environment. Design/methodology/approach – In this paper, Fuzzy Preference Ranking Organization Method for Enrichment Evaluations (Fuzzy PROMETHEE) technique has been used for MCDM problems. The team of decision makers is constituted to integrate their opinion. The analysis is done using Geometrical Analysis for Interactive Aid (GAIA) plane, available in Decision Lab 2000 software, which provides valuable help in understanding the conflicts among criteria. Findings – The selection of best alternative is done on the basis of generally conflicting criteria. Fuzzy PROMETHEE technique has been proposed and the same is demonstrated using Decision Lab 2000 software. This software can be used for as many criteria as possible and also in a fuzzy environment, where the crisp data for criteria comparison are not available. It is found that the analysis of the results becomes very easy and effective with this software. A case study is conducted for a cement company to select the logistic service providers (LSPs) to demonstrate its ease and effectiveness of use. Originality/value – The research provides a model to choose the best alternative using Decision Lab 2000 software for Fuzzy PROMETHEE technique. The proposed methodology can be used in a fuzzy environment with ease and effectiveness. In the competitive scenario, this could help the industry in prompt and efficient decision making in MCDM problems. Keywords Computer software, Group decision support systems, Decision makers, Fuzzy PROMETHEE, Fuzzy analytic hierarchy process, Geometrical analysis for interactive aid, Multi-criteria decision making Paper type Research paper

1. Introduction The evaluation and selection of the best suitable alternative is a cumbersome job when the criteria, on the basis of which the best alternative is to be chosen, are conflicting. The multi-criteria decision making (MCDM) is the process of finding the best option from all of the feasible alternatives. Several approaches and relevant methods have been developed and proposed to deal with MCDM problems. One of the most recent methods is PROMETHEE that was developed by Brans (1982) which was further extended by Brans and Vincke (1985). It is a quite simple ranking method in conception and

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 899-921 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267727

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application compared with other methods used for multi-criteria analysis. It is well adapted to the problems where a finite set of alternatives are to be ranked according to several, sometimes conflicting criteria (Albadvi et al., 2007; Dagdeviren, 2008). The PROMETHEE is family of outranking methods, including the PROMETHEE I for partial ranking of the alternatives and the PROMETHEE II for complete ranking of the alternatives. The rankings are influenced by the weights allocated to the criteria. The PROMETHEE GDSS for group decision making (Macharis et al., 1998), and the visual interactive module GAIA for graphical representation (Mareschal and Brans, 1988; Brans and Mareschal, 1994) were developed to help in more complicated decision making situations. The GAIA plane, a descriptive tool, provides valuable help in understanding the conflicts among criteria and in dealing with the problem of the weights related to them. However, the PROMETHEE method like other traditional MCDM methods lack of ability to process fuzzy data in the actual decision making environment. To resolve the vagueness, ambiguity and subjectivity of human judgment, Zadeh (1965) introduced fuzzy sets theory to express the linguistic terms in the decision making process. Thus, applications on solving MCDM problems by fuzzy sets theory have been published in many professional journals of diversified disciplines. Ho (2006) combined the fuzzy set theory and PROMETHEE method developed the Fuzzy PROMETHEE, which is more flexible. Wang and Yang (2007) conducted a research on information systems outsourcing. They employed a hybrid integration of PROMETHEE II and AHP to provide powerful tools for ranking of candidate information systems and analyzing of the relations between criteria. Araz et al. (2007) developed a new multi-criteria sourcing method based on the PROMETHEE method, PROMSORT, to sort suppliers based on their preference relations and to select them for strategic partnership, supplier development programs, competitive partnership, and pruning. Dulmin and Mininno (2003) used PROMETHEE for an outsourcing research, applied for a mid-sized Italian firm operating in the field of public road and rail transportation, in order to choose the relevant suppliers. Leyva-Lo´pez and Ferna´ndez-Gonza´lez (2003) conducted a comparative study of PROMETHEE II for group decision with an extension of the ELECTRE III multi-criteria outranking methodology. In the context of transportation, Radojevic and Petrovic (1997) combined PROMETHEE and fuzzy IF-THEN rules to rank alternative roads in Belgrade-Birmingham route problem, based on four criteria: distance, traveling time, traveling cost, and road quality. Rao and Patel (2010) integrated PROMETHEE and AHP for decision making in manufacturing sector. They illustrated the method by giving four examples of real life situations. Brans and Mareschal (1994) proposed PROMETHEE I and II to rank 12 potential alternative sites based on five criteria, and PROMETHEE V to select the suitable sites under six constraints. The research intended to enhance the network of distribution centers in Europe for a large North American distribution company. Ferna´ndez-Castro and Jime´nez (2005) combined PROMETHEE II, III and V, based on fuzzy evaluations, to rank and select distribution centers for a firm in four areas of Belgium. Elevli and Demirci (2004) employed PROMETHEE I and II to select the most suitable underground ore transport system for a chromites mine in Turkey. The research included five possible ore transport systems and six criteria to evaluate them. Tuzkaya et al. (2010) integrated FANP and F-PROMETHEE for the selection of material handling equipment. Logistic outsourcing is seen as the management mantra now a days to reduce inventory, work in capital and initial investment which is further supplemented with

the professional approach of these experienced service providers. It has witnessed rapid growth in recent years. Preferably, the decision making is to be done by a team and not by a single person. Also in maximum of the situations in industry, the crisp data is not available for comparing two or more alternatives to take decision. So in this paper, we are proposing a fuzzy PROMETHEE GDSS approach to evaluate various alternatives. The proposed methodology is explained by conducting a case study to rank various logistic service providers (LSPs) for a cement company situated in the Northern part of India. The implementation of PROMETHEE requires two additional types of information, namely (Macharis et al., 2004): (1) Information on the relative importance (i.e. the weights) of the criteria considered. (2) Information on the decision-makers’ preference function, which he uses when comparing the contribution of the alternatives in terms of each separate criterion. As PROMETHEE cannot assign weights to the criteria so this is done using FAHP. For each criterion, the preference function translates the difference between the evaluations obtained by two alternatives into a preference degree ranging from 0 to 1. Brans and Vincke (1985) proposed six basic preference functions: (1) usual criterion; (2) U-shape criterion; (3) V-shape criterion; (4) level criterion; (5) V-shape with indifference criterion; and (6) Gaussian criterion. DMT is to choose any one of these for comparing two alternatives. By using Decision Lab software, DMs can improve the quality and reliability of the decision making processes, because of the structured procedure, accompanied by computational help, and the analytical aids. The methodology of the proposed fuzzy PROMETHEE GDSS is described in the next section. 2. Methodology First the DMT is constituted, then alternatives and the criteria are shortlisted. Then after, the weights of the criteria are calculated using FAHP and the rest of the calculations are completed via F-PROMETHEE approach. The detailed steps of each phase are discussed as follows. Step 1. Fuzzy logic to assign weights to the DMs Step 1.1. Constituting team. Decision-makers from various departments constitute DMT (Jharkharia and Shankar, 2007). Step 1.2. Define linguistic scale and their corresponding fuzzy number. This study adopts four linguistic variables, which are one of eight kinds of linguistic terms proposed by Chen and Hwang (1992), namely “low”, “medium”, “high” and “very high”, which were expressed in triangular fuzzy numbers (Table I).

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Step 1.3. Assigning weights to DMs by developing fuzzy conversion scale. As the DMs have different experience, designation and qualification, there opinion enjoys different weights in the decision making, so the weights have been assigned to the analysts on this basis. By merging the opinions of almost everybody in the senior management, it is established that the opinion of the DM with more experience, higher designation and higher qualification is more reliable. The linguistic variables for the experience, designation and qualification can be quantified using triangular fuzzy numbers as per Table I. These linguistic variables can be expressed in positive triangular fuzzy numbers, as shown in Figure 1. Step 2. Generation of criteria The DMT shortlist the various criteria on the basis of which final selection of the alternatives will be done. As the objective function is different for different companies, the criteria chosen are just a matter of subjectivity to a specific requirement. Define a vector containing the weights, which are a measure for the relative importance of each criterion, w T ¼ [w1, . . . , wn]. Where “n” is the number of criteria. If all the criteria are of the same importance in the opinion of the DM, all weights can be taken as being equal. Step 3. Assigning weights to the criteria The weight factors to be assigned to the criteria chosen are proposed to be obtained using FAHP. Step 3.1. Pairwise comparison of the criteria. Each DM is asked to do the pairwise comparison of the criteria with respect to the overall goal to assess the weights using fuzzy linguistic scale (Table II). The data is further converted to fuzzy triangular number (Kahraman et al., 2007). The fuzzy synthetic extent analysis based FAHP technique is used to determine the weights for the criteria.

Table I. Triangular fuzzy conversion scale

Experience

Linguistic scale

0 to , 10 10 to , 20 20 to , 30 30 and above

Low Medium High Very high

FTN (0.0, (0.2, (0.4, (0.6,

0.2, 0.4, 0.6, 0.8,

0.4) 0.6) 0.8) 1.0)

Designation

Qualification

Up to manager Manager to SM SM to GM Sr GM and above

Under graduate Graduate Specialized graduation Post graduate

Notes: SM – senior manager; GM – general manager

LOW (L)

AVERAGE (AVG) HIGH (H) VERY HIGH (VH)

1

Figure 1. Linguistic scale for assigning weights to experience, designation and qualification of DM 0.0

0.2

0.4

0.6

0.8

1.0

Triangular fuzzy scale

Linguistic scale Just equal ( JE) Equally more important (EMI) Weakly more important (WMI) Strongly more important (SMI) Very strongly more important (VSMI) Absolutely more important (AMI)

(1, 1, 1) (0.5, 1, 1.5) (1, 1.5, 2) (1.5, 2, 2.5) (2, 2.5, 3) (2.5, 3, 3.5)

Reciprocal linguistic scale Just equal ( JE) Equally less important (ELI) Weakly less important (WLI) Strongly less important (SLI) Very strongly less important (VSLI) Absolutely less important (ALI)

Triangular fuzzy reciprocal scale (1, 1, 1) (0.667, 1, 2) (0.5, 0.667, 1) (0.4, 0.667, 1)

903

(0.333, 0.4, 0.5) (0.286, 0.33, 0.4)

The pairwise comparison matrix will be obtained as shown below: 3 2 ð1; 1; 1Þ ðl 12 ; m12 ; u12 Þ . . . ðl 1n ; m1n ; u1n Þ A1 7 6 ð1; 1; 1Þ . . . ðl 2n ; m2n ; u2n Þ 7 A2 6 7 6 ðl 21 ; m21 ; u21 Þ 7 6 d ~ 7 6 Ad ¼ ð~aij Þn£n ¼ . 6 7 . . . . .. 6 .. .. .. .. 7 7 6 5 4 An ðl n1 ; mn1 ; un1 Þ ðl n2 ; mn2 ; un2 Þ . . . ð1; 1; 1Þ

ð1Þ

where a~ ij is the relative importance of ith criterion over jth criterion as assigned by dth DM. Where d ¼ 1; 2; . . . ; D and “D” is the number of total DMs. Step 3.2. Obtaining decision comparison matrices. Total of “D” decision comparison matrices are obtained, one from each DM. As the weights of the DMs are different, the weighted comparison matrix for all DMs is obtained as below: ðb~ ij Þn£n ¼ ðeij ; f ij ; gij Þ ¼

d¼D X

wd ^ð~aij Þdn£n

ð2Þ

d¼1

for i # j and wd ¼ individual weight of the dth DM and:
 1 1 1 21 ~ ~ ðbij Þn£n ¼ ðbji Þn£n ¼ ; ; for gji f ji eji

i.j

ð3Þ

To calculate a priority vector of the above triangular fuzzy comparison matrix (Chang, 1996; Sachdeva et al., 2009) suggested an extent analysis method, which is summarized as follows. Step 3.3. Find the sum of each row of the fuzzy comparison matrix by fuzzy arithmetic operations. ! j¼n j¼n j¼n j¼n X X X X ~Sri ¼ ~bij ¼ ~ e~ ij ; fij ; g~ ij ð4Þ j¼1

j¼1

j¼1

j¼1

Selection of LSP

Table II. Triangular fuzzy conversion scale

JMTM 23,7

Where S~ ri is the sum of ith row. Step 3.4. Find the sum of all the rows as per the following equation. i¼n X S~ ri S~ t ¼

ð5Þ

i¼1

904

Step 3.5. Divide the sum of each row by the sum total of all the rows as per the following equation. ð6Þ S~ t ¼ S~ ri ^½S~ t
21 To obtain the estimates for the vectors of weights under each criterion, principal of comparison of fuzzy numbers need to be applied. It is required to determine the degree of possibility of greatest or least fuzzy number among the several fuzzy synthetic extents. Step 3.6. Compute the degree of possibility of S~ i $ S~ j by the following equation. 8 1 if f i $ f j > > < g i 2ej VðS~ i $ S~ j Þ ¼ ðgi 2f i Þþð f j 2ej Þ if ej # gi i; j ¼ 1; . . . ; n; j – i ð7Þ > > :0 others Step 3.7. Computing degree of possibility. Calculate the degree of possibility of S~ i over all other (n 2 1) fuzzy numbers by: V ðS~ i $ S~ j j j ¼ 1; . . . ; n; j – i Þ ¼ |{z} min VðS~ i $ S~ j Þ;

i ¼ 1; . . . ; n

j[{1; ... ;n}; j–i

If

d 0 ðAi Þ ¼ min VðS~ i $ S~ j Þ

ð8Þ

Then, for j ¼ 1, . . . ,n; j – i, the weight vector is given by: W 0 ¼ ðd0 ðA1 Þ; d0 ðA2 Þ; . . . ; d0 ðAn ÞÞT

ð9Þ

Normalizing the weight vector, we get the weights of the criteria: W ¼ ðdðA1 Þ; dðA2 Þ; . . . ; dðAn ÞÞT

ð10Þ

where W and W0 are non-fuzzy numbers and are the weights of the criteria. Step 4. Generation of alternatives Through brainstorming sessions, all the DMs jointly reach a consensus and shortlist the possible alternatives including their extended description (e.g. strategies, investments, locations, production schemes, marketing actions, etc depending on the problem). This brainstorming procedure is extremely useful; it often generates alternatives that were unforeseen at the beginning. Step 5. Fuzzy PROMETHEE The basic steps of the PROMETHEE algorithm can be outlined as described by Brans et al. (1986) and Geldermann et al. (2000). In this study, the F-PROMETHEE technique is preferred because of the fuzzy nature of the decision problem. Goumas and Lygerou (2000), Bilsel et al. (2006), Geldermann et al. (2000) and Chou et al. (2007) have used F-PROMETHEE earlier for MCDM problems.

Step 5.1. Formulate individual evaluation tables. In the decision making, we come across various types of multi criteria problems, e.g. to maximize {g1(a), g2(a), . . . , gn(a)ja]k} where “k” is subset of finite number of possible alternatives, out of which one best alternative is to be selected. {g1(a),g2(a), . . . , gn(a)} is set of criteria on the basis of which the alternatives are to be evaluated. All the shortlisted alternatives are evaluated against each criterion selected for the evaluation. Then we get the evaluation matrix of (k £ n) size as shown below. All the DM’s execute the same matrix. It is the judgment or preference of the DM to evaluate each alternative on each criterion either by the crisp value (if such data is available, e.g. “price” of owing one alternative) or on fuzzy scale (if the crisp data cannot be obtained, e.g. “reliability” of the alternative) (Chou et al., 2007). For further detail about PROMETHEE methodology, please see for instance Brans (1982), Brans et al. (1984, 1986), Brans and Mareschal (1994) and Mareschal and Brans (1988) (Table III). Step 5.2. Determine the deviations based on pairwise comparisons. dj ða; bÞ ¼ gj ðaÞ 2 gj ðbÞ

Selection of LSP

905

ð11Þ

where dj(a,b) is the difference between the evaluation of “a” and “b” on jth criterion. Step 5.3. Determine the preference of “a” with regard to “b” (Pj(a,b)). For small deviations, the DM will allocate a preference to the better alternative. This means that for each criterion, the decision-maker has in mind one of the six preference function proposed by Brans and Vincke (1985): Pj ða; bÞ ¼ fj ½dj ða; bÞ


;

a; b [ A

and

0 # Pj ða; bÞ # 1

ð12Þ

In case of a criteria to be maximized (e.g. higher the “reliability”, better the alternative is), larger dj(a,b) means the preference of “a” over “b”. Reverse is the case when the criteria is to be minimized (e.g. “price”, i.e. lower the price, better is the alternative), i.e. Pj(a,b) ¼ f [2 dj(a,b)]. In this study, PROMETHEE’s usual function has been chosen which is mostly used with qualitative criteria (Figure 2). a

g1 ( )

g2( )

...

gj( )

...

gn( )

a1 .a. 1 . a. i .. ak

g1(a1) g .. 1(a2) . g .. 1(ai) . g1(ak)

g2(a1) g .. 2(a2) . g .. 2(ai) . g2(ak)

... ... ... ... ... ...

gj(a1) g .. j(a2) . g .. j(ai) . gj(ak)

... ... ... ... ... ...

gn(a1) g .. n(a2) . g .. n(ai) . gn(ak)

Type 2: p U-shape 1 Criterion P(d) =

o

q

d

Table III. Evaluation table

{ 10 dd >≤ qq Figure 2. Usual preference function

JMTM 23,7

Step 5.4. Calculate the global preference index. Calculate the global preference index for the preference of “a” over all other alternatives and preference of all other alternatives over “a”:

p ða; bÞ ¼

j¼k X

Pj ða; bÞwj

ð13Þ

j¼1

906 p ðb; aÞ ¼

j¼k X

Pj ðb; aÞwj

;

a; b [ A

ð14Þ

j¼1

where p (a,b) is the weighted sum of Pj(a,b) for each criterion and wj. p (a,b) is expressing with which degree “a” is preferred to “b” over all the criteria and p (b,a) how “b” is preferred to “a”. The following properties hold for all a,b]A: 8 p ða; aÞ ¼ 0; > > > > > < 0 # p ða; bÞ # 1; 0 # p ðb; aÞ # 1; > > > > > : 0 # p ða; bÞ þ p ðb; aÞ # 1 It is clear that p (a,b) < 0 implies a weak preference of a over b and p (a,b) < 1 implies a strong preference of a over b. Step 5.5. Determining positive outranking flow. Each alternative “a” is facing (k 2 1) other alternatives in the set of “A” alternatives. As a measure for the strength of alternatives a’A, the leaving flow (positive outranking flow or “outranking character” of “a”) is calculated as per the following equation: Fþ ðaÞ ¼

n 1 X p ða; bÞ k 2 1 b]A

ð15Þ

Step 5.6. Determining negative outranking flow. As a measure for the weakness of the alternatives a]A, the entering flow (negative outranking flow or “outranked character” of “a”) is calculated as per the following equation: n 1 X F2 ðaÞ ¼ p ðb; aÞ ð16Þ k 2 1 b]A The positive outranking flow expresses how an alternative is outranking all the others. It is its power, its outranking character. Higher the Fþ ðaÞ, better the alternative. The negative outranking flow expresses how an alternative is outranked by all the others. It is its weakness, its outranked character. Lower the F2 ðaÞ, better the alternative. Step 5.7. Determination of PROMETHEE I partial ranking. The PROMETHEE I partial ranking is obtained from the positive and negative outranking flows. In PROMETHEE I, alternative “a” is preferred to alternative “b” (i.e. aPb), if at least one of the elements of following equations is satisfied (Dagdeviren, 2008):

a P b0

if : Fþ ðaÞ . Fþ ðbÞ and F2 ðaÞ , F2 ðbÞ or þ

þ

2

Selection of LSP

2

F ðaÞ . F ðbÞ and F ðaÞ ¼ F ðbÞ or Fþ ðaÞ ¼ Fþ ðbÞ and F2 ðaÞ , F2 ðbÞ PROMETHEE I evaluation allows indifference and incomparability situations. Two alternatives are indifferent, if both “a” and “b” has the same leaving and entering flows: i:e:

a I b0

if : Fþ ðaÞ ¼ Fþ ðbÞ and F2 ðaÞ ¼ F2 ðbÞ

Two alternatives are considered incomparable, if alternative “a” is better than alternative “b0 ” in terms of leaving flow, while the entering flows indicate the reverse: i:e:

a R b0

if : Fþ ðaÞ . Fþ ðbÞ and F2 ðaÞ . F2 ðbÞ

or Fþ ðaÞ , Fþ ðbÞ and F2 ðaÞ , F2 ðbÞ PROMETHEE I fails to rank if two or more alternatives are indifferent or incomparable. Then net outranking flow is used for complete ranking as per PROMETHEE II. It is always recommendable to consider both PROMETHEE I and PROMETHEE II for the analysis purpose. Step 5.8. Ranking of alternatives. Calculate the net outranking flow to obtain PROMETHE II complete ranking. The net flow values of alternatives can be calculated as follows: Fnet ðaÞ ¼ Fþ ðaÞ 2 F2 ðaÞ

ð17Þ

Here, if net flow of the alternative “a” is bigger than the net flow of the alternative “b”, then alternative “a” outranks “b”. Step 6. Individual PROMETHEE-GAIA analysis The evaluation matrix of (k £ n) size obtained in Step 5.1 for each DM with assigned criteria weights can be used to find PROMETHEE I and II rankings using Decision Lab software. GAIA plane provides valuable help in understanding the conflicts among criteria and in dealing with the problem of the weights related to them. The net outranking flow of alternatives and the GAIA plane of each DM are collected. Step 7. Group decision The PROMETHEE GDSS has been developed to provide decision aid to a group of decision-makers (DM1,DM2, . . . , DMd). An additional global evaluation is done by the group. At the end, the consensus is reached to take the final decision. The net outranking flow {Fnet ðaÞ} vectors of all the DM’s are collected and put in a (k £ d) matrix as follows: w1

w2

...

wd

DM1

DM2

...

DMd

907

8 net F11 ðA1 Þ Fnet > 12 ðA1 Þ > > > > net net > > > F21 ðA2 Þ F22 ðA2 Þ > > < .. .. . . > > > .. .. > > . . > > > > > net : Fnet k1 ðAk Þ Fk2 ðAk Þ

JMTM 23,7

908

... ... .. . .. . ...

9 Fnet 1d ðA1 Þ > > > > net > F2d ðA2 Þ > > > > > = .. . > > > .. > > . > > > > net ; Fkd ðAk Þ >

ð18Þ

k£d

Fnet kd ðAk Þ

where is the net flow of kth alternative by dth DM, wd is the weight of the dth DM. The final weighted net flow of jth alternative by all “d” DMs is calculated using the following equation: 9 8 net F1 ðA1 Þ > > > > > > > > > > net > > ðA Þ F > > 2 2 > > > > > > i¼d = < X . . net net . Fi ðAj Þ^wi ¼ ð19Þ Fj ðAj Þ ¼ > > > > i¼1 > > . > > .. > > > > > > > > > > > net ; : Fk ðAk Þ > k£1

where “j” varies from 1 to k. Here, in (k £ d) matrix, each criterion of this matrix expresses the point of view of a particular DM. Each of these criteria has a weight of wd. The conflicts between them are clearly visualized in the GAIA plane. Each of these DM has a weight which can be varied for sensitivity analysis. A global PROMETHEE II ranking and the associated GAIA plane are then computed. The associated PROMETHEE decision axis gives the direction in which to decide according to the weights allocated to the DM’s. If the conflicts are too sensitive, the DMT could reconsider the decision making process in the backward direction, i.e. from the weighting of the DM’s to the individual evaluations and finally back to the set of criteria and alternatives. The whole procedure can be summarized through Figure 3. Step 8. Sensitivity analysis A special feature of the software, called the walking weights, allows to modify the weights of different criteria and to observe the resulting modifications of the PROMETHEE II ranking. 3. Case study To foster the better understanding of the proposed methodology, a real world application is investigated. This application is realized in a cement manufacturing company (named ABC) which is located in Northern part of India. ABC is one of the biggest cement producing company and has an important worldwide market share. The management is interested to select the LSPs who could take up the responsibility to transport cement to the consumption points all over India. There are many LSPs available but the management is interested to choose one for long-term perspective.

individual evaluation matrix (k × n) (total d matrices)

individual net flow (k × 1) (total d matrices)

w1 DM1

w2 DM2

k×n

k×n

k×n

φ11net(A1)

φ12net(A1)

φ1dnet(A1)

φ21net(A2)

φ22net(A2)

φ2dnet(A2)

φk1net(Ak)

φk2net(Ak) w2

w1

global evaluation (k × d) matrix) (total one matrix)

....

....

Selection of LSP

wd DMd

..... .....

909

φkdnet(Ak) wd

.....

φ11net(A1)

φ12net(A1)

φ1dnet(A1)

φ21net(A2)

φ22net(A2)

φ2dnet(A2)

φk1net(Ak)

φk2net(Ak)

φkdnet(Ak)

φ1net(A1) final weighted net flow (k × 1) matrix

φ2net(A2)

Figure 3. Overview of PROMETHEE GDSS process

φknet(Ak)

To rank the alternatives, we proposed a methodology which explained in Section 2. A team of three members (named DM1, DM2 and DM3) from different departments is constituted (Step 1). They are well aware of the company requirement and are authorized to take final decision. DM1 is Sr manager having an experience of 32 years with the degree of BE (Mechanical), DM2 is Sr GM with an experience of 22 years with the degree of MBA and DM3 is Sr GM having experience of 35 years with MBA qualification. So the weights given to these DMs (Table I) are as follows (Table IV). The evaluation criteria used for the selection of best alternatives have been widely discussed by many researches (Jharkharia and Shankar, 2007; Lynch, 2002; Razzaque and Sheng, 1998; van Hoek, 2001). The DMT identifies all possible decision criteria specific to the requirement through brain storming session (Step 2) and finally shortlist

Designation Qualification Experience Aggregate weights Defuzzified value DM1 0.4, 0.6, 0.8 DM2 0.6, 0.8, 1 DM3 0.6, 0.8, 1

0.4, 0.6, 0.8 0.6, 0.8, 1 0.6, 0.8, 1

0.6, 0.8, 1 0.096, 0.288, 0.64 0.4, 0.6, 0.8 0.144, 0.384, 0.8 0.6, 0.8, 1 0.216, 0.512, 1

0.341333 0.442667 0.576

Normalized weight 0.25 0.32 0.42

Table IV. Assignment of weights to experts

JMTM 23,7

910

five criteria namely environmental conditions, price, geographic location, reliability and flexibility. These criteria are named as C1, C2, C3, C4 and C5, respectively. F-AHP is used to assign weights to these criteria (Step 3). This stage begins with the DMT’s linguistic preferences for the pair-wise comparisons of the criteria (Step 3.1). Here, each DM compares the evaluation criteria linguistically according to their affect on the realization of the main goal and is converted to fuzzy triangular number (Table V) using Table II. The weighted comparison matrix for all the DMs is obtained (Step 3.2) using equations (2) and (3). Then sum of the individual row (Step 3.3) is calculated as per equation (4) and the sum total of all the rows (Step 3.4) using equation (5). Divide the sum of each row by the sum total of all the rows (Step 3.5) using equation (6). We get Table VI. Compute the degree of possibility of S~ i $ S~ j where i, j ¼ 1, . . . ,n; j – i (Step 3.6). For clarity, the calculations for the degree of possibility of S1 . S2 is shown below:

C1 C2 C3 C4 Table V. Pair wise comparison of each criterion by each DM

C5

DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3

C1 C1 (1, 1, 1)

Table VI. The weighted comparison matrix for all DMs and the alternative row sum

C1

C2

C3

C4

C5

(1, 1, 1) (1, 1, 1) (1, 1, 1) (1.5, 2, 2.5) (1, 1.5, 2) (1.5, 2, 2.5) (0.4, 0.5, 0.667) (0.667, 1, 2) (0.5, 0.667, 1) (0.5, 1, 1.5) (0.5, 1, 1.5) (0.5, 1, 1.5) (0.5, 0.667, 1) (0.5, 1, 1.5) (1, 1.5, 2)

(0.4, 0.5, 0.667) (0.5, 0.667, 1) (0.4, 0.5, 0.667) (1, 1, 1) (1, 1, 1) (1, 1, 1) (0.286, 0.333, 0.4) (0.286, 0.333, 0.4) (0.286, 0.333, 0.4) (0.5, 0.667, 1) (0.5, 0.667, 1) (0.5, 0.667, 1) (0.5, 0.667, 1) (0.4, 0.5, 0.667) (0.4, 0.5, 0.667)

(1.5, 2, 2.5) (0.5, 1, 1.5) (1, 1.5, 2) (2.5, 3, 3.5) (2.5, 3, 3.5) (2.5, 3, 3.5) (1, 1, 1) (1, 1, 1) (1, 1, 1) (2.5, 3, 3.5) (2, 2.5, 3) (2, 2.5, 3) (1, 15, 2) (0.5, 1, 1.5) (1.5, 2, 2.5)

(0.667, 1, 2) (0.667, 1, 2) (0.667, 1, 2) (1, 1.5, 2) (1, 1.5, 2) (1, 1.5, 2) (0.286, 0.333, 0.4) (0.33, 0.4, 0.5) (0.33, 0.4, 0.5) (1, 1, 1) (1, 1, 1) (1, 1, 1) (0.5, 0.667, 1) (0.4, 0.5, 0.667) (0.667, 1, 2)

(1, 1.5, 2) (0.667, 1, 2) (0.5, 0.667, 1) (1, 1.5, 2) (1.5, 2, 2.5) (1.5, 2, 2.5) (0.5, 0.667, 1) (0.667, 1, 2) (0.4, 0.5, 0.667) (1, 1.5, 2) (1.5, 2, 2.5) (0.5, 1, 1.5) (1, 1, 1) (1, 1, 1) (1, 1, 1)

C2

C3

(0.43, 0.55, (0.97, 1.47, 0.77) 1.97) C2 (1.34, 1.84, (1, 1, 1) (2.5, 3, 3.5) 2.34) C3 (0.53, 0.73, (0.29, 0.33, (1, 1, 1) 1.23) 0.4) C4 (0.5, 1, 1.5) (0.5, 0.66, (2.13, 2.63, 1) 3.13) C5 (0.71, 1.12, (0.43, 0.54, (1.05, 1.55, 1.58) 0.75) 2.05) Sum total of all rows ¼

C4

C5

(0.667, 1, 2) (0.68, 0.99, 1.58) (1, 1.5, 2) (1.37, 1.87, 2.37) (0.32, 0.38, (0.51, 0.70, 0.47) 1.18) (1, 1, 1) (0.95, 1.45, 1.95) (0.54, 0.75, (1, 1, 1) 1.32)

Sum of row elements (3.75, 5.01, 7.32) (7.16, 9.18, 11.18) (2.63, 3.099, 4.08) (5.06, 6.73, 8.56) (3.42, 4.66, 6.20) (22.025, 28.68, 37.36)

Dividing each row sum by sum total of all rows (0.1004, 0.3325) (0.1917, 0.5079) (0.0703, 0.1855) (0.1354, 0.3889) (0.0914, 0.2816)

0.1748, 0.3199, 0.1081, 0.2346, 0.1623,

As ej # gi for this case; so VðS~ 1 $ S~ 2 Þ ¼ ¼

g i 2 ej ðgi 2 f i Þ þ ð f j 2 ej Þ

Selection of LSP

ð0:3325 2 0:1917Þ ¼ 0:492414 ð0:3325 2 0:1748Þ þ ð0:3199 2 0:1917Þ

911 Similarly, VðS~ 1 $ S~ 3 Þ ¼ 1:341191, VðS~ 1 $ S~ 4 Þ ¼ 0:767109 and VðS~ 1 $ S~ 5 Þ ¼ 1:054428. So d 0 (A 1 ) ¼ min[VðS~ 1 $ S~ j Þ] ¼ min[0.492414, 1.341191, 0.767109 and 1.054428] ¼ 0.492414 (Table VII). The calculated values for [d0 (C1), d0 (C2), d0 (C3), d0 (C4) and d0 (C5)] are [0.4924, 1.0, 0.0, 0.6980, 0.3632]. After normalizing we get the weights of the criteria (C1, C2, C3, C4 and C5) as (0.193, 0.392, 0.0, 0.273 and 0.142), respectively, (Step 3.7). This shows that the importance of the criteria “C3, i.e. geographic location” is negligible and hence can be removed from the list of criteria for the evaluation of the alternatives. For the ranking purpose, most of the companies usually consider four to eight potential alternatives (Vaidyanathan, 2005). DMT identifies all the probable LSPs for logistic outsourcing from the internet, industrial directories, conferences, journals, self-experience, personal rapport, by calling request for proposal or from any other possible source. The LSPs, which are evaluated average or below in the linguistic scale by any of the DMs on any of the selected four criteria (environmental conditions, price, reliability and flexibility), are rejected. At the end, DMT shortlists the most suitable four alternatives (named A1, A2, A3 and A4) for further evaluations (Step 4). Now after the criteria, the criteria weights and LSPs (alternatives) are shortlisted, Fuzzy PROMETHEE calculations are realized for the ranking of these LSPs. Now each DM is asked to evaluate each alternative on each criterion as discussed in Step 5 (Table III). As the data for all the criteria cannot be taken in the crisp value so the evaluation for environmental conditions, reliability and flexibility is done on linguistic scale (Step 5.1). The crisp data for the criterion price is made available to the DMs and they are asked to evaluate the criteria “price” on linguistic scale as well. We get the evaluation Table VIII. The preference of “a” with regard to “b” on each criterion is determined (Steps 5.2 and 5.3). Then the global preference index for the preference of “a” over all other alternatives [Fþ (a)], preference of all other alternatives over “a” [F2 (a)] and the net outranking flow is calculated for each DM (refer equations (12)-(17) and from Steps 5.4 to 5.8). For clarity, it is shown in details (Tables IX-XIII) for DM1. The results for DM2 and DM3 are shown in Tables XIV and XV. .

S1 . S2 0.4924 S2 . S1 1.5534 S3 . S1 0.5605 S4 . S1 1.2617 S5 . S1 0.9357 S1 . S3 1.3412 S2 . S3 1.9387 S3 . S2 20.030 S4 . S2 0.6981 S5 . S2 0.3632 S1 . S4 0.7671 S2 . S4 1.2971 S3 . S4 0.2835 S4 . S3 1.6588 S5 . S3 1.3455 S1 . S5 1.0544 S2 . S5 1.6089 S3 . S5 0.6342 S4 . S5 1.3209 SS5 . S4 0.6691 Minimum 0 *(equation (2)) 0.6980 0.3632 value 0.4924 1 *(equation (2)) Normalized wts 0.1928 0.3916 0 0.2734 0.1422

Table VII. The degree of possibility of S~ i $ S~ j

JMTM 23,7 A1 A2

912 A3 Table VIII. Evaluation table of each alternative on each criterion by each DM

A4

PRICE Table IX. Preference of “a” with regard to “b” on price

Table X. Preference of “a” with regard to “b” on reliability

Table XI. Preference of “a” with regard to “b” on flexibility

Table XII. Preference of “a” with regard to “b” on EC

DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3

Price

Reliability

Flexibility

Economic conditions

VH VH H VL L L VVL VL L VL VL L

VVH VVH H VH A A H VH VH VH H H

VVH H VH VH H H L L A H L L

VH VH VH H H H A A A A H H

A1

A1 A2 A3 A4

A2

A3

A4

0

0 0

0 0 1

1* 1 1

1 0

0

A2

A3

A4

1

1 1

1 0 0

REL

A1

A1 A2 A3 A4

0* 0 0

0 0

1

FLEX

A1

A2

A3

A4

1

1 1

1 1 0

A1 A2 A3 A4

0* 0 0

EC

A1

A1 A2 A3 A4

0* 0 0

0 0

1

A2

A3

A4

1

1 1

1 1 0

0 0

0

AGGREGATE A1 A2 A3 A4 [F2 (a)] equation (16)

Net flow [Fnet (a)] Ranking [Fþ (a)] equation (15) equation (17) of LSPs

A1

A2

A3

A4

0 0.392 * 0.392 0.392 0.392

0.608 0 0.392 0 0.333

0.608 0.608 0 0.415 0.544

0.608 0.335 0.392 0 0.445

0.608 0.445 0.392 0.269

0.216 0.1127 2 0.152 2 0.176

1 2 3 4

Note: ( *cell value for A2A1 for price £ wt of P) þ ( *cell value for A2A1 for price £ wt of R) þ ( *cell value for A2A1 for price £ wt of flex) þ ( * cell value for A2A1 for price £ wt of EC) ¼ (1 £ 0.392) þ (0 £ 0.273) þ (0 £ 0.142) þ (0 £ 0.193) ¼ 0.392

AGGREGATE A1 A2 A3 A4 [F2 (a)] equation (16)

AGGREGATE A1 A2 A3 A4 [F2 (a)] equation (16)

A1 0 0.392 0.665 0.392

A1

A2

A3

A4

0 0.392 0.392 0.392 0.392

0.466 0 0.665 0.665 0.5987

0.608 0.335 0 0.193 0.3787

0.608 0.142 0.273 0 0.341

A2

A3

A4

0.608 0 0.273 0.273

0.335 0.335 0 0.193

0.335 0.142 0.415 0

Net flow [Fnet (a)] [Fþ (a)] equation (15) equation (17) 0.5607 0.2897 0.4433 0.4167

0.1687 20.3090 0.0647 0.0757

Net flow [Fnet (a)] [Fþ (a)] equation (15) equation (17) 0.4260 0.2897 0.4510 0.2860

2 0.0570 2 0.0950 0.1633 2 0.0113

Selection of LSP

913 Table XIII. the global preference index for DM1

Ranking of LSPs 1 4 3 2

Table XIV. The global preference index for DM2

Ranking of LSPs 3 4 1 2

0.483 0.384667 0.287667 0.297333

PROMETHEE I and PROMETHEE II ranking is drawn for DM1 using Decision Lab software (Figures 4 and 5). PROMETHEE I cannot explain the dominance of any single alternative, whereas PROMETHEE II gives the ranking in the preference order of A1 . A2 . A3 . A4 which is similar to the ranking we get as per Table XIII. Step 6 GAIA plane is a powerful graphical visualization tool for the analysis of a multicriteria problem. The discriminating power of the criteria, the conflicting aspects, as well as the “quality” of each alternative on the different criteria is becoming particularly clear. GAIA plane is drawn for DM1 (Figure 6). The following inferences can be drawn from the GAIA plane diagram: . The criteria flexibility and environmental condition are expressing similar preferences and alternatives A1 and A2 are good on these criteria.

Table XV. The global preference index for DM3

JMTM 23,7

3

1 A1

A3

Φ+

0.61

Φ+

0.39

Φ–

0.39

Φ–

0.54

914

2

4 A2

Figure 4. PROMETHEE I (partial ranking) for DM1

A4

Φ+

0.44

Φ+

0.27

Φ–

0.33

Φ–

0.44

1

3 A1 Φ

A3 Φ

0.22

Figure 5. PROMETHEE II (complete ranking) for DM1

–0.15

2

4 A2 Φ

A4 Φ

0.11

A4

A3 P

R Flex A2 Pl EC

Figure 6. GAIA plane for DM1

–0.18

A1

. . . . .

Selection of LSP

Criterion reliability is strongly conflicting with criterion price. The alternative A3 and A4 are good on criteria price. The alternative A1, A2 and A4 are good on criteria reliability. The criteria environmental condition and price are independent. The criteria flexibility and reliability are independent.

The decision axis “pi” is the weighted resultant of all the criteria axes. As “pi” is not long enough, the PROMETHEE decision axis has no strong decision power. Hence, the final choice for alternative A1 has a weak preference. In the same way, the entering flow, leaving flow and net flow is calculated for all other DMs (shown in Table XIV for DM2 and in Table XV for DM3). The PROMETHEE II complete ranking for DM2 and DM3 are shown in these tables for the reference and their analysis is not discussed here.

915

Step 7. Group decision The PROMETHEE GDSS has been developed to provide decision aid to a group of decision-makers. The aggregate group ranking is done using equation (19) as explained in Figure 3. We get Table XVI. The final group ranking of the alternatives is A1 . A3 . A4 . A2. The same can also be done using Decision Lab software. The PROMETHEE I partial ranking and PROMETHEE II complete ranking for the group decision are shown in Figures 7 and 8. Based on this partial ranking, A1 outranks all other alternatives and A2 is the worst choice. Similar results are displayed by PROMETHEE II. The final ranking of the group decision is A1 . A3 . A4 . A2. GAIA plane is drawn for group decision. Here, in (k £ d) matrix, each criterion of this matrix expresses the point of view of a particular DM. Each of these criteria has a weight of wd. The conflicts between them are clearly visualized in the GAIA plane (Figure 9). The following inferences can be drawn from the GAIA plane diagram: . DM1 and DM3 are is strongly conflicting with each other. . DM3 prefers alternative A3 and A4 and strongly reject A1 and A2. 0.26 Wts of DMs A1 A2 A3 A4

1

0.42

i¼d X

DM1

0.32 Net flow by DMs DM2

DM3

i¼1

0.216 0.112 2 0.152 2 0.176

0.169 20.309 0.065 0.076

20.057 20.095 0.163 20.011

2 Φ+ Φ–

A1 0.72 0.28

Fnet i ðAj Þ^wi 0.086 20.110 0.050 20.026

3 Φ+ Φ–

A2 0.61 0.39

Aggregate rank of group decision 1 4 2 3

4 Φ+ Φ–

A4 0.49 0.51

Φ+ Φ–

A2 0.17 0.83

Table XVI. The global preference index for Group decision (aggregate for DM1, DM2 and DM3) Figure 7. PROMETHEE I (partial ranking) for group decision (aggregate for DM1, DM2 and DM3)

JMTM 23,7

.

. .

916

DM2 and DM3 as well as DM1 and DM2 are giving just independent opinion and their preferences are not matching. DM1and DM2 prefer alternative A1. Alternative A2 is not the choice of DM and DM3.

The decision axis is quite long in size and hence it has a strong decision power. Hence, the decision taken by these three DMs can be considered final with confidence. Step 8. Analyzing the result and sensitivity analysis As can be seen from Figures 7 and 8, results indicate the superiority of A1 to the other alternatives. This situation arises from some reasons. First of all, A1 has an absolute 3

1 A1 Φ

Figure 8. PROMETHEE II (partial ranking) for group decision (aggregate for DM1, DM2 and DM3)

Figure 9. GAIA plane for group decision (aggregate for DM1, DM2 and DM3)

A4 Φ

0.44

–0.01

4

2

A2

A3 Φ

0.23

Φ

–0.65

superiority to all the other alternatives for reliability, flexibility and economic conditions. For price, A2, A3 and A4 are superior to A1. However, the sides that A1 is superior to the others can tolerate the A1’s unsatisfying sides and A1 is the most proper LSP for the decision making problem. In this stage, the sensitivity of the results to the changes in the criteria weights is analyzed. As an example for all other sensitivity analysis of criteria weights, here, only the results’ sensitivity to “price” weights is presented. From the Figure 10, changes on the alternatives’ leaving flows as the change on the price weight can be seen. At the point where “price” weight is “0”, the leaving flow value of A1 takes its maximum value, and the leaving flow value of A3 and A4 takes their minimum value. While the weight of “P” increases, the leaving flow values of A1 decreases but A3 and A4 increase. The leaving flow value of A2 is not much affected by the change in the weight of “price” criteria. This is why, while A3 and A4 have good evaluation values for “price”, A1’s evaluation is worse on this criterion when comparing with the others. When considering the entering flows, with the increase of the weight of “P” from 0 to 100 percent, the entering flows of A1 increase and the entering flows of A2, A3 and A4 decrease (Figure 11). These results are similar to the leaving flow analysis. When considering the net flows, with the increase of the weight of “P” from 0 to 100 percent, the net flows of A1 is getting worse, and the net flows of A2, A3 and A4 are getting better (Figure 12). This is why, A1’s evaluation for “P” is below the average when comparing with the others and the increase on the “P” weight amplifies this situation.

Selection of LSP

917

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

A1

A2

A3

A4

P = 100%

P = 80%

P = 60%

P = 40%

P = 20%

P = 0%

0

Figure 10. Changes on alternatives’ leaving flow as the change on criteria “price” weight for DM1

JMTM 23,7

1.2 1 0.8 0.6

918

0.4 0.2

0% P

P

=

10

80 % =

60 % P

= P

=

40 %

% 20 P

P

Figure 11. Changes on alternatives’ entering flow as the change on criteria “price” weight for DM1

=

=

0%

0

A1

A2

A3

A4

1 0.5 0 –0.5 –1

P

P

=

10 0%

80 % =

60 % P

=

40 % P

=

20 % = P

P

Figure 12. Changes on alternatives’ net flow as the change on criteria “price” weight for DM1

=

0%

–1.5

A1

A2

A3

A4

The preference of alternative changes from A1 (at price ¼ 0 percent weight) to A3 (at price ¼ 100 percent weight) because A3 is best on this criterion. Similar sensitivity analysis can be done for other criteria for DM1 as well as for all other DMs. 4. Conclusions Selection of LSP is an important decision making area for the companies since it has a direct effect on rapport and quality of service. In this study, a new methodology for MHESP is proposed: an integrated F-AHP and F-PROMETHEE methodology. This methodology has some advantages comparing the previously proposed methodologies. First of all, the vagueness embedded in this decision making area may easily

incorporated into the decision making process with this methodology. Also, the DMT who constitutes members with different experience, qualification and designation enjoy different influence to the decision making. They are assigned different weights. Moreover, DMT is not asked to give accurate values for the evaluations. Contrarily, both the criteria evaluations and the alternative evaluations are started with the linguistic preferences. This situation increases the usefulness and easiness of the methodology. As PROMETEE cannot assign weights to the criteria, FAHP has been used to allocate weights to the criteria. Each DM evaluates LSPs using F-PROMETHEE, then, the results of all the DMs are integrated using PROMETHEE GDSS approach to take final decision. The analysis is done using GAIA plane which provides valuable help in understanding the conflicts among criteria. The proposed approach is unique both in the LSP and MCDM literature. The use of Decision Lab software further eases the numerical calculations and analysis of the results. The methodology is applied for a manufacturing company to prove its effectiveness. Also, sensitivity analysis phase shows that the results are sensitive to the changes in the weights to the criteria. The proposed approach can also be applied to other MCDM application areas where the vagueness is a specification of them. Also for the third party LSP problems, a comparison study may be realized with the other MCDM techniques such as TOPSIS, ANP, DEA or by integrating any of such techniques. References Albadvi, A., Chaharsooghi, S.K. and Esfahanipour, A. (2007), “Decision making in stock trading: an application of PROMETHEE”, European Journal of Operation Research, Vol. 177, pp. 673-83. Araz, C., Ozfirat, P.M. and Ozkarahan, I. (2007), “An integrated multicriteria decision making methodology for outsourcing management”, Computers and Operations Research, Vol. 34, pp. 3738-56. Bilsel, R.U., Buyukozkan, G. and Ruan, D. (2006), “A fuzzy preference-ranking model for a quality evaluation of hospital web sites”, International Journal of Intelligent Systems, Vol. 21, pp. 1181-97. Brans, J.P. (1982), L’inge´nierie de la de´cision. Elaboration d’instruments d’aide a` la de´cision. Me´thode PROMETHEE, Universite´ Laval, Que´bec. Brans, J.P. and Mareschal, B. (1994), “PROMCALC and GAIA: a new decision support system for multicriteria decision aid”, Decision Support Systems, Vol. 12 Nos 4/5, pp. 297-310. Brans, J.P. and Vincke, P. (1985), “A preference ranking organization method: the PROMETHEE method for MCDM”, Management Science, Vol. 31, pp. 641-56. Brans, J.P., Mareschal, B. and Vincke, P. (1984), “PROMETHEE: a new family of outranking methods in MCDM”, IFORS’84, North Holland, Amsterdam. Brans, J.P., Vincke, P. and Mareschal, B. (1986), “How to select and how to rank projects: the PROMETHEE method”, European Journal of Operational Research, Vol. 24, pp. 228-38. Chang, D.-Y. (1996), “Application of the extent analysis method on fuzzy AHP”, European Journal of Operational Research, Vol. 95 No. 3, pp. 649-55. Chen, S.J. and Hwang, C.L. (1992), Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer, Berlin. Chou, W.C., Lin, W.T. and Lin, C.Y. (2007), “Application of fuzzy theory and PROMETHEE technique to evaluate suitable ecotechnology method: a case study in Shismen Reservoir Watershed, Taiwan”, Ecological Engineering, Vol. 31, pp. 269-80.

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Dagdeviren, M. (2008), “Decision making in equipment selection: an integrated approach with AHP and PROMETHEE”, Journal of Intelligent Manufacturing, Vol. 19 No. 4, pp. 397-406. Dulmin, R. and Mininno, V. (2003), “Supplier selection using a multi-criteria decision aid method”, Journal of Purchasing and Supply Management, Vol. 9, pp. 177-87. Elevli, B. and Demirci, A. (2004), “Multicriteria choice of ore transport system for an underground mine: application of PROMETHEE methods”, Journal of The South African Institute of Mining and Metallurgy, Vol. 104 No. 5, pp. 251-6. Ferna´ndez-Castro, A.S. and Jime´nez, M. (2005), “PROMETHEE: an extension through fuzzy mathematical programming”, Journal of the Operational Research Society, Vol. 56, pp. 119-22. Geldermann, J., Spengler, T. and Rentz, O. (2000), “Fuzzy outranking for environmental assessment. Case study: iron and steel making industry”, Fuzzy Sets and Systems, Vol. 115, pp. 45-65. Goumas, M. and Lygerou, V. (2000), “An extension of the PROMETHEE method for decision making in fuzzy environment: ranking of alternative energy exploitation projects”, European Journal of Operational Research, Vol. 123, pp. 606-13. Ho, C.Y. (2006), Applying Fuzzy Multicriteria Decision-making for Evaluating ERP System Development Methods and Implementation Strategies, Institute of Information Management, I-Shou University, Kaohsiung. Jharkharia, S. and Shankar, R. (2007), “Selection of logistics service provider: an analytic network process (ANP) approach”, Omega, Vol. 35 No. 3, pp. 274-89. Kahraman, C., Yasin, A.N., Cevik, S., Gulbay, M. and Ayca, E.S. (2007), “Hierarchical fuzzy TOPSIS model for selection among logistics information technologies”, Journal of Enterprise Information Management, Vol. 20 No. 2, pp. 143-68. Leyva-Lo´pez, J.C. and Ferna´ndez-Gonza´lez, E. (2003), “A new method for group decision support based on ELECTRE III methodology”, European Journal of Operational Research, Vol. 148, pp. 14-27. Lynch, C.F. (2002), “3PLs: the state of outsourcing”, Logistics Management, Vol. 41 No. 6, pp. T47-T50. Macharis, C., Brans, J.P. and Mareschal, B. (1998), “The GDSS PROMETHEE procedure – a PROMETHEE-GAIA based procedure for group decision support”, Journal of Decision Systems, Vol. 7, pp. 283-307. Macharis, C., Springael, J., De Brucker, K. and Verbeke, A. (2004), “PROMETHEE and AHP: the design of operational synergies in multicriteria analysis: strengthening PROMETHEE with ideas of AHP”, European Journal of Operational Research, Vol. 153, pp. 307-17. Mareschal, B. and Brans, J.P. (1988), “Geometrical representations for MCDA”, European Journal of Operational Research, Vol. 34, pp. 69-77. Radojevic, D. and Petrovic, S. (1997), “A fuzzy approach to preference structure in multicriteria ranking”, International Transaction in Operation Research, Vol. 4 Nos 5/6, pp. 419-30. Rao, R.V. and Patel, B.K. (2010), “Decision making in the manufacturing environment using an improved PROMETHEE method”, International Journal of Production Research, Vol. 48, pp. 4665-82. Razzaque, M.A. and Sheng, C.C. (1998), “Outsourcing of logistics functions: a literature survey”, International Journal of Physical Distribution and Logistics Management, Vol. 28 No. 2, pp. 89-107. Sachdeva, A., Kumar, D. and Kumar, P. (2009), “Multi-factor failure mode critically analysis using TOPSIS”, Journal of Industrial Engineering International, Vol. 5 No. 8, pp. 1-9.

Tuzkaya, G., Gulsun, B., Kahraman, C. and Ozgen, D. (2010), “An integrated fuzzy multi-criteria decision making methodology for material handling equipment selection problem and an application”, Expert Systems with Applications, Vol. 37, pp. 2853-63. Vaidyanathan, G. (2005), “A framework for evaluating third-party logistics”, Communications of the ACM, Vol. 48 No. 1, pp. 89-94. van Hoek, R.I. (2001), “The contribution of performance measurement to the expansion of third party logistics alliances in the supply chain”, International Journal of Operations and Production Management, Vol. 21 Nos 1/2, pp. 15-29. Wang, J.J. and Yang, D.L. (2007), “Using a hybrid multi-criteria decision aid method for information systems outsourcing”, Computers and Operations Research, Vol. 34, pp. 3691-700. Zadeh, L.A. (1965), “Fuzzy sets”, Information and Control, Vol. 8, pp. 338-53. Further reading Brans, J.P. and Mareschal, B. (2005), Figueira, J., Greco, S. and Ehrgott, M. (Eds), PROMETHEE Methods’, Decision in Multicriteria Decision Analysis: State of the Art Survey, Kluwer Academic Publishers, Boston, MA, pp. 163-96. About the authors Dr Rajesh Gupta is Assistant Professor in the Department of Mechanical Engineering at Giani Zail Singh College of Engineering and Technology, Bathinda, Punjab, India. He has 13 years of experience in teaching and seven years in Industry. He is research scholar in the department of Industrial Engineering at Dr B.R. Ambedkar NIT, Jalandhar. Dr Anish Sachdeva is Assistant Professor in the Department of Industrial and Production Engineering at Dr B.R. Ambedkar NIT, Jalandhar, India. He has 16 years of experience in teaching. His areas of research are reliability and maintenance engineering, logistics and supply chain. Dr Anish Sachdeva is the corresponding author and can be contacted at: [email protected] Dr Arvind Bhardwaj is Professor in the Department of Industrial and Production Engineering at Dr B.R. Ambedkar NIT, Jalandhar, India. He has 23 years of experience in teaching. His area of research is logistics and supply chain.

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Selection of LSP

921

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JMTM 23,7

Determining the parameters of MSG algorithm for multi period layout problem

922 Received 27 March 2011 Revised 13 November 2011 Accepted 13 November 2011

Berna Ulutas and Tugba Sarac¸ Department of Industrial Engineering, Eskisehir Osmangazi University, Eskisehir, Turkey Abstract Purpose – The facility layout problem aims to assign machines/departments to locations and modeled as a quadratic assignment problem (QAP). Multi period facility layout is a special case of this problem where the sum of material handling and re-layout costs are minimized. Since the problem is proved to be NP-hard, several exact and heuristic methods are proposed in the literature. The purpose of this paper is to solve the multi period layout problem by using the modified sub-gradient (MSG) algorithm for the first time and to determine its parameters. Design/methodology/approach – The MSG algorithm can solve a large-scale of optimization problems that also includes multi period facility layout. Since the performance of the algorithm depends on parameters, a design of experiment is made to determine the appropriate parameter values. Findings – The proposed method evaluates the parameters of the MSG algorithm and most suitable general algebraic modeling solvers. It is observed that the parameter a value and solver type have main effects for small and large size test problems. Further, the results stated that solver type has more influence on large size test problem. Research limitations/implications – This study is limited with the determination of the MSG algorithm parameters and solver types on the well known small and large size test problems. Further studies may include other test problem results obtained from the presented MSG algorithm parameters and compare them with best known results in the literature. Originality/value – The paper determines the parameters of the MSG algorithm that is used to solve the multi period layout problem, for the first time in the literature. Keywords Genetic algorithms, Mathematical modelling, Materials handling, Dynamic facility layout problem, Modified sub-gradient algorithm, Design of experiments, General algebraic modeling system solvers Paper type Research paper

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 922-936 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267736

1. Introduction Layouts that change during time are termed as dynamic layout problem. If not addressed properly, inefficient layouts may result in increased materials handling and resource (re)location costs. Depending on the type and extent of the problem, a period can be given in terms of months, quarters, years, etc. The costs associated with the dynamic facility layout problem (DFLP) are those pertaining to the flow of the personnel, material, and those involved with rearrangement of the layouts. The material flow costs are calculated as a product of flow and distance. For simplicity, it will be assumed that the initial cost of assigning facility i to any location j is independent of the location. However, rearranging the layout will result in some shifting costs depending on the facilities involved in this shift. The rearrangement costs may be viewed such as fixed costs, costs depending on the facilities involved in the change, costs depending on the facilities involved and the distance between the various

locations, or any combination of the above. Various researchers proposed new or improved models and algorithms to solve DFLP. Based on the accessible literature, it can be stated that the modified sub-gradient (MSG) algorithm is not used to solve DFLP. It is proven that the MSG algorithm can solve a large-scale of optimization problems including quadratic assignment problem (QAP). In this paper, DFLP is modeled as a type of QAP and the MSG algorithm is used for the first time to solve the problem. The MSG algorithm was proposed by Gasimov for solving a continuous non-linear model in 2002. To use the MSG algorithm, first, the DFLP model should be converted into the continuous form. In this study, the formulation proposed by Li (1992) was used because this procedure adds only one new constraint to the model and it does not require adding new variables. After converting the model, the augmented Lagrangean function is used to obtain the dual problem with “zero duality gap”. To solve the dual problem, different methods or solvers can be used. The solutions generated by the MSG algorithm may be influenced by the parameters of the algorithm and the solution method of the dual problem. In this study, Minos, Conopt, Lgo, Msnlp, Pathnlp, and Snopt solvers of the general algebraic modeling system (GAMS) software are used for solving the problem. To determine the effect of solver and MSG parameters to solution success, a design of experiments study is also made. In the following section, the mathematical model of DFLP which aims to minimize the material handling and relocation costs is provided. Then, a brief literature survey is given and the computational complexity of the problem is discussed. After introducing the MSG algorithm, design of experiments is applied to optimize parameters of the algorithm by use of different solvers and two data sets. Finally, the results are discussed and concluded. 2. The multi-period layout problem Multi-period layout problem provides effective results to meet the requirements of the changing environments. The problem considers several planning periods rather than static layouts with the material handling and relocation costs. Balakrishnan and Cheng (1998) had modeled the DFLP as follows: N

the number of departments or the locations;

T

the number of periods;

ftik

flow in period t between department i to department k;

djl

the distance between the locations j and l;

Atijl the fixed cost of moving department i at location j to l at period t; Ctijkl the material handling cost at period t between department i at location j and department k at location l: ( 1; if department i is attained to position j at period xtij ¼ 0; otherwise C tijkl ¼ f tik *djl ytijl ¼ xðt21Þij xtil

Parameters of MSG algorithm

923

JMTM 23,7

Min

T X N X N X N X t¼2 i¼1 j¼1 l¼1

Atijl ytijl þ

T X N X N X N X N X

C tijkl xtij xtkl

ð1Þ

t¼1 i¼1 j¼1 k¼1 l¼1

subject to:

924

N X

xtij ¼ 1;

i ¼ 1; 2; :::; N ;

s ¼ 1; 2; :::; T;

ð2Þ

xtij ¼ 1;

j ¼ 1; 2; :::; N ;

s ¼ 1; 2; :::; T;

ð3Þ

j¼1 N X i¼1

xtij [ {0; 1};

;i; j; t

ð4Þ

The objective function (1) enables to minimize the sum of relocation and material handling costs throughout the planning horizon. Constraint (2) states that each department is assigned to a location in each period and (3) guarantees that each location is occupied by a department in each period. The decision variables are kept either at 1 or at 0 by constraint (4). In an n department, t period DFLP, there would be (n!)t layouts to guarantee the optimal solution where n! is the number of possible layout combinations in each period. Optimal algorithms to solve this problem are NP-complete and exact solutions can be computed only for small or greatly restricted problems. Rosenblatt (1986) developed a model and solution procedure to determine an optimal layout for each of several pre-specified future planning periods. Improvements to the branch and bound procedure of Rosenblatt (1986) were carried on by a number of following papers, including Balakrishnan (1993) and Batta (1987). Variants of the basic DFLP were studied in Balakrishnan (1993) and Montreuil and Venkatadri (1991). A review of paper on DFLP was provided by Balakrishnan and Cheng (1998). Conway and Ventakaraman (1994) also Balakrishnan and Cheng (1998) modeled DFLP by use of genetic algorithms (GA). Dunker et al. (2005) provided an algorithm that combines dynamic programming (DP) and genetic search. Kochhar and Heragu (1999) used a GA based methodology and Urban (1993) “pair-wise exchange” procedure. Balakrishnan et al. (2000) had improved Urban’s methodology. Baykasoglu and Gindy (2001) also McKendall et al. (2006) provided simulated annealing for DFLP. McKendall and Shang (2006) had made some arrangements at the methodology given Gambardella et al. (1999) and developed a hybrid ant system. Baykasoglu et al. (2006) introduced an ant colony optimization. Erel et al. (2003) presented a three-phase approach. Rodriguez (2005) combined GA with tabu seach and claimed to reach better results. Based on the accessible DFLP literature, there is no study concerning MSG algorithm although it is appropriate to solve this problem. The algorithm is introduced in the following section. 3. The MSG algorithm One class of the exact methods used for solving 0-1 integer problems with non-convex objective and/or constraints is based on penalty function approaches. In many cases, the simple examples illustrate that the solution for the penalty problem can be made sufficiently lose to the optimal solution of the original problem by choosing the penalty

parameter large enough. However, solving a penalty problem with a very large penalty parameter leads to computational difficulties (Bazaraa et al., 2006; Bertsekas, 1995). Ordinary Lagrangian duality underlies many efficient algorithms for convex minimization problems. A key ingredient is the strong duality. Lagrangian relaxation and decomposition methods have been extensively used for solving linear integer problems (Michelon and Maculan, 1993; Michelon and Veuilleux, 1996). Unfortunately, ordinary Lagrangian methods often end up with a duality gap and fail to identify an optimal solution of the primal integer optimization problems such as the quadratic 0-1 problems which are non-convex in general (Li, 1999). In recent years, different augmented Lagrangian duality schemes that are able to eliminate duality gap in a wide class of non-convex optimization problems and to provide solution algorithms have been studied (Gasimov, 2002, Gasimov and Rubinov, 2004; Burachik et al., 2006; Gasimov and Ustun, 2007; Burachik et al., in press). The MSG algorithm was proposed by Gasimov (2002) for solving dual problems constructed with respect to sharp augmented Lagrangean function. Gasimov and Rubinov (2004) introduced a general version of this algorithm by modifying it for generalized augmented Lagrangian dual problems and extended the circle of problems solvable by this method. Gasimov and Ustun (2005) examined the MSG algorithm by applying it to solve the non-convex zero-one QAP. Burachik et al. (2006) gave a new convergence analysis for the MSG algorithm and proposed new formulas for the step-size parameters. Gasimov and Ustun (2007) proposed a generalized version of the MSG algorithm to solve sharp augmented Lagrangian dual problems. Burachik et al. (2010) proposed an inexact version of the MSG algorithm that may allow solving problems with less computational effort. The MSG algorithm can solve the non-convex optimization problems with equality constraint. If the problem is not convex, using the classical Lagrangean may lead to non-zero duality gap. However, if the sharp augmented Lagrangean function is used; this problem can be eliminated for a large-scale of problems. It is proven that when the objective and constraint functions are all Lipschitz then the sharp augmented Lagrangean guaranties the zero duality gap (Gasimov, 2002). The MSG algorithm has some outstanding properties. That is the reason why the MSG algorithm is preferable. For example, the MSG algorithm is convergent. It does not require convexity or differentiability conditions on the primal problem; it does not use any penalty parameter and it guarantees the zero duality gap for the problems such that its objective and constraint functions are all Lipschtz. In other words, the MSG algorithm can be able to find the optimal solution if the proper parameter values are chosen. However, it may not be exactly known whether the obtained solution value is optimal. Nevertheless, it is observed that the MSG algorithm can solve the problems in reasonable short times. The MSG algorithm is explained shortly as follows. Let the primal problem P is given as follows: min P ¼ min f ðxÞ x[S

subject to gðxÞ ¼ 0 where S is a subset of a metric space X and f: X ! R and g: X ! R n are given functions. The sharp augmented Lagrangean function L: S £ R n £ Rþ ! R associated

Parameters of MSG algorithm

925

JMTM 23,7

926

with P : Lðx; u; cÞ ¼ f ðxÞ þ ckgðxÞk 2 kgðxÞ; ul where c and u are the dual variables, k.k is the Euclidean norm and , .,. . is the Euclidean inner product on R n. The dual function H: R n £ Rþ ! R associated with the problem P is defined as: H ðu; cÞ ¼ min Lðx; u; cÞ; x[S

for u [ R n ; and c [ Rþ

Then the dual problem P * is given by: max H ðu; cÞ

ðu;cÞ[R n £Rþ

The steps of the MSG algorithm by Gasimov and Ustun (2005) are as follows. Initialization step. Chose a vector (u1,c1)[ R n £ Rþ . Let k ¼ 1. Step 1. Given Lagrange multipliers (uk,ck), solve the following sub problem: Minimize x[S

f ðxÞ þ c k kgðxÞk 2 kuk ; gðxÞl

subject to f ðxÞ þ c k kgðxÞk 2 kuk ; gðxÞl # H
Let xk be a local solution of this problem. If kgðxk Þk ¼ 0 then stop. (uk,ck) is a solution for the dual problem (P *), xk is a solution for (P). Otherwise, go to step 2: Step 2. Let: ukþ1 ¼ uk 2 sk gðxk Þ;

ckþ1 ¼ ck þ ðsk þ 1k Þkgðxk Þk;

ð5Þ

where sk and 1k are positive scalar step sizes, replace k by k þ 1 and repeat step 1. In practice, the step-size formulation in Equation (6) can be used: Sk ¼

dðH
2 Lðxk ; uk ; ck Þ 5kgðxk Þk

2

ð6Þ

where H
is an approximate optimal value or an upper bound for the dual problem and 0 , d , 2. Choosing a value for the upper bound H
is very important for the performance of the MSG algorithm. In practice, such a value may be taken by different ways. An upper bound for DFLP can easily be found from any random assignment. Another important issue is to calculate the 1k value. An interval was defined for 1k by Gasimov (2002). Theorem 1. Let {(uk, ck)} be the sequence of dual variables generated by the MSG algorithm. Assume that (uk, ck) is not a solution of the dual problem for any k, that is, g(xk) – 0 for all k:

.

Parameters of MSG algorithm

Assume that there exists a dual solution. If: 0 , 1k , s k ¼

aðH
2 Lðxk ; uk ; ck ÞÞ 2

5kgðxk Þk

;

then, dkþ 1 2 dk, 0, where dk ¼ dðð
u; c
Þ; ðuk ; ck ÞÞ is defined as the distance between the optimal dual solution and the pair of dual variables calculated at the kth iteration of the algorithm and 0 , d , 2. .

Again, assume that there exists a dual solution and that f and g are continuous, S is compact, and a feasible solution exists. If: 0 , 1k , s k ¼

ðH
2 Lðxk ; uk ; ck ÞÞ 5kgðxk Þk

2


then, Lðxk ; uk ; ck Þ ! H. Since the objective and constraint functions of the problem (CNP) are all continuous and the set S for CNP is compact, it guarantees the duality gap property and the existence of solutions for (P ). Gasimov and Ustun (2007), proposed new formulations (7)-(9) instead of (5) and (6). These formulations are given below: ukþ1 ¼ uk 2 ask gðxk Þ; S 1k ¼

ckþ1 ¼ ck þ ð1 þ aÞS k kgðxk Þk

dðaðH
2 Lðxk ; uk ; ck ÞÞ þ ð
c 2 ck Þkgðxk ÞkÞ ða 2 þ ð1 þ aÞ2 Þkgðxk Þk S 2k ¼

2

daðH
2 Lðxk ; uk ; ck ÞÞ ða 2 þ ð1 þ aÞ2 Þkgðxk Þk

2

ð7Þ ð8Þ ð9Þ

where a . 0 and 0 , d , 2. Burachik et al. (2006) illustrated that s1k is efficient. Therefore, s1k is used in this study. 4. Computational results The MSG algorithm is able to find the optimal solution if the proper parameter values and solution method of dual problem are chosen. Therefore, two well known DFLP test problems from the literature are selected to determine the algorithm parameters. 4.1 Test problems In this paper, two data sets from literature for DFLP are considered: . Test problem I: the problem of Rosenblatt (1986) is a common test problem for DFLP. The number of alternative layouts for six machines five periods problem can be calculated as ð6!Þ5 ¼ 1:93 £ 1014 . The data are given in Figure 1. . Test problem II: nine machines five periods problem proposed by Conway and Ventakaraman (1994) has ð9!Þ5 ¼ 6:2 £ 1027 alternative layouts. The relevant data are given in Figure 2.

927

JMTM 23,7 Period 1

928 Period 2

Period 3

Period 4

Period 5

Figure 1. Data set from Rosenblatt (1986)

4.2 GAMS and solvers GAMS is a high-level modeling system for mathematical programming and optimization. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large-scale modeling applications, and allows building large maintainable models that can be adapted quickly to new situations (www.gams.com/). For the purpose of this study, non-linear programming solvers are considered. The available solvers such as Conopt, Lgo, Minos, Msnlp, Pathnlp, and Snopt are used to solve dual DFLP. The algorithm was stopped after 10,000 iterations for each solver. 4.3 Design of experiments The success of MSG algorithm depends on the parameters and GAMS solvers used. Therefore, a design of experiments analysis is made to determine the factors that affect the output for the problem and figure out the suitable levels for the factors that can be controlled. Independent variables that may be related to a response variable are called factors. The value assumed by a factor in an experiment is called a level. Table I summarizes the factors and related levels.

Parameters of MSG algorithm

929

Figure 2. Data set from Conway and Ventakaraman (1994)

JMTM 23,7

930

Table I. Design factors and levels for the MSG algorithm

4.3.1 Test results. Results for Test problem I are given in Table II. The parameter values chosen in this study are given in the first five columns of Table II. The results obtained from GAMS solvers and related norm values are illustrated in the following columns. The zero norm values in Tables II and III states that feasible solutions were obtained. The solutions with norm values different from zero are replaced with penalty values; 100,000 for Test problem I and 1,000,000 for Test problem II. 4.3.2 Analysis for design of experiments. Based on the MSG algorithm parameters and solver type, a full factorial design with 216 tests were made. The analysis of variance (ANOVA) was performed to determine the significant factors. Table IV summarizes the ANOVA results for Test problem I. When a factor has an effect on the performance measure, it gets a high F (Fisher’s test) value. It is investigated from Table IV that, since F0.05,2,161 ¼ 3 and F0.05,5,161 ¼ 2.21 we conclude that the main effects of C1 (a value) and C5 (solver type) effects solution success (C6). Since F0.05,10,161 ¼ 1.83 , 2.48, there is an interaction between C1 and C5. This means that, while solving DFLP, MSG algorithm parameter a and solver type have main and interaction effects on the solution. Further, since F-values are smaller than the F table values for the other main factors and interaction, there is no significant evidence that these factors affect the response. Figure 3 shows appropriate level of each design factor. The objective in the DFLP is to minimize the total costs. Therefore, the levels for Test problem I are selected by considering values that may increase solution success. Based on Figure 3, parameter values of a (2), g (1,25), H
(10,000), and ck (3) are determined. In a similar way, ANOVA tests for Test problem II are made and results are summarized in Table V. When Test problem II in Table V is investigated; since F0.05,2,161, F0.05,5,161, and F0.05,10,161-values are smaller than the F-values at ANOVA results, it can be stated that a and solution type effects the solution quality and there is an interaction between them. Figure 4 shows the optimal levels values for Test problem II. Figure 4 states that a value should be 1.7, g could be either 1.60 or 1.90. Any value for ck and H
can be taken. While solving Test problem II, solvers Lgo, Msnlp, and Snopt can provide good solutions. Interaction plot for a and solver is given in Figure 5. The level of C5 may be determined according to main effect plot, since interaction effect of C1 and C5 is more critical than the main effect of C1. Therefore, the level of C1 should be selected according to interaction plot. When solver Lgo, Msnlp, and Snopt are used, C1 value should be 1.5 according to Figure 5.

Factor Solver

Level 1 Minos

Level 2 Conopt

Level 3 Lgo

d a ck H
(R) H
(C)

1.25 1.5 3 8,000 700,000

1.60 1.7 5 10,000 1,000,000

1.90 2

Level 4 Msnlp

Level 5 Pathnlp

Level 6 Snopt

g

1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95 1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95 1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95

a

1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 2 2 2 2 2 2 2 2 2 2 2 2

No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000 8,000 8,000 10,000 10,000

Hust 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5

Ckat 85,492 85,492 83,962 83,962 85,432 79,536 84,709 84,709 82,243 79,649 89,541 89,541 86,121 86,121 88,164 88,164 87,986 87,986 86,106 86,106 83,463 83,463 86,083 86,083 82,440 82,440 83,409 83,409 84,329 84,329 84,123 84,123 84,329 84,329 84,329 84,329

Minos 0 0 0 0 0 1.06 0 0 0 0.45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Norm 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706 87,706

Conopt 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Norm 85,574 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 79,797 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258 81,258

Lgo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Norm 87,645 87,645 87,645 87,645 87,645 87,645 87,645 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 87,039 85,802 85,802 85,802 85,802 85,802 85,802 85,802 85,802 85,802 85,802

Msnlp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Norm 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Pathnlp 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75 7.75

Norm

Norm 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Snopt 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114 86,114

Parameters of MSG algorithm

931

Table II. Solver results for the Test problem I

1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 2 2 2 2 2 2 2 2 2 2 2 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Table III. Solver results for the Test problem II

a

1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95 1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95 1.25 1.25 1.25 1.25 1.60 1.60 1.60 1.60 1.95 1.95 1.95 1.95

Gama

700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000 700,000 700,000 1,000,000 1,000,000

Hust 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5

Ckat 725,494 725,494 725,494 725,494 725,761 725,761 707,881 707,881 718,568 718,568 733,884 733,884 719,396 719,396 719,396 719,396 710,020 710,020 710,020 710,020 710,972 711,734 1,333,343 1,333,342 706,219 706,219 3,446,312 3,446,312 147,063 147,063 4,011,933 4,011,933 137,071 137,071 3,947,177 3,947,177

Minos 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 507.19 507.19 39.24 39.24 317.18 317.18 55.51 55.51 643.11 643.11 57.94 57.94 626.37 626.37

Norm 527,203 527,227 527,227 527,227 527,227 527,227 527,227 527,227 213,011 791,738 791,734 537,907 537,884 537,884 683,327 713,318 712,490 712,490 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202 709,202

Conopt 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 7.48 6.92 6.93 5.82 5.83 5.84 1.43 0.13 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Norm 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705 704,705

Lgo 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Norm 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727 713,727

Msnlp 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Norm 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Pathnlp 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39 10.39

Norm

932

No.

719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428 719,428

Snopt

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Norm

JMTM 23,7

Source

DF

Seq SS

Adj SS

Adj MS

F

P

C1 C2 C3 C4 C5 C1*C2 C1*C3 C1*C4 C1*C5 C2*C3 C2*C4 C2*C5 C3*C4 C3*C5 C4*C5 Error Total

2 2 1 1 5 4 2 2 10 2 2 10 1 5 5 161 215

54,844,770 5,481,788 7,889,449 9,858,153 6,844,868,439 22,904,121 21,813,291 19,716,306 89,412,377 2,174,455 11,610,490 33,270,066 10,382,803 13,512,446 24,958,023 579,747,858 7,752,444,836

54,844,770 5,481,788 7,889,449 9,858,153 6,844,868,439 22,904,121 21,813,291 19,716,306 89,412,377 2,174,455 11,610,490 33,270,066 10,382,803 13,512,446 24,958,023 579,747,858

27,422,385 2,740,894 7,889,449 9,858,153 1,368,973,688 5,726,030 10,906,645 9,858,153 8,941,238 1,087,228 5,805,245 3,327,007 10,382,803 2,702,489 4,991,605 3,600,918

7.62 0.76 2.19 2.74 380.17 1.59 3.03 2.74 2.48 0.30 1.61 0.92 2.88 0.75 1.39

0.001 0.469 0.141 0.100 0.000 0.179 0.051 0.068 0.009 0.740 0.203 0.513 0.091 0.587 0.232

Parameters of MSG algorithm

933

Table IV. ANOVA results for the Test problem I

98,000

C6

94,000 90,000 86,000 82,000 C1

C2

C3

C4

C5

5. Conclusions The DFLP that considers relocation costs of machines between time periods and material handling costs is considered in this study. There are several heuristics and exact solution methods to solve DFLP in the literature. However, the MSG algorithm is not used to solve this problem. This paper aims to determine the MSG algorithm parameters and appropriate GAMS solvers for solving DFLP. Following the brief introduction of DFLP, the steps of the algorithm is explained in detail. Then, two test problems from the literature are selected to analyze the parameters. An experimental design is conducted to determine the parameters for the problems. In Test problems I and II, a value (C1) and solver type (C5) have main effects also C1 and C5 have interaction effect on the solution. Furthermore, it is observed that solver type has more influence on large size test problem (Test problem I). As a result, it is shown that the MSG is a promising and competitive algorithm to solve DFLP with suitable parameters and solution type. In the following studies, large sized problems with different features, such as unequal facility area, can be solved with MSG.

Figure 3. Main effects plot for the Test problem I

JMTM 23,7

934

Table V. ANOVA results for the Test problem II

Source

DF

Seq SS

Adj SS

Adj MS

F

P

C1 C2 C3 C4 C5 C1*C2 C1*C3 C1*C4 C1*C5 C2*C3 C2*C4 C2*C5 C3*C4 C3*C5 C4*C5 Error Total

2 2 1 1 5 4 2 2 10 2 2 10 1 5 5 161 215

1.4608 £ 10þ 15 3.6533 £ 10þ 14 411,689 2,688 2.8625 £ 10þ 17 7.3048 £ 10þ 14 210,583 5,376 1.2559 £ 10þ 17 1.0957 £ 10þ 15 5,376 8.3980 £ 10þ 15 2,688 2.1907 £ 10þ 15 13,441 3.3225 £ 10þ 16 4.5930 £ 10þ 17

1.4608 £ 10þ 15 3.6533 £ 10þ 14 411,689 2,688 2.8625 £ 10þ 17 7.3048 £ 10þ 14 210,583 5,376 1.2559 £ 10þ 17 1.0957 £ 10þ 15 5,376 8.3980 £ 10þ 15 2,688 2.1907 £ 10þ 15 13,441 3.3225 £ 10þ 16

7.3039 £ 10þ 14 1.8267 £ 10þ 14 411,689 2,688 5.7249 £ 10þ 16 1.8262 £ 10þ 14 105,291 2,688 1.2559 £ 10þ 16 5.4787 £ 10þ 14 2,688 8.3980 £ 10þ 14 2,688 4.3814 £ 10þ 14 2,688 2.0637 £ 10þ 14

3.54 0.89 0.00 0.00 277.41 0.88 0.00 0.00 60.86 2.65 0.00 4.07 0.00 2.12 0.00

0.031 0.415 1.000 1.000 0.000 0.474 1.000 1.000 0.000 0.073 1.000 0.000 1.000 0.065 1.000

1.00E+08 75,000,000 50,000,000 25,000,000

Figure 4. Main effects plot for Test problem II

0 C1

C2

C3

C4

C5

1.00E+08

50,000,000

Figure 5. Interaction plot (a*solver) for the Test problem II

0 1

2

3

4 C5

5

6

References Balakrishnan, J. (1993), “Notes: the dynamics of plant layout”, Management Science, Vol. 39 No. 5, pp. 654-5. Balakrishnan, J. and Cheng, C.H. (1998), “Dynamic layout algorithms: a state of the art survey”, Omega, Vol. 26 No. 4, pp. 507-21. Balakrishnan, J., Cheng, C.H. and Conway, D.G. (2000), “An improved pair-wise exchange heuristic for the dynamic plant layout problem”, International Journal of Production Research, Vol. 38 No. 13, pp. 3067-77. Batta, R. (1987), “Comment on: the dynamics of plant layout”, Management Science, Vol. 33, p. 1065. Baykasoglu, A. and Gindy, N.N.Z. (2001), “A simulated annealing algorithm for dynamic layout problem”, Computers & Operations Research, Vol. 28, pp. 1403-26. Baykasoglu, A., Dereli, T. and Sabuncuoglu, I. (2006), “An ant colony algorithm for solving budget constrained and unconstrained dynamic facility layout problems”, Omega, Vol. 34 No. 4, pp. 385-97. Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (2006), Nonlinear Programming: Theory and Algorithms, 3rd ed., Wiley, New York, NY, p. 853. Bertsekas, D.P. (1995), Nonlinear Programming, Athena Scientific, Belmont, MA. Burachik, R.S., Kaya, C.Y. and Mammadov, M. (2010), “An inexact modified subgradient algorithm for non-convex optimization”, Computational Optimization and Applications, Vol. 45 No. 1, pp. 1-24. Burachik, R.S., Gasimov, R., Ismayilova, N. and Kaya, C.Y. (2006), “On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian”, Journal of Global Optimization, Vol. 34 No. 1, pp. 55-78. Conway, D.G. and Ventakaraman, M.A. (1994), “Genetic search and the dynamic facility layout problem”, Computers & Operations Research, Vol. 2 No. 8, pp. 955-60. Dunker, T., Radons, G. and Westkamper, E. (2005), “Combining evolutionary computation and dynamic programming for solving a dynamic facility layout problem”, European Journal of Operational Research, Vol. 165, pp. 55-69. Erel, E., Ghosh, J.B. and Simon, J.T. (2003), “New heuristic for the dynamic layout problem”, Journal of Operational Research Society, Vol. 54, pp. 1275-82. Gambardella, L.M., Taillard, E.D. and Dorigo, M. (1999), “Ant colonies for the quadratic assignment problem”, Journal of Operational Research Society, Vol. 50, pp. 167-76. Gasimov, R.N. (2002), “Augmented Lagrangean duality and nondifferantiable optimization methods in non-convex programming”, Journal of Global Optimization, Vol. 24, pp. 187-203. Gasimov, R.N. and Rubinov, A.M. (2004), “On augmented Lagrangeans for optimization problems with a single constraint”, Journal of Global Optimization, Vol. 28 No. 2, pp. 153-73. Gasimov, R.N. and Ustun, O. (2005), “Solving the quadratic assignment problems using modified subgradient algorithm”, in Durmusoglu, M.B. and Kahraman, C. (Eds), Proceedings of 35th International Conference on Computers & Industrial Engineering, 19-22 June, Istanbul, Turkey, pp. 757-62. Gasimov, R.N. and Ustun, O. (2007), “Solving the quadratic assignment problem using F-MSG algorithm”, Journal of Industrial and Management Optimization, Vol. 3 No. 2, pp. 173-91. Kochhar, J.S. and Heragu, S.S. (1999), “Facility layout design in a changing environment”, International Journal of Production Research, Vol. 11, pp. 2429-46.

Parameters of MSG algorithm

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Li, D. (1999), “Zero duality gap in integer programming: P-norm surrogate constraint method”, Operations Research Letters, Vol. 25, pp. 89-96. Li, H.L. (1992), “An approximate method for local optima for nonlinear mixed integer programming problems”, Computers & Operations Research, Vol. 19 No. 5, pp. 435-44. McKendall, A.R. and Shang, J. (2006), “Hybrid ant systems for the dynamic facility layout problem”, Computers & Operations Research, Vol. 33 No. 3, pp. 790-801. McKendall, A.R., Shang, J. and Kuppusamy, S. (2006), “Simulated annealing heuristics for the dynamic facility layout problem”, Computers & Operations Research, Vol. 33 No. 8, pp. 2431-44. Michelon, P. and Maculan, N. (1993), “Lagrangean methods for 0-1 quadratic problems”, Discrete Applied Mathematics, Vol. 42, pp. 257-69. Michelon, P. and Veuilleux, L. (1996), “Lagrangean methods for the 0-1 quadratic knapsack problem”, European Journal of Operational Research, Vol. 92, pp. 326-41. Montreuil, B. and Venkatadri, U. (1991), “Strategic interpolative design of dynamic manufacturing systems layout”, Management Science, Vol. 37, pp. 682-94. Rodriguez, J.M. (2005), “GATS – an algorithm for the solution of the dynamic plant layout problem”, PhD thesis, Department of Mechanical Engineering, The University of Brunswick, Canada. Rosenblatt, M.J. (1986), “The dynamics of plant layout”, Management Science, Vol. 3, pp. 76-86. Urban, T.L. (1993), “A heuristic for the dynamic facility layout problem”, IIE Transactions, Vol. 25 No. 4, pp. 57-63. Further reading Balakrishnan, J. and Cheng, C.H. (2000), “Genetic search and the dynamic layout problem”, Computers & Operations Research, Vol. 27, pp. 587-93. About the authors Dr Berna Ulutas is an Assistant Professor of Industrial Engineering at Eskisehir Osmangazi University, Turkey. Her main research includes modelling and optimization of facility layout problems by use of bio-inspired heuristics. She also conducts research related to decision-making methods (i.e. DEA, ANP) to solve real-life problems. Berna Ulutas is the corresponding author and can be contacted at: [email protected] Dr Tugba Sarac¸ is an Assistant Professor of Industrial Engineering at Eskisehir Osmangazi University, Turkey, whose primary research focus is operational research, mathematical modeling and programming, integer programming (cutting stock problem, knapsack problem, cell formation problem), and genetic algorithms.

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A genetic algorithm-based approach for job shop scheduling

Job shop scheduling

Rakesh Kumar Phanden, Ajai Jain and Rajiv Verma Department of Mechanical Engineering, National Institute of Technology, Kurukshetra, Kurukshetra, India

937

Received 9 March 2011 Revised 15 November 2011 Purpose – The purpose of this paper is to optimise the job shop scheduling problem using simulation Accepted 23 November 2011

Abstract

and genetic algorithm. Design/methodology/approach – The paper presents a simulation-based genetic algorithm approach for the job shop scheduling problem. In total, three cases have been considered to access the performance of the job shop, with an objective to minimise mean tardiness and makespan. A restart scheme is embedded into regular genetic algorithm in order to avoid premature convergence. Findings – Simulation-based genetic algorithm can be used for job shop scheduling problems. Moreover, a restart scheme embedded into a regular genetic algorithm results in improvement in the fitness value. Single process plans selected on the basis of minimum production time criterion results in improved shop performance, as compared to single process plans selected randomly. Moreover, availability of multiple process plans during scheduling improves system performance measures. Originality/value – The paper presents a simulation-based genetic algorithm approach for job shop scheduling problem, with and without restart scheme. In this paper the effect of multiple process plans over single process plans, as well as criterion for selection of single process plans, are studied. The findings should be taken into account while designing scheduling systems for job shop environments. Keywords Genetic algorithms, Simulation, Production scheduling, Job shop scheduling Paper type Research paper

1. Introduction Scheduling problems are quite common occurrences in real world. It exists whenever there is a choice as to the order in which a number of tasks can be performed (Conway et al., 1967). Generally, scheduling can be described as the allocation of a set of resources in a period of time, to perform a set of tasks. Resources may be machines in a shop floor, runways in an airport, crews at a construction site or processing units in a computing environment. Tasks may be operations in a shop floor, takeoffs and landing in an airport, stages in a construction project or computer programs to be executed (Vinod and Sridharan, 2008). Thus, scheduling is a decision-making process which can help to improves productivity of system (Ponnambalam et al., 2001). In manufacturing, the scheduling depends upon the shop floor environment such as flow shop, job shop and open shop. Job shop scheduling (JSS) is the most typical class of scheduling. Analysis of JSS problem provides important insight into the solution of the scheduling problems encountered in more realistic and complicated system (Kutanoglu and Sabuncuoglu, 1999). Job shop performs “n” number of tasks on “m” number of machines. In a job shop, products are made to order in low volume. The work flow in a job shop is not unidirectional, each machine in the shop can be characterized by the input and This research is supported by Government of India (GOI), Science and Engineering Research Council (SERC), Department of Science and Technology (DST) New Delhi (SR/SR3/MERC-098/2007).

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 937-946 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267745

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output flows of work. JSS problem is well known as one of the most difficult NP-hard combinational optimisation problem (Pinedo, 1995). Hence, heuristics are preferred for JSS (Maccarthy and Liu, 1993). Genetic algorithm (GA) is the best-known optimising ability for a class of combinatorial problems (Wang and Zheng, 2002; Jia et al., 2007; Buzatu and Bancila, 2008). In this paper, a simulation-based GA approach is used for JSS problem. The evaluation of fitness function is carried out using simulation. Simulation is utilised to compute performance measures as it yields performance measure closed to actual system performance in comparison to mathematical functions. Mean tardiness and makespan are considered as performance measure. This paper is organised as follows. Section 2 provides review of literature on JSS. Section 3 presents the details of adopted methodology. Section 4 gives the descriptions of results and finally conclusions from present work are drawn in Section 5. 2. Literature review JSS represents several real situations of planning and for that many efforts have been made to investigate an effective implementation, along the past decade, particularly with GA. Davis (1985) was first to use GA to solve JSS problem. In literature, two important issues have been studied to solve JSS problem utilising GA’s. One is how to encode (representation) a solution of the JSS problem into a chromosome so as to ensure that a chromosome will correspond to a feasible solution. In this direction a brief survey of existing representation schemes can be found in Amirthagadeswaran and Arunachalam (2006). Also, they proposed a method of representation and schedule deduction method utilising a heuristic technique in order to minimise makespan. Li and Chen (2010) designed a two-row chromosome structure based on working procedure and machine distribution in order to minimise makespan. Another issue is how to enhance performance of genetic search (local) by incorporating traditional heuristic methods. Moreover, JSS is a hard problem that cannot be solved effectively by applying any single technique and a great deal of research has focussed on various methods of hybridisation (Cheng et al., 1999). Lee et al. (1997) proposed a framework utilising GA with machine learning and heuristics-space, in order to determine the sequence of job release order as well as the sequence for dispatching jobs at each individual machine. Yamada and Nakano (1997) proposed a multi-step crossover fusion (MSXF) as a unified operator and a recombination operator in GA local search for JSS, in order to solve large-size problems only. Ghedjati (1999) proposed a heuristics mixing method based on GA to solve JSS problem with consideration of parallel machines and precedence constraints in order to minimise the maximum completion time. Author concluded that proposed method obtained improvement due to heuristics but with longer running time. In Xie (2001) the job batch size and operation sequences were considered as two variables in order to achieve optimal job completion time. Authors concluded that job completion time could be reduced if batch size is considered. Goncalves et al. (2002) combines a GA to define the priority of operations and delay time, a schedule generator procedure to generate parameterized active scheduled, and a local search heuristics procedure to improve the solution. Wang and Zheng (2002) proposed a modified GA (MGA) for JSS using operation-based representation and decoding the solution into an active schedule during the search process, replacing the classical mutation of GA by the metropolis sample process of simulated annealing (SA) with probabilistic jumping property, applying

multiple state generators in a hybrid way. Mattfeld and Bierwirth (2004) considered release and due-dates in order to measure tardiness. Authors concluded that the weakness of GA to search for increasing problem size could be mitigated by a tuneable schedule builder and multi-stage decomposition technique which reduces the size of the search space. Hasan et al. (2007) combines a heuristics job ordering with GA for small to medium size JSS problems in order to find a valid schedule that yields the minimum makespan. Buzatu and Bancila (2008) integrate GA and combinations of heuristic rules, such as shortest processing time (SPT), minimal slack (MS), longest processing time (LPT) in order to generate the initial individuals. Zhou et al. (2009) proposed a hybrid framework in which GA determined first operation of each machine while heuristics determined the assignment of remaining operations in order to minimise weighted tardiness. Jia et al. (2007) integrate GA and Gantt chart (GC) for JSS in order to determine combination of process plans as well as operation schedule for small-sized or medium-size scheduling problems for a distributed manufacturing system. Some studies have been attempted for designing multi objective GA (MOGA) for JSS problem (Ponnambalam et al., 2001). Jain and Meeran (1999) provides a comprehensive survey of methods by which JSS problem has been approached. They concluded that meta-heuristic technique appears to work best for JSS problem. Among the various approaches to JSS problem, there has been an increasing interest in applying GA. A GA exhibits parallelism, contains certain redundancy and historical information of past solutions, and is suitable for implementation on massively parallel architectures (Wang and Zheng, 2002). The combined use of a GA and a heuristic is a typical form of meta-heuristics (Zhou et al., 2009). Literature reveals that numerous GA approaches to solve JSS problem have been utilised. These approaches differ strongly from each other with respect to the encoding and operators used, the constraints handled and the goals pursued. Despite these differences, all approaches have in common knowledge is required in order to produce competitive schedules. GA has been approved as an effective and efficient optimisation tool for JSS problems. Literature review divulges that simulation-based GA is not studied deeply for JSS problem. Whereas, simulation provides a meaningful understanding of real world system’s nature. Thus, a simulation-based GA can be settled as an emphatic approach to accomplish JSS. The JSS problem can be defined as: there are “n” numbers of jobs that have to process on “m” numbers of machines in order to find an optimal job schedule. Each job “i” is to be processed on a set of machines and the processing time of each operation is known in advance. The resulting schedule is subjected to the constraint of job and machines, i.e. one machine can process only one operation at a time and pre-emption of any operation is prohibited. 3. Adopted methodology The present work utilises a simulation-based GA approach. Encoding/representation is the first step of GA. A sequence oriented representation is used in the present work. Here, a bit (gene) of a chromosome is formed by a process plan number (i.e. alphabets) of a part type. Each bit of the chromosome is in fixed sequence/order to represent associate process plan of a part type. For example, if there are three part types A, B and C having of multiple process plans (MPP), respectively. Each part-type can be processed through any of its given MPP. Then, this information can be encoded as: {2, 1, 4}. Where, 2 represents

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processing of part-type A by following its second process plan, 1 represents processing of part-type B by first process plan and 4 represents processing of part-type C by its fourth process plan. In this work, initial population is generated randomly. The present work utilise linear ranking (LR) selection method with stochastic universal sampling (SUS). In this method, individuals in the population are ranked according to their fitness and the expected value of each individual depends on its rank rather than on its absolute fitness (Baker, 1985). Once the expected values have assigned, the SUS method is applied to sample the population (i.e. choose parents). Thus, a mating pool consisting of selected individual is formed (Mitchell, 2002). In this study, two-point crossover approach is considered and it is applied on the individuals of mating pool. For two-point crossover, two strings are selected randomly from the mating pool to make a pair. For each pair, essentiality of carrying out crossover is determined using crossover probability (pc ¼ 0.8). In two-point crossover site is selected randomly twice from first to last position. The present work utilise reciprocal exchange type of mutation operator with a mutation probability (pm ¼ 0.2) and it is applied on the off-springs produced after the crossover operation. The mutation position (from first to last bit) is selected randomly twice and process plans at these sites are interchanged, keeping other bits unchanged. After mutation, some illegal off-spring may generate, i.e. one part type may exceeds the limit of given MPP in the individuals which undergoes mutation operation. Thus, a repairing strategy is required to resolve this illegitimacy of off-springs. In the present work, after mutation, all the individuals which undergoes mutation operation are checked to ensure that not any part type exceed the given range of process plans. Moreover, a repairing procedure also checks if at any position/site of string exceeds the specified number of concerned process plan of part type, it shall replaced by any one process plan from the given range of process plans randomly. For reproduction, the elitism way is embedded with the LR selection. Elitism transfer few good individuals from the previous population to the population of next generation. In the present work, an elitism rate of 0.9 is considered in order to transfer the best individual form pervious population to the population of next generation. In the present work maximum number of generation (max_gen) is considered as the termination criterion, i.e. equal to the number of jobs (n) £ number of machines (m), as considered in Ponnambalam et al. (2001). To overcome premature convergence in the population a restart scheme based on the ideas of a similar scheme used by Ruiz and Maroto (2006) is used. Accordingly, at each generation the maximum fitness value is store. If the best fitness value is not changed for more than a pre-specified number of generations (best_count), the restart phase commences to regenerate the population. In the present work, the value the counter (best_count) is set at 15, i.e. if the highest fitness value in the population does not change for more than 15 generations, the restart phase will be activate. This works as follows: Step 1. Short the population in descending order of fitness value. Step 2. Skip the first 20 percent of individuals from the shorted list. Step 3. The remaining 80 percent of individuals in shorted list are disregarded and regenerated in the following way:

.

.

Generate first half (50 percent) of new chromosomes by reciprocal exchange mutation operation of the first 20 percent best (shipped) individuals. Generate another half of new chromosomes randomly.

All newly generated genetic material will only replace the 80 percent worst individual of the population if they yield fitness value better than that of the worst individual of previous population. Also, the repetition of the chromosomes in the newly generated 80 percent population is not allowed. The evaluation of fitness function is carried out using simulation. Simulation is used to compute performance measures as it yields performance measure close to actual system performance in comparison to mathematical functions. The present work considers the minimisation of mean tardiness of jobs and makespan. Figure 1 shows the flow chart of the working of GA. In the present work, JSS environment for simulation can be characterized as follows: inter machine part transportation time is included/considered. Set-up time and inspection time are independent of schedule/sequence and are included in processing time. Infinite buffer location capacities are assumed in front of individual machine and each part enters in buffer location before the processing at machine. Ready time/release time of all jobs are zero, i.e. all jobs are available at the commencement of processing. Operation time and job arrival time are known and fixed before the job is released to shop. The routing of each job through the machine is random; for any given job, two consecutive operations on one machine are not allowed, but a job may return to that machine after being processed on other machines. The dispatching rule of SPT is used to process the jobs. First come first serve (FCFS) rule is used as a tie breaker. Due-dates are specified according to the total work content (TWK) criterion and MPP for each part type are considered. Machines are independent from each other and are available at zero time. Jobs are independent from each other. A part leaves the shop after all its operations are completed. Order cancellation, rework and machine breakdowns are not permitted.

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Encoding

Fitness Evaluation

Stop?

Simulation

Yes

Results

No Selection

Crossover

Mutation

Figure 1. Flow chart of working of genetic algorithm

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Table I. Production order details

4. Results and discussion In order to implement adopted methodology, a job shop consisting of 15 machines is taken into consideration. Table I shows the details of a case study used for implementation. Uniform transportation time of three units is assumed between two machines. Three cases are considers in order to measure the comparative performance of job shop. In all cases, mean tardiness and makespan are regarded as the performance measures. First case consists of randomly selected single process plan for each part type of production order. In second case, single process plan for each part type is considered according to minimum production time criterion. Third case deals with MPP for each part type as reported in production order. These three cases are optimised using adopted methodology and Table II presents the results. It clearly reveals the randomly selected single process plan performs worst for

PT

Q

DD

PP no.

A

20

1000

B

15

455

C

18

345

J

22

265

K

11

335

L

14

670

1 2 1 2 3 4 1 2 3 4 5 1 2 3 1 2 3 1 2 3 4 5

TM

TT

TP

14(10)-15(61)-12(43)-11(39)-8(47) 14(10)-15(18)-13(30)-4(32)-11(39)-8(47) 5(10)-9(10)-1(33)-5(38) 5(10)-8(6)-4(40)-5(38) 6(25)-10(41)-14(24)-6(38)-10(37) 6(25)-10(41)-13(12)-12(30)-7(39)-10(37) 4(29)-2(19)-7(21) 4(29)-8(29)-6(9)-7(13) 5(39)-14(33)-2(11)-1(10)-12(16) 5(39)-1(6)-5(30)-3(39)-2(29)-1(19) 10(69)-13(33)-8(29) 4(33)-15(20) 1(22)-13(20)-7(35)-9(31)-12(45)-14(17) 1(22)-12(76)-9(19)-3(48)-14(17) 10(27)-1(40) 2(6)-13(36) 6(30)-5(73)-4(31) 11(29)-15(44)-5(5)-12(41)-11(15) 11(29)-15(24)-2(42)-11(15) 3(22)-1(5)-9(39)-13(19) 3(18)-6(5)-4(18)-7(39)-10(7) 3(22)-7(10)-12(38)-13(19)

200 176 91 94 165 184 69 80 109 162 131 53 170 182 67 42 134 134 110 85 87 89

12 15 9 9 12 15 6 9 12 15 9 3 15 12 3 3 6 12 9 9 12 9

212 191 100 103 177 199 75 89 121 177 140 56 185 194 70 45 140 146 119 94 99 98

Notes: PT – part-type; Q. – production quantity; DD – due-dates; PP no. – process plan number; MPP – multiple process plans; TM – total machining time; TT – total transportation time; Mi (Ti) – machining number (processing time); TT – total production time

Performance measures

Table II. Results of case studies

MPP’s {Mi (Ti)}

Mean tardiness Makespan

Single process plan (randomly selected)

Single process plan (selected with minimum production time criterion)

MPP

651 2,292

413 2,268

263 1,541

Note: MPP – multiple process plans

both makespan and mean tardiness performance measures and MPP case yields least makespan and mean tardiness. Thus, it can safely be concluded that if only single process plan is to be made available than process plan selected according to minimum production time criterion yields better results than randomly selected process plans. Moreover, availability of MPP assists scheduler in selecting right combination of process plan for different part type resulting in the least makespan and mean tardiness. This work also considers the suitability of restart scheme. Figure 2 shows the convergence curve of regular GA without restart scheme when MPP for each part type are available. The average fitness value obtained from regular GA is 0.00296. Figure 3 shows the convergence curve of GA with restart scheme for the above mentioned case. The average fitness value comes out to be 0.00331. Thus, embedding results scheme in regular GA avoids premature convergence and improves fitness value.

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0.0035 0.003

Fitness Values

0.0025 0.002 0.0015 0.001 0.0005 0 0

20

40 60 Number of Generations

80

100

Figure 2. Convergence curve of regular GA (without restart scheme)

0.004 0.0035

Fitness values

0.003 0.0025 0.002 0.0015 0.001 0.0005 0 0

20

40 60 Number of generations

80

100

Figure 3. Convergence curve with restart scheme

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5. Conclusions A simulation-based GA approach has been applied effectively to solve JSS problem. Mean tardiness and makespan are regarded as performance measures. Results indicates that the consideration of MPP for each part type have superior performance than single process plan for each part type. The comparative analysis shows that the embedding restart scheme into regular GA improves the fitness value of fitness function. References Amirthagadeswaran, K.S. and Arunachalam, V.P. (2006), “Improved solutions for job shop scheduling problems through genetic algorithm with a different method of schedule deduction”, The International Journal of Advanced Manufacturing Technology, Vol. 28 No. 5, pp. 532-40. Baker, J.E. (1985), “Adaptive selection methods for genetic algorithms”, Proceeding on the First International Conference on Genetic Algorithms and their Applications, Lawrence-Erlbaum, Mahwah, NJ, pp. 101-11. Buzatu, C. and Bancila, D. (2008), “A hybrid algorithm for job shop scheduling”, Proceedings of 6th International DAAAM Baltic Conference, INDUSTRIAL ENGINEERING, Tallinn, Estonia, 24-26 April. Cheng, R., Gen, M. and Tsujimura, Y. (1999), “A tutorial survey of job shop scheduling problems using genetic algorithms. Part II: hybrid genetic search strategies”, Computer and Industrial Engineering, Vol. 36, pp. 343-64. Conway, R.W., Maxwell, W.L. and Miller, L.W. (1967), Theory of Scheduling, Addison-Wesley, Reading, MA. Davis, L. (1985), “Job shop scheduling with genetic algorithms”, Proceedings of the First International Conference on Genetic Algorithms, Lawrence-Erlbaum, Mahwah, NJ, pp. 136-40. Ghedjati, F. (1999), “Genetic algorithms for the job-shop scheduling problem with unrelated parallel constraints: heuristic mixing method machines and precedence”, Computers & Industrial Engineering, Vol. 37 No. 1, pp. 39-42. Goncalves, J.F., Magalhaes, J.J., de Rua, D., Frias, R., Jose, J., Mendes, M. and Resende, M.G.C. (2002), “A hybrid genetic algorithm for the job shop scheduling problem”, AT&T Labs Research Technical Report TD-5EAL6J, September. Hasan, S.M.K., Sarker, R. and Cornforth, D. (2007), “Hybrid genetic algorithm for solving job-shop scheduling problem”, 6th IEEE/ACIS International Conference on Computer and Information Science, ICIS, pp. 519-24. Jain, A.S. and Meeran, A. (1999), “A state-of-the-art review of job-shop scheduling techniques”, European Journal of Operations Research, Vol. 113, pp. 390-434. Jia, H.Z., Fuh, J.Y.H., Nee, A.Y.C. and Zhang, Y.F. (2007), “Integration of genetic algorithm and Gantt chart for job shop scheduling in distributed manufacturing systems”, Computers & Industrial Engineering, Vol. 53 No. 2, pp. 313-20. Kutanoglu, E. and Sabuncuoglu, I. (1999), “An analysis of heuristics in a dynamic job shop with weighted tardiness objectives”, International Journal of Production Research, Vol. 37 No. 1, pp. 165-87. Lee, C.Y., Piramuthu, S. and Tsai, Y.K. (1997), “Job shop scheduling with a genetic algorithm and machine learning”, International Journal of Production Research, Vol. 35, pp. 1171-91.

Li, Y. and Chen, Y. (2010), “A genetic algorithm for job-shop scheduling”, Journal of Software, Vol. 5 No. 3, pp. 269-74. Maccarthy, B.L. and Liu, J. (1993), “Addressing the gap in scheduling research: a review of optimization and heuristic methods in production scheduling”, International Journal of Production Ressearch, Vol. 31, pp. 59-79. Mattfeld, D.C. and Bierwirth, C. (2004), “An efficient genetic algorithm for job shop scheduling with tardiness objectives”, European Journal of Operational Research, Vol. 155 No. 3, pp. 616-30. Mitchell, M. (2002), An Introduction to Genetic Algorithms, Prentice-Hall, New Delhi. Pinedo, M. (1995), Scheduling: Theory, Algorithms and Systems, Prentice-Hall, Upper Saddle River, NJ. Ponnambalam, S.G., Ramkumar, V. and Jawahar, N. (2001), “A multiobjective genetic algorithm for job shop scheduling”, Production Planning & Control, Vol. 12 No. 8, pp. 764-74. Ruiz, R. and Maroto, C. (2006), “A genetic algorithm for hybrid flow shops with sequence dependent setup times and machine eligibility”, European Journal of Operational Research, Vol. 169 No. 3, pp. 781-800. Vinod, V. and Sridharan, R. (2008), “Scheduling a dynamic job shop production system with sequence-dependent setups: an experimental study”, Robotics & Computer-Integrated Manufacturing, Vol. 24, pp. 435-49. Wang, L. and Zheng, D.Z. (2002), “A modified genetic algorithm for job shop scheduling”, International Journal of Advance Manufacturing Technology, Vol. 20, pp. 72-6. Xie, H. (2001), “A genetic algorithm approach to job shop scheduling problems with a batch allocation issue”, 17th International Workshop on Artificial Intelligence, Seattle, WA, 1 August, pp. 126-31. Yamada, T. and Nakano, R. (1997), “Genetic algorithms for job-shop scheduling problems”, Proceedings of Modern Heuristic for Decision Support, London, 18-19 March, p. 67. Zhou, H., Cheung, W. and Lawrence, C.L. (2009), “Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm”, European Journal of Operational Research, Vol. 194 No. 3, pp. 637-49.

About the authors Rakesh Kumar Phanden obtained his B.Tech in Mechanical Engineering from GLA Institute of Technology and Management (now GLA University), Mathura and his M.Tech in Integrated Product Design and Manufacturing from Guru Jambheshwar University of Science & Technology, Hisar. At present, he is working as a Senior Research Fellow in the Mechanical Engineering Department at the National Institute of Technology, Kurukshetra. He is pursuing a PhD in Integration of Process Planning and Scheduling from the Mechanical Engineering Department at NIT Kurukshetra. His research interests include computer aided process planning, scheduling, and artificial intelligence to manufacturing systems, flexible manufacturing systems and CAD/CAM. Ajai Jain obtained his BSc in Mechanical Engineering from Dayalbagh Educational Institute, Agra, his ME in Production & Industrial System Engineering from University of Roorkee, Roorkee (now IIT Roorkee) and his PhD in Mechanical Engineering from Kurukshetra University, Kurukshetra. Currently he is working as Associate Professor in the Department of Mechanical Engineering, National Institute of Technology, Kurukshetra. His areas of

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current interest are design and operations of manufacturing systems, specifically in scheduling. He has published articles in refereed and cited national and international journals. Ajai Jain is the corresponding author and can be contacted at: [email protected] Rajiv Verma is working as a Lecturer in the Department of Mechanical Engineering at the National Institute of Technology, Kurukshetra. He obtained his BSc in Mechanical Engineering from Z.H. College of Engineering and Technology, AMU Alighar, his ME in Production & Industrial System Engineering from University of Roorkee, Roorkee (now IIT Roorkee) and his PhD Mechanical Engineering from the National Institute of Technology, Kurukshetra.

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Factorial analysis of lifting task to determine the effect of different parameters and interactions Sarbjeet Singh Department of Mechanical Engineering, Government College of Engineering & Technology, Jammu, India, and

Sunand Kumar

Factorial analysis of lifting task 947 Received 4 April 2011 Revised 24 November 2011 Accepted 13 December 2011

Department of Mechanical Engineering, National Institute of Technology, Hamirpur, India Abstract Purpose – The purpose of this paper is to evaluate the effect of main parameters and their interactions on the workers’ Lifting Index in a steel rolling mill. Design/methodology/approach – NIOSH (National Institute for Occupational Safety and Health) lifting equation has been used to evaluate the risk of lifting tasks with respect to low back injury under varying load (10, 15, 20 kg), frequency (2, 3, 4 lifts/min), and twisting angle (0, 30, 45 degree). Findings – The level of importance of the parameters on lifting index at origin and destination has been determined using analysis of variance (ANOVA).The analysis draws on lifting parameters and uses both main effects and interactions to describe the variation in Lifting Index and to identify the social influence associated with back injury. The interactions between object weight and twisting angle and object weight and lifting frequency turn out to be significant ( p , 0.05), whereas the interaction between twisting angle and lifting frequency is less significant ( p ¼ 0.061). Research limitations/implications – The study includes a specific location (steel rolling mills located in Jammu region of India) only. Practical implications – The findings suggest that focus should be made on all lifting parameters, rather than sole emphasis on the load to be lifted. Originality/value – The paper supports the view that load, twisting angle and lifting frequency greatly influence the physical stressfulness of the task. It is suggested that the workplace should be designed for negligible twisting and moderate lifting frequency, so as to have minimum Lifting Index. Keywords Steelmaking, Occupational health and safety, Materials handling, Lifting parameters, Lifting index, Interactions performance management Paper type Research paper

1. Introduction Lower back pain is the most susceptible part of the musculoskeletal system from injury point during manual material handling (MMH) tasks in all industries. The prevalence of back pain has been of concern to medical and research community for quite some time. Manual handling of material is an expensive industrial problem considering that industries pay not only for workman’s compensation, but also spend billion of dollars on tests, treatments, claims and surgeries. MMH creates problems for workers around the world. Workers engaged in lifting, lowering, carrying, pushing and pulling of heavy materials increases the rates of musculoskeletal injuries. The National Institute for Occupational Safety and Health (NIOSH) developed a lifting equation in 1981

Journal of Manufacturing Technology Management Vol. 23 No. 7, 2012 pp. 947-953 q Emerald Group Publishing Limited 1741-038X DOI 10.1108/17410381211267754

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and revised in 1991 uses a series of lifting multipliers (parameters) to calculate corresponding recommended task weight limits. The load constant recommended in the NIOSH equation depicts that young Korean males are well protected (Lee et al., 1996). The NIOSH equations horizontal distances are positively related to box width and here was also a significant interaction between box width and starting height (Potvin and Bent, 1997). Lifting index (LI), an index of relative physical stress, can be used to identify hazardous lifting tasks. Although the 1991 equation has not been fully validated, the recommended weight limits derived from the revised equation are consistent with or lower than those generally reported in the literature. NIOSH believed that the revised 1991 lifting equation is more likely than the 1981 equation to protect most workers (Keyserling, 1989; Waters et al., 1993). Three criteria used in establishing NIOSH psychophysical, biomechanical, and physiological were validated for manual lifting against the data published by different researchers in the subject literature. Results of the cross-validation for psychophysical criterion confirmed the validity of assumptions made in the 1991 NIOSH revised lifting equation. However, the results of cross-validation for the biomechanical and physiological criteria were not in total agreement with the 1991 NIOSH model (Vincent, 2005; Hidalgo et al., 1995). A review of the existing literature failed to come up with a detailed description of procedures for obtaining the equation variables at a worksite and a systematic approach for data collection was therefore proposed (Hashemi et al., 1997; Ja¨ger and Luttmann, 1997). Multiple regression analysis revealed that lifting repetitiveness contributed to the occurrence of LBP (Xiao et al., 2004). The detailed description of the procedure for measuring the variables of the Revised NIOSH lifting equation were adopted during the evaluation of a lifting and lowering task (Okimoto and Teixeira, 2009). The asymmetry multiplier incorporated in the 1991 National Institute for Occupational Safety and Health lifting equation adequately controls the biomechanical spine loads during asymmetric lifting (Lavender et al., 2009). The present paper examines the effect of object weight, twisting angle and lifting frequency and their interactions on lifting index both at origin and destination of the lift. 2. Materials and method In the study ergonomic acceptable limits according to the NIOSH method for an industrial lifting station of a steel rolling mill have been evaluated. Subjects with no history of chronic or acute illness, not having hypertension or any other major health issues, and not under any prescribed medication were selected for the study. Five male workers, having at-least six years of working experience were included in the study. In this study the effect of three lifting frequencies (2, 3, 4 lifts/minutes), three load weights (10, 15 and 20 kg) and three asymmetric angels (08, 308, 458) were considered. The maximum reach point was identified as the highest location to which the subject could lift the load without hyper flexing the body, and generally it was near the eye-ear line level. The other parameters like horizontal distance of load 35 cm, vertical distance 120 cm, fair coupling, and moderate lifting duration of 2 hours were kept constant. Subjects were doing lifting following free-style posture. The lifting index (origin and destination) were considered as the response variables. Lifting index (LI) is associated with an estimate of the level of physical stress associated with a particular manual lifting task. By brainstorming through a cause and effect diagram, the lists of factors of interest that may have an impact on the lifting index have been identified (Table I).

Object weight 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 20 20 20 20 20 20 20 20 20

Twisting angle

Lifting frequency

LI (origin)

LI (destination)

0 0 0 30 30 30 45 45 45 0 0 0 30 30 30 45 45 45 0 0 0 30 30 30 45 45 45

2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4

1.08 1.15 1.26 1.20 1.28 1.41 1.26 1.34 1.49 1.63 1.74 1.90 1.81 1.92 2.11 1.89 2.01 2.21 2.17 2.31 2.50 2.41 2.57 2.82 2.52 2.68 2.98

0.97 1.06 1.12 1.08 1.15 1.26 1.13 1.20 1.32 1.43 1.55 1.71 1.62 1.72 1.89 1.70 1.80 1.98 1.95 2.07 2.24 2.16 2.30 2.52 2.26 2.40 2.64

The design of the experiment and selection of orthogonal array depends upon the number of factors and interactions of interest and the number of levels for the factors of interest. The minimum required DOF in the experiment is the sum of all the factor and interaction. In the present experimental setup there are three levels for all three factors. The number of degree of freedom associated with these three factors and three two-level interactions is 18. As the degree of freedom required for the experiment is 18 so the orthogonal array that is to be selected should have degree of freedom higher than 18. The most suitable orthogonal array that can be used for this experiment is L27. The assignment of main factors and the desired interactions could be easily done by using linear graphs. In this experiment, the assignment of factors and interactions was carried out using MINITAB software. The data is than analyzed by analysis of variance (ANOVA). It is a common statistical technique to determine the percent contribution of each factor for results of the experiment. It has also decided to study the effect of interactions between the main factors, i.e. object weight vs twisting angle (A £ B), object weight vs lifting frequency (A £ C), twisting angle vs lifting frequency (B £ C). To examine the influence of the independent variables, repeated measures ANOVA has been conducted with an alpha level of 0.05 was used for all statistical tests, and conformation tests were conducted at optimized conditions. In the study dependent variables are lifting index (origin and destination) and independent variables are the twisting angle, object weight and lifting frequency.

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Table I. Lifting index (origin and destination)

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Table II. Analysis of variance for lifting index (origin)

3. Results and discussion The effects of the three independent variables (lifting frequency, load weight and twisting angle) and their interactions were evaluated using ANOVA and factorial design analysis. In addition, plots of the significant factors and interactions were developed to show significance in the statistical procedure to calculate the contribution of different parameters based on the individual sum of square values. The purpose of the ANOVA and significant factors plot was to identify the important parameters in prediction lifting index at origin and at destination. The data were analyzed using MINITAB statistical analysis software. The results wherein the two response variables for each of 27 trials conducted are shown in Table II. The ANOVA analysis has been conducted for analyzing the influence of object weight, twisting angle and lifting frequency on lifting index (origin and destination). The experiments were conducted for each combination of factors as per the selected orthogonal array. It is observed from ANOVA of lifting index (origin) that object weight, twisting angle and lifting frequency are significant ( p , 0.05) whereas the interactions between object weight MINITAB statistical analysis software. The results wherein the two response variables for each of 27 trials conducted are shown in Table II. The ANOVA analysis has been conducted for analyzing the influence of object weight, twisting angle and lifting frequency on lifting index (origin and destination). The experiments were conducted for each combination of factors as per the selected orthogonal array. It is observed from ANOVA of lifting index (origin) that object weight, twisting angle and lifting frequency are significant ( p , 0.05) whereas the interactions between object weight and twisting angle, object weight and lifting frequency were found to be significant ( p , 0.05) and needs further analysis. Further, it has been observed from ANOVA of lifting index (destination) that object weight, twisting angle and lifting frequency are significant ( p , 0.05) whereas the interactions between object weight and twisting angle and object weight and lifting frequency were found to be significant ( p , 0.05) and needs further analysis. The interaction between twisting angle and lifting frequency comes out to be less significant for lifting index (origin and destination). It has been observed that lifting task with load weight of 15 kg (at 2, 3, 4 lifts/min and 308 and 458) lies between 1.62 and 2.21 clearly indicating that the task at origin and destination would be physically stressful for some of the industrial workers. Further, the load weight 20 kg (at 2, 3, 4 lifts/min and 08, 308 and 458) lies between 1.95 and 2.98 indicates that the task would be stressful for almost all industrial workers. The findings have been reflected in Figures 1 and 2 (Table III). Source

DF

Seq. SS

Adj. SS

Adj. MS

F

p

Object weight Twisting angle Lifting frequency Object weight £ twisting angle Object weight £ lifting frequency Twisting angle £ lifting frequency Error Total

2 2 2 4 4 4 8 26

5.83682 0.31562 0.31896 0.02569 0.02289 0.00236 0.00133 6.52367

5.83682 0.31562 0.31896 0.02569 0.02289 0.00236 0.00133

2.91841 0.15781 0.15948 0.00642 0.00572 0.00059 0.00017

17510.47 946.87 956.87 38.53 34.33 3.53

Sig. Sig. Sig. Sig. Sig. 0.061

angle

bad

1.0 20

0

30

45

f

Mean

Mean

1.5

15

angle

bad

2.0

10

Factorial analysis of lifting task

Main Effects Plot (data mean) for LI (origin)

Main Effects Plot (data mean) for LI (destination) 2.4 2.1 1.8 1.5 1.2

951 10

15

20

0

30

45

f 2.4 2.1 1.8 1.5 1.2

2.0 1.5 1.0 2

3

4

2

3

4

(a)

(b) Interaction Plot for Lifting Index (D)

Interaction Plot for Lifting Index (O) 0

30

45

2

3

Figure 1. Main effect plots for lifting index (a) origin (b) destination

0

4 3

load 10 15 20 load 10 angle 0 30 45

2

load

1 3 2

angle

30

45

2

3

4 2.4 1.8

load

load 10 15 20

1.2 2.4 1.8

angle

angle 0 30 45

1.2

1 f

f

(a)

(b)

Source

DF

Seq. SS

Adj. SS

Adj. MS

F

p

Object weight Twisting angle Lifting frequency Object weight £ Twisting angle Object weight £ lifting frequency Twisting angle £ lifting frequency Error Total

2 2 2 4 4 4 8 26

7.33445 0.40356 0.41583 0.03201 0.02848 0.00510 0.00132 8.22076

7.33445 0.40356 0.41583 0.03201 0.02848 0.00510 0.00132

3.66723 0.20178 0.20791 0.00800 0.00712 0.00128 0.00016

22250.58 1224.29 1261.51 48.56 43.20 7.74

Sig. Sig. Sig. Sig. Sig. 0.007

4. Conclusion The goal of this study was to determine ergonomic acceptable limits according to the NIOSH method for an industrial lifting station. The data collected demonstrates that object weight, lifting frequency and twisting angle are the factors effecting lifting task. Results of the study show that several factors require examination to determine an ergonomically correct lifting station. Each of these factors (multipliers) is summarized

Figure 2. Interaction plot for lifting index (a) origin (b) destination

Table III. Analysis of variance for lifting index (destination)

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into lifting index. In case of lifting index at origin the interactions between object weight, lifting frequency and twisting angle were found to be significant and needs further elaboration. Further, the interactions between object weight and lifting frequency, object weight and twisting angle were found to be significant and needs further elaboration where as interaction between lifting frequency and twisting angle was found to be insignificant. An examination of the lifting index reveals areas of concentration in order to reduce overall task stress and lower back related injuries.

References Hashemi, L., Webster, M.S., Barbara, S. and Clancy, A. (1997), “Length of disability and cost of workers’ compensation low back pain claims”, Journal of Occupational & Environmental Medicine, Vol. 39 No. 10, pp. 937-45. Hidalgo, J., Genaidy, A., Karwowski, W., Christensen, D. and Stambough, J. (1995), “A cross-validation of the NIOSH limits for manual lifting”, Ergonomics, Vol. 38 No. 12, pp. 2455-64. Ja¨ger, M. and Luttmann, A. (1997), “Critical survey on the biomechanical criterion in the NIOSH method for the design and evaluation of manual lifting tasks”, International Journal of Industrial Ergonomics, Vol. 23 No. 4, pp. 331-7. Keyserling, W.M. (1989), “Analysis of manual lifting tasks: a qualitative alternative to the NIOSH work practices guide”, AIHA Journal, pp. 165-73. Lavender, S.A., Li, Y.C., Natarajan, R.N. and Andersson, G.B.J. (2009), “Does the asymmetry multiplier in the 1991 NIOSH lifting equation adequately control the biomechanical loading of the spine”, Ergonomics, Vol. 52 No. 1, pp. 71-9. Lee, K.S., Park, H.S. and Chun, Y.H. (1996), “The validity of the revised NIOSH weight limit in a Korean young male population: a psychophysical approach”, International Journal of Industrial Ergonomics, Vol. 18, pp. 181-6. Okimoto, M.L.R. and Teixeira, E.R. (2009), “Proposed procedures for measuring the lifting task variables required by the revised NIOSH lifting equation – a case study”, International Journal of Industrial Ergonomics, Vol. 39 No. 1, pp. 15-22. Potvin, J.R. and Bent, L.R. (1997), “NIOSH equation horizontal distances associated with the Liberty Mutual (Snook) lifting table box widths”, Ergonomics, Vol. 40 No. 6, pp. 650-5. Vincent, C.M. (2005), “Revisited: comparison of two techniques to establish maximum acceptable forces of dynamic pushing for male industrial workers”, International Journal of Industrial Ergonomics, Vol. 37, pp. 877-82. Waters, T.R., Anderson, V.P., Garg, A. and Fine, L.J. (1993), “Revised NIOSH equation for the design and evaluation of manual lifting tasks”, Ergonomics, Vol. 36, pp. 749-76. Xiao, G., Dempsey, P.G., Lei, L., Ma, Z.H. and Liang, Y.X. (2004), “Study on Musculoskeletal disorders in a machinery manufacturing plant”, Journal of Occupational and Environmental Medicine, Vol. 46 No. 4, pp. 341-6.

About the authors Dr Sarbjeet Singh is working in the Department of Mechanical Engineering at Government College of Engineering & Technology. The author has published research papers in journals of

national and international importance. Projects of industrial related problems and renewable sources of energy have been completed. The author is life member of three premier institutions/association, viz. Indian Society of Technical Education (ISTE), Indian Institution of Engineers and Indian Ergonomic Association (IEA). The area of specialization is Industrial and Production Engineering. Sarbjeet Singh is the corresponding author and can be contacted at: [email protected] Dr Sunand Kumar is Professor in the Department of Mechanical Engineering at National Institute of Technology, Hamirpur. The author has published research papers in journals of national and international importance. The area of specialization is Industrial Engineering.

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