An extent analysis of 3PL provider selection criteria: A case on Turkey cement sector

Bulgurcu, Berna; Nakiboglu, Gulsun Article An extent analysis of 3PL provider selection criteria: A case on Turkey cement sector Cogent Business & Management Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Bulgurcu, Berna; Nakiboglu, Gulsun (2018) : An extent analysis of 3PL provider selection criteria: A case on Turkey cement sector, Cogent Business & Management, ISSN 2331-1975, Taylor & Francis, Abingdon, Vol. 5, https://doi.org/10.1080/23311975.2018.1469183 This Version is available at: https://hdl.handle.net/10419/206067 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ OPERATIONS MANAGEMENT | RESEARCH ARTICLE An extent analysis of 3PL provider selection criteria: A case on Turkey cement sector Berna Bulgurcu 1 *and Gulsun Nakiboglu 1 Abstract: Outsourcing has become an increasingly popular means for businesses to improve their efficiency. Logistics outsourcing can be described as transferring some of the logistics functions to an external firm. This paper aims to identify the selection criteria that are used by logistics service providers in Turkey’scementsectorinchoosing the third-party service provider. By drawing focus on Chang’s Extent Analysis on Fuzzy Analytical Hierarchy Process (FAHP), the present paper evaluates cost, service/operation quality, competencies, general attributes of firms and relational factors as the main criteria, and considers explanatory 29 sub-criteria. In doing so, a questionnaire that was prepared in the pairwise comparison model was used as a large sample to collect data from a total of 25 experts working in 14 cement companies. As a result, the analysis identifies service/operation quality as the most important one among the main criteria, and determines the service price as the most preferred criterion among the sub-criteria. The study and results both provides particular insight into a specific sector as it is based on the data collected from a large number of experts in one sector, and offers an opportunity for other sectors from the same point of view. Subjects: Operations Research; Business; Management and Accounting; Operational Research / Management Science; Operations Management; Supply Chain Management; Manufacturing Industries; Transport Industries; Service Industries ABOUT THE AUTHORS Berna Bulgurcu is a researcher and holds a PhD in Management Science from Cukurova University. She works as an Assistant Professor at Business Department of the same university since 2016. Her research interests are MultiCriteria Decision Making Techniques, Fuzzy Logic, Artificial Neural Network and Adaptive Neuro Fuzzy Inference Systems (E-mail: [email protected]. tr; Tel: 090-322 338 72 54, ext 273). Gulsun Nakiboglu is assistant professor in Production Management at Cukurova University, Business Department. She received her PhD in Industrial Engineering Department from same university. Her teaching and research interests include supply chain management, logistics and production planning in sustainability perspective (E-mail: ngulsun@cu. edu.tr; Tel: 090-322 338 72 54, ext 277). PUBLIC INTEREST STATEMENT Outsourcing of logistics process is a frequently preferred practice of enterprises to focus on their core competencies. Deciding the appropriate logistics service provider (LSP) should be done for the continuous and smooth progress of the logistics process. For this reason, the decision makers determines the criteria in the best way, which is appropriate to the sector, product, distribution network and own business characteristics. In this study, important LSP criteria for a sector (cement sector) have been identified. The criteria used for the LSP were searched from literature, the list was shortened in the interviews made by experts, and the form that includes 29 pairwise comparisons of criteria was asked to 25 experts from 14 cement firms. In the comparison of the criteria, the multi-criteria decision method fuzzy AHP was used and the criteria were evaluated. Because it has been done with a large number of experts from the same sector, it will be able to give ideas to similar sectors and LSPs. Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 © 2018 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Received: 04 January 2018 Accepted: 22 April 2018 First Published: 11 May 2018 *Corresponding author: Berna Bulgurcu, Department of Business Administration, Cukurova University, Adana, 01330, Turkey E-mail: [email protected] Reviewing editor: Shaofeng Liu, University of Plymouth, UK Additional information is available at the end of the article Page 1 of 17 Keywords: 3PL; logistics service provider; selection criteria; fuzzy AHP; Chang’s extent analysis; cement industry; outsourcing 1. Introduction Logistics is one of the most important parts of supply chain management that has a significant effect on the success, efficiency and cost of the entire supply chain. More specifically, logistics involve the tasks of planning, implementing, and controlling the efficient, effective forward, and reversing the flow and storage of goods, services and related information between the point of origin and the point of consumption in order to meet customers’requirements (Council of Supply Chain Management Professionals, 2016). This function typically includes inbound and outbound transportation management, fleet management, warehousing, materials handling, order fulfilment, logistics network design, inventory management (CSCMP, 2016). In today’s global and competitive world, firms wish to focus on their best areas and core competencies and prefer to use outsourcing for other activities and processes. Transactional, operational and repetitive activities are largely outsourced (Langley & Capgemini, 2016). The purpose of outsourcing is to create value from an expert firm on the chosen area (Liou, Wang, Hsu, & Yin, 2011), and thus to help that firm to reduce operating costs and improve competitiveness (Uygun, Kacamak, & Kahraman, 2015). The logistics process has been identified as an important function that may be used in outsourcing to reduce the costs and increase the efficiency. Transferring the entire or some part of the logistics function process to (an) external firm(s) can be defined as logistics outsourcing. In the entire supply chain, these logistics service providers (LSPs) perform the activities between the supplier and the buyer as a third party (Hwang, Chen, & Lin, 2016) and hence these external firms are referred to as third party logistics (3PL). 3PL can be defined as the outsourcing of all or much of a company’s logistics operations to a specialized company (CSCMP, 2016) and 3PL provider (hereafter referred to as LSP) is an external provider who manages, controls and delivers logistics activities for firms (Hertz & Alfredsson, 2003). LSPs may carry out transportation, warehousing, inventory management, order processing, consolidate shipments, select carriers, information system, packaging activities, and returns handling (Aghazadeh, 2003; Aguezzoul, Rabenasolo, & Jolly-Desodt, 2006; Liu & Wang, 2009). Globally, the most outsourced logistics processes are domestic transportation (80%), warehousing (66%), international transportation (60%), freight forwarding (48%), customs brokerage (45%) and reverse logistics (34%) (Langley & Capgemini, 2016). For most of the manufacturing firms, logistics is neither their core competency nor a core business function, but an essential function for them to gain competitive advantage. This brings logistics function to the fore as a very suitable candidate for outsourcing. Total business spending for logistics activities, which is very important for competitiveness may be very high (Banomyong & Supatn, 2011). Outsourcing may facilitate the reduction of the cost and achievement of effectiveness in logistics activities (Hwang et al., 2016). The main benefits of logistics outsourcing include the following: concentrating on core competencies, improving performance, receiving a higher level of service quality, achieving cost saving opportunities, reducing logistics costs, reducing asset base, gaining flexibility in supply chain, shortening average order-cycle lengths, extending the market boundaries, gaining access to leading edge technology, achieving flexibility in adapting to changes in the market, increasing the market knowledge and data access, enhancing innovation performance, reaching a greater level of flexibility to respond to the customer needs, achieving expertise and experience, increasing customer satisfaction, making better use of resources, improving service quality and restructuring supply chain (Aghazadeh, 2003; Alkhatib, Darlington, & Nguyen, 2015a; Alkhatib, Darlington, Yang, & Nguyen, 2015b; Hsiao, Kemp, Van Der Vorst, & Omta, 2010; Hwang et al., 2016; Jharkharia & Shankar, 2007; Kumar, Singh, & Dureja, 2012; Langley & Capgemini, 2016; Li et al., 2012; Liu & Wang, 2009; Percin & Min, 2013; Razzaque & Sheng, 1998; Selviaridis & Spring, 2007; Wong & Karia, 2010). In other words, logistics outsourcing Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 2 of 17 enhances the efficiency and strengthens the business. LSPs are viewed as strategic partners who play a vital role in improving the performance and achieving the competitive advantage (Jothimani & Sarmah, 2014). Historically, transportation and warehouse management processes are largely outsourced, but today LSPs have more strategic roles in achieving effective intraand inter-firm relationships and integration (Zacharia, Sanders, & Nix, 2011). Since their service area is widened, the wrong choice of service provider causes ineffective activities, low-quality logistics services and some several problems, such as delayed shipments, higher costs, risks related to exposure and damaged reputation. Logistics outsourcing has a lot of advantages that are mentioned earlier. However, it also has problematic aspects and risks mainly related to long-term commitments and failures of service providers in performing their tasks (Alkhatib et al., 2015b). Therefore, selecting the right service provider represents an important decision to make. There is a lot of related research in literature that focus on LSP selection, as well as a great deal of academic papers that work solely on a firm’s decision problem. Unlike existing papers in literature, this study focuses on the perspective of one sector rather than on a firm’s selection of service provider. In other words, this paper aims to pinpoint the criteria that play a significant role in the selection of LSP from a single industry’s point of view. This paper is organized in four sections. Section 1delineates the need for and importance of supplier evaluation and selection criteria. Section 2provides an overview of the literature on the selection of supplier or LSP. Section 3summarizes supplier selection criteria. Section 4explains the methodology used in this research and explains Chang’s extent analysis based on Fuzzy Analytical Hierarchy Process (FAHP) method step by step. Section 5present important outcomes about selection criteria for Turkey’s cement industry. This is finally followed by Section 6, which contains inferences based on the findings of this research. 2. Literature review Boyson et al. (1999) state that the research topics in logistics outsourcing may be explored as the motivational factors for logistics outsourcing, evaluating the contribution of logistics outsourcing to competitiveness of the buyer firm and selection and evaluation of logistics service suppliers (as cited in Percin & Min, 2013). There is a great deal of literature related to the supplier selection the earliest of which is Dickson (1966)’s study. Considering the LSP and its selection problem, Maloni and Carter (2006) provide a review of 45 surveys based on LSP papers between 1989 and 2004. Their paper analyze many factors, such as the functions of outsourcing, analysis approach, success factors and barriers of LSP. Selviaridis and Spring (2007) who provide an overview of the literature on the topic focus on research purposes, methods of use, theoretical approaches and levels of analysis based on 114 articles within the period between 1990 and 2005. Additionally, Marasco (2008) reviewed 152 articles published between 1989 and 2006. In this paper, the frameworks are constructed at five phases as the context within the thirdparty logistics relationship takes place (external or internal), the relationship’sstructural characteristics, the process, the outcomes that result from the relationship (at internal level and external level) and comprehension. Aguezzoul (2014) provides a comprehensive literature review related to the methods and criteria by analyzing 67 articles that were published between 1994 and 2013. Cost, relationship, services, quality and information and equipment system are determined as the criteria that are most commonly used in the selection of LSP. The methods applied were categorized under five groups, such as multi-criteria decision making (MCDM) techniques, statistical approaches, artificial intelligence, mathematical programmingandhybridmethods.Further,Alkhatibetal.(2015a) provide a literature review for the decisions in selecting and evaluating LSP by using MCDM methods to determine the methods and criteria based on 56 articles published between 2008 and 2013. This study Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 3 of 17 finds out that cost/price, quality and reliability, flexibility and compatibility, services and financial measures are the five criteria mostly used in the literature. As the subject of selecting supplier service providers is expanded, selecting the best appropriate service provider becomes more important because businesses differ from one another in terms of properties, activities and quality levels, and a lot of enterprises decided to use outsourcing at logistics activities. This subject has generated a great deal of academic discussion as it attracted the attention of many researchers (Percin & Min, 2013). So far, different types of methods (mainly, multi criteria decision making methods, statistical techniques, data analysis techniques and mathematical modelling techniques) have been designed and applied to address the supplier selection. It is possible to find a greater number of techniques used for selecting and evaluating LSPs in literature, such as AHP, DEA, ANP, TOPSIS, ELECTRE, mathematical models, service quality approach, discriminant analysis, expert systems, QFD, case based reasoning, rule based reasoning, Interpretive Structural Model (ISM), factor analysis, etc. (Ho, Xu, & Dey, 2010; Isiklar, Alptekin, & Buyukozkan, 2007; Kumar & Singh, 2012; Liu & Wang, 2009; Percin & Min, 2013; Vijayvargiya & Dey, 2010). Particularly, some of the papers that investigate the selection of LSPs are discussed later. In their research, Bottani and Rizzi (2006) present fuzzy TOPSIS method to select the most appropriate LSP based on the criteria such as compatibility, financial stability, flexibility, performance, price, physical equipment and information system, quality, strategic attitude, trust and fairness. Aguezzoul et al. (2006) apply the ELECTRE method for sorting service providers based on the selection criteria. Jharkharia and Shankar (2007) represent ANP based LSP selection. In this paper, overall weighted index determinants are compatibility, cost, quality and reputation with dimensions of long-term relations, operational performance, financial performance and risk management. Gol and Catay (2007) apply AHP in Turkish automobile company’s problem of selecting LSP with respect to 27 criteria and five main criteria, which are general company considerations, capabilities, quality, client relationship and labour relations. In 2009, Liu and Wang implement fuzzy Delphi, fuzzy inference and fuzzy linear assignment techniques for the selection of provider. Percin (2009) introduces Delphi for determining the evaluation criteria, AHP for determining the weights and TOPSIS for service providers’preference order. Bhatti, Kumar, and Kumar (2010) implements AHP to determine the criteria used by a lead logistics provider (LLP) in selecting the 3PL. As the main criteria, they looked at vendor status, logistics competence of service provider, quality of service and IT competencies. Soh (2010) uses FAHP and finds that information technology capability is the most important selection criterion among the others, which include finance, service level, relationships, management and infrastructure. Vijayvargiya and Dey (2010) identify the best logistics providers among six automobile components firms by using AHP. Kumar and Singh (2012) use FAHP and TOPSIS methods for evaluating the performance of LSP. They consider nine criteria as logistics cost, service quality, compatibility, consignment tracking capability, time delivery, information systems, total revenue, geographical coverage, range of service provided, concluding that cost and logistics service quality are two most important factors. Falsini, Fondi, and Schiraldi (2012) propose a model that combines AHP, DEA and linear mathematical model to select the LSP. In their paper, Li et al. (2012) establish a model for the evaluation of LSP by using fuzzy sets that have the criteria of management success, business strength, service quality and business growth. Kumar et al. (2012) introduce VIKOR and CFPR (consistent fuzzy preference relation) method for the selection of 3PLs providers in firms manufacturing automobile parts. Ho, He, Lee, and Emrouznejad (2012) develop an integrated approach based on using QFD for determining the criteria and FAHP methods for prioritizing the criteria to select the LSP. Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 4 of 17 Gupta, Sachdeva, and Bhardwaj (2012) apply fuzzy MCDM methods for selecting LSP in a cement industry by means of five criteria, which are price, geographic location, reliability, flexibility and environmental conditions. Daim, Udbye, and Balasubramanian (2012) investigate the selection of LSP for international business by implementing AHP with the five main criteria, which are cost, service, global capabilities, information technology, experience and local presence. Percin and Min (2013) propose a QFD and fuzzy linear regression methodology to select the service provider. Bansal, Kumar, and Issar (2013) apply their approach at a glass manufacturing firm. To select the LSP, they have consensus with management based on eight criteria, which are transportation cost, quality of services, number of value added services, reliability of services, flexibility, geographic coverage, market reputation and infrastructure. Akman and Baynal (2014) implement FAHP and fuzzy TOPSIS methods for examining the LSP selection problem at a tire manufacturing company in Turkey. Alkhatib et al. (2015b) state that LSP selection is important especially for developing countries. They use fuzzy DEMATEL and fuzzy TOPSIS methods and consider tangible and intangible logistics resources based on resource-based view in order to overcome uncertainty related to the data. In a recent paper, Hwang et al. (2016) use qualitative and quantitative approaches to determine the LSP selection on IC manufacturing sector in Taiwan and obtain the sequencing of the main criteria, which are performance, cost, service and quality. For LSP selection, Awasthi and Balezentis (2017) used a hybrid approach based on BOCR (benefits, costs, opportunities and risks) and fuzzy MULTIMOORA. Raut, Kharat, Kamble, and Kumar (2018) interested with the LSP problem from environmental sustainability and implemented DEA and ANP methods. In Bianchini (2018)’s paper, which is applied on a company, AHP is used to determine the relative weights of the evaluation criteria and TOPSIS is used to rank the potential LSP. 3. Supplier selection criteria Global competition and fluctuations in short-term demands make it necessary to meet customer’s needs very quickly, which cause pressure on firms to improve their logistics activities in terms of cost and service quality. Effective and efficient logistics services help firms to gain competitive advantage. Therefore, it is vital to select the appropriate service provider and it is not enough to select less costly LSP. Logistics outsourcing is different from traditional purchasing in terms of time frame and relations. The firms that want to use logistics outsourcing are faced with the inevitable need to select the best suitable service provider to meet their needs. Despite the benefits involved, it is not necessarily easy to implement the outsourcing in logistics function and apply successful coordination with the service provider (Hwang et al., 2016). Due to the complexity of the selection process, it is necessary to develop a framework related to the selection and evaluation of LSP. The criteria list and indexing construction is very important for the selection of LSPs. The research done in this area draws on a wider range of criteria, including operational, organizational and relational factors (Coltman, Devinney, & Keating, 2011). Table 1gives a brief list of the criteria that are used in the studies related to logistics outsourcing. The characteristics of the supplier selection procedure vary depending on the country (culture, economic conditions, etc.) in general and on the firm, in particular. Further, different industries have unique characteristics and specific requirements and priorities. Therefore, the selection criteria and the importance of these criteria may be different (Aghazadeh, 2003;Liu&Hai, 2005;Liu&Wang,2009). Previous studies show that firms from different industries have different logistics service provider selection decisions (Hwang et al., 2016). This study selects Turkey’s cement industry as the application area of the supplier selection problem. 4. Methodology MCDM methodologies serve as effective decision support tools to analyze complex decision problems, which involves multiple criteria, goals or objectives of conflicting nature (Kahraman, Onar, & Oztaysi, Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 5 of 17 2015). They have been widely accepted and used in academic and industrial circles since they were developedbyKeeneyandRaiffain(1976). LSP selection and evaluation process is a typical complex multi-criteria decision problem in which both qualitative and quantitative factors are involved. These factors provide an opportunity to use both kinds of criteria. Thus, MCDM methods enable decision makers to reach a specific judgement as a collective group idea (Liou et al., 2011). FAHP, which is one of MCDM methods, can be used to improve an acceptable way of understanding complex decision selection process where there are many decision makers and when there is a need for ideas. FAHP as an advanced version of Saaty’s widely used AHP technique first appeared in Van Laarhoven and Pedrycz (1983). AHP is based on the decision maker’s preferences to find the best decision (Vijayvargiya & Dey, 2010). By using AHP, decision makers make a pairwise comparison and determine the numerical quantification of weights of the criteria. In practice, for the reasons, such as incomplete data, ambiguous nature of decision making process where people are involved as well as the complexity and uncertainty of business environment, decision makers have difficulty making exact comparisons between the levels Table 1. The list of the criteria mostly used in the selection of logistics service provider in the literature Main criteria Sub-criteria Literature on the selection of logistics supplier Cost/ Financial criteria Price Continuous cost reduction Flexibility in payment Gol and Catay (2007), Liu and Wang (2009), Soh (2010), Kumar et al. (2012), Ho et al. (2012), Gupta et al. (2012), Bansal et al. (2013), Akman and Baynal (2014), Jothimani and Sarmah (2014), Hwang et al. (2016), Jharkharia and Shankar (2007) Operations and service quality Customer satisfaction Flexibility in operations Capability to handle specific business requirements Transportation safety Range of service provided Number of value added services Geographical coverage Key performance indicators tracking ISO compliance Location Asset ownership Accuracy in operations On time delivery Reliability of services Data security Infrastructure Document accuracy Ho et al. (2012), Li et al. (2012), Kumar et al. (2012), Aguezzoul et al. (2006), Gupta et al. (2012), Liu and Wang (2009), Soh (2010), Akman and Baynal (2014), Bansal et al. (2013), Daim et al. (2012), Gol and Catay (2007), Hwang et al. (2016), Jothimani and Sarmah (2014), Kumar and Singh (2012) Technology and information Information system, IT capability Information sharing Aguezzoul et al. (2006), Isiklar et al. (2007), Gol and Catay (2007), Jharkharia and Shankar (2007), Liu and Wang (2009), Vijayvargiya and Dey (2010), Soh (2010), Kumar and Singh (2012), Ho et al. (2012), Daim et al. (2012), Li et al. (2012), Akman and Baynal (2014) Intangibles, business related Responsiveness Problem solving capability Experience Trust Financial stability Reputation Past performance Cultural fit Gol and Catay (2007), Liu and Wang (2009), Hwang et al. (2016), Soh (2010), Jharkharia and Shankar (2007), Kumar et al. (2012), Daim et al. (2012), Isiklar et al. (2007), Percin (2009), Li et al. (2012), Ho et al. (2012), Bansal et al. (2013), Akman and Baynal (2014), Aguezzoul et al. (2006), Kumar and Singh (2012) For detailed information about the definitions of the criteria please see Akman and Baynal (2014), Gol and Catay (2007), Hwang et al. (2016), Kumar and Singh, (2012). Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 6 of 17 of importance for criteria (Soh, 2010). Therefore, it is very suitable to use FAHP as a methodological framework in this study. Although AHP is a popular method, it may be inadequate for analyzing complex decision problems in terms of fuzziness and uncertainness attributes. To handle these mutual attributes, FAHP combines the Fuzzy Set Theory (FST) with AHP under uncertain conditions and fuzzy data set is used for the evaluation of a simplified decision model. FST is a very powerful tool to process imprecise data and fuzzy expressions that are more natural for humans than constant mathematical rules and equations (Kreng & Wu, 2007). Among several techniques, which are used in FAHP, one of them is van Laarhoven and Pedrycz’s logarithmic least squares method (LLSM) to get triangular fuzzy weights from a triangular fuzzy comparison matrix in 1983. This method has serious uncertainties even under certain conditions because of approximate calculation of the triangular fuzzy numbers (Wang, Elhag, & Hua, 2006). In the chronological list of weighting methods, Buckley’s method (1985) comes after LLSM. Therefore, this method was later used to calculate fuzzy weights in a rather simple manner. Despite the advantage of utilising this method, high computational requirements and geometric row calculation cause disadvantages when a perfect consistency is not provided (Csutora & Buckley, 2001). Finally, Chang (1996) suggested the Extent Analysis Method and made a comparison using triangular fuzzy numbers to obtain the priorities of alternatives from pairwise comparisons. Among all, Chang’s Extent Analysis on FAHP became popular due to the simplicity of steps and intelligibility and successful application in many fields (Ding, Yuan, & Li, 2008). It evaluates different possible weight values obtained by different decision makers by using the pairwise comparison matrix, which includes corresponding triangular fuzzy numbers. Furthermore, if one criterion is not important in Chang’s method, it can get a weight of 0. Wang, Luo, & Hua (2008) argue that making zero-weight assignments to any of the main and sub criteria results in making incorrect decisions. On the contrary, according to Meixner (2009), the zero-weight assignment to any of the criteria indicates that the method has a strong representation of reality. Meixner (2009) also notes that it is an advantage to emphasize the most important criterion. According to the extended analysis method, each object is handled to achieve an aim. With the extended statement, it expresses how much this object fulfils its purpose. Accordingly, X¼x1;x2;...;xn fg is accepted as a set of object, and U¼fu1;u2;...;um} is accepted as a set of goal. Every objective is obtained and extent analysis is applied for every goal giin turn. Thus, m expansion analysis values for each object are calculated with Equation (1). M1 gi;M2 gi;.........:Mm gii¼1;2;3......:nðÞ (1) All Mj gij¼1;2;3......:mðÞshow triangular fuzzy numbers. The following steps are based on the Chang’s Extent Analysis Method. Step 1. Determine the fuzzy synthetic extent values for object i. Si¼∑ m j¼1 Mj gi∑ n i¼1 ∑ m j¼1 Mj gi "# 1 (2) While Sishows synthesis value of ith goal, Mj gishows a triangular fuzzy number, which represents the significance ratio among iand jin comparison with the goal k. With Mj gi, the comprehensive member of a fuzzy pairwise comparison matrix is obtained. To get ∑ m j¼1 Mj gi, fuzzy calculation for specific matrix of mextent analysis is as in the following matrix (Equation (3)): Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 7 of 17 ∑ m j¼1 Mj gi¼∑ m j¼1 lj;∑ m j¼1 mj;∑ m j¼1 uj ! (3) To find ∑ n i¼1 ∑ m j¼1 Mj gi "# 1 , the operation of fuzzy addition of Mj gij¼1;2;3......:mðÞvalues are carried out and then the reverse of vector in Equation (4) is calculated. ∑ n i¼1 ∑ m j¼1 Mj gi "# 1 ¼1 ∑n i¼1ui ;1 ∑n i¼1mi ;1 ∑n i¼1li ! (4) Step 2. Compare the fuzzy numbers of g M1¼l1;m1;u1 ðÞand f M2¼l2;m2;u2 ðÞ While f M1and f M2represent a fuzzy number, the rank of probability f M2f M1is shown as Vf M2f M1  ¼supyxmin μe M1 xðÞ;μe M2 yðÞ hi (5) For this equation, y≥xis expressed by expansion principle. This equality shows the magnitude relation between the pairs of numbers (x, y) with relation, such as y≥xand μe M1 xðÞ¼μe M2 yðÞ. Vf M2f M1  ¼height f M1\f M2  ¼μe M2 dðÞ¼ 1;if m2m1 0;if l1u2 l1u2 m2u2 ðÞm1l1 ðÞ ;otherwise 8 > > > > < > > > > : (6) The probability of being greater than f M1;the middle value of f M2is equal to 1 as seen in Figure 1. When something else is not the case, the probability calculation must be done. For this calculation, the rates of Vf M1f M2  and Vf M2f M1  has to be calculated and compared. ddenotes the final intersection point among μe M1 and μe M2 . Step 3. Determination of the degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers f Mii¼1;2;......;kðÞ. V~ Mf M1;f M2;......f Mk  ¼V~ Mf M1  ;f ðMf M2 h ;... ~ Mf Mk  ¼min V ~ Mf M1  ¼1;2;::k(7) Under the assumption of d0Ai ðÞ¼minVð~ S_ I~ SkÞ, the weight vector is calculated for all Sj, k¼1;2; ::; n;kÞj. Figure 1. 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Journal of Business Logistics, 32(1), 40–54. doi:10.1111/jbl.2011.32.issue-1 Bulgurcu & Nakiboglu, Cogent Business & Management (2018), 5: 1469183 https://doi.org/10.1080/23311975.2018.1469183 Page 16 of 17 © 2018 The Author(s). This open access article is distributed under a Creative Commons Attribution(CC-BY) 4.0 license. You are free to: Share —copy and redistribute the material in any medium or format. Adapt —remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution —You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. 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