A multicriteria approach based on fuzzy QFD for choosing criteria for supplier selection

Accepted Manuscript A multicriteria approach based on Fuzzy QFD for choosing criteria for supplier selection Francisco Rodrigues Lima Junior, Luiz Cesar Ribeiro Carpinetti PII: DOI: Reference:

S0360-8352(16)30354-0 http://dx.doi.org/10.1016/j.cie.2016.09.014 CAIE 4470

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Computers & Industrial Engineering

Received Date: Revised Date: Accepted Date:

9 October 2015 5 July 2016 13 September 2016

Please cite this article as: Lima, F.R. Junior, Carpinetti, L.C.R., A multicriteria approach based on Fuzzy QFD for choosing criteria for supplier selection, Computers & Industrial Engineering (2016), doi: http://dx.doi.org/10.1016/ j.cie.2016.09.014

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Title: A multicriteria approach based on Fuzzy QFD for choosing criteria for supplier selection First author: Francisco Rodrigues Lima-Junior Affiliation: Production Engineering Department School of Engineering of São Carlos, University of São Paulo Av. Trabalhador Sancarlense, 400, São Carlos, SP, Brazil.

Second author: Luiz Cesar Ribeiro Carpinetti Affiliation: Production Engineering Department School of Engineering of São Carlos, University of São Paulo Av. Trabalhador Sancarlense, 400, São Carlos, SP, Brazil. Corresponding author: Luiz Cesar Ribeiro Carpinetti School of Engineering of São Carlos, University of São Paulo Av. Trabalhador Sancarlense, 400 13566-590, São Carlos, SP, Brazil E-mail: [email protected] Phone number: +55 16 33739421

A multicriteria approach based on fuzzy QFD for choosing criteria for supplier selection

Abstract This paper proposes a new multicriteria decision making method to aid the choice and weighting of criteria to be used in the supplier selection process. The method combines the fuzzy QFD technique for weighting the criteria with a procedure for assessing the difficulty to obtain information to evaluate the suppliers on each criterion. The choice and weighting of the criteria derive from a systematic procedure based on the use of linguistic terms to judge the importance of the related requirements and the intensity of the relationship between requirements and criteria. In the final step, the proposed method classifies the criteria into four groups (priority, critical, complementary and costly) so as to guide the final choice of criteria. The method was implemented in Excel and applied to a pilot case in an automotive company, which classified the criteria into groups so as to guide the decision in the final selection. Competitive price, delivery in full on time, product conformance and quality certification were categorized into the priority group meaning that they should be used in the supplier selection process. On the other hand, commitment to cost reduction, financial situation, responsiveness to demand change, commitment to quality improvement and potential for collaboration were classified as critical, meaning that they are important but they require a bigger effort of data collection. The results of the application were considered by the decision makers as consistent and aligned with the strategic competitive priorities of the supply chain. Differently from other studies, the type of item as well as the type of supply chain was formally considered in the determination of the initial list of requirements and criteria. Moreover, final selection of the set of criteria is also dependent on the linguistic evaluation of the degree of difficulty of data collection.

Keywords: Supplier selection; Fuzzy QFD; criteria selection; supplier management; multicriteria decision making; supply chain management.

1. Introduction Purchasing decisions affect important activities of a company such as inventory management, production planning and control and cash flow management (Katsikeas et al., 2004, Govindan et al., 2010). They also have a significant influence on the quality, delivery and cost of the services and manufactured products. Some authors say that approximately 50 to 70% of production costs are spent on purchased materials and components (Prajogo et al., 2012). Thus, purchasing and supplier relationship management have become very critical activities for performance management of organizations and supply chains. A very important activity in purchasing is supplier selection. Basically, supplier selection is a decision making process with the purpose of defining an order of preference among potential suppliers based on a set of evaluation criteria. Several multicriteria decision making techniques are proposed in the literature to tackle the problem of supplier selection (De Boer et al., 2001, Ho et al., 2010, Wu & Barnes, 2011, Chai et al., 2013). These techniques allow process automation and can bring efficiency and rationality to the decision making process (De Boer et al., 1998). They are adequate to deal with decision making problems that involve evaluation of given alternatives, taking into account multiple decision criteria with the main goal of selecting, ordering or categorizing the alternatives (De Boer et al., 2001, Lima Junior et al., 2013; Rezaei & Ortt, 2013). Since each criterion may lead to a different order of preference of alternatives, these techniques aim to yield a global classification based on the ratings of each alternative when simultaneously considering all the multiple criteria and their respective weights. Therefore the correct choice of a set of criteria and the quantification of their relative weight are of fundamental importance to the alignment of purchasing decisions with strategic and performance objectives of the buying organization. The literature on supplier selection presents dozens of criteria and sub-criteria that can guide the decision making process (Dickson, 1966, Germain & Dröge, 1990, Weber et al., 1991, Verma & Pullman, 1998, Kannan & Tan, 2002, Katsikeas et al., 2004,

Jabbour & Jabbour, 2009, Ku et al., 2010, Frödell, 2011). In general, the criteria are related to performance requirements or other desired attributes that a supplier should fulfil. Choosing a set of criteria to evaluate supplier alternatives in the selection process is in itself a multicriteria decision making problem in which the initial list of possible criteria are the alternatives to be evaluated and selected. In this sense, multicriteria decision making (MCDM) methods can be used with this purpose (De Boer et al., 2001). Some studies propose methodologies in which the criteria are selected based only on their weight, given by several decision makers (Jakowski et al., 2010, Chang et al., 2011). In this case, the decision on what alternative criteria to pick is based on a single factor: the relative importance judged by the decision makers. However, the decision on which criteria to choose should be based on multiple requirements related to performance and strategic objectives, which in turn depends on the type of item to be purchased (Kraljic, 1983, Wilson, 1994, De Boer et al., 2001, Hätönen & Ruokonen, 2010, Park et al., 2010, Osiro et al. 2014) as well as on the type of industry (Wu & Barnes, 2010). Another important aspect is that the effectiveness of the supplier selection process should rely on information as complete and accurate as possible within the time and budgetary constraints (Wu & Barnes, 2010). This relates to the degree of difficulty and amount of resources required to obtain information needed to evaluate the supplier scores on each alternative criterion. In this regard, the decision making process to criteria selection should take into account the availability of information needed for supplier evaluation and other required resources such as time and people. Therefore, the criteria selection process should simultaneously consider the importance of the criteria as well as the degree of difficulty of data collection. The only study found in the indexed literature that presents a multicriteria decision making approach to criteria selection was proposed by Wu & Barnes (2010). In this paper, evolving from the framework proposed by Lin & Chen (2004), the authors propose first to extract industry oriented criteria from a general list of criteria based on judgments of decision makers. Next, Wu & Barnes (2010) propose the application of non-linear programming to determine what the authors call the optimal configuration hierarchy of criteria. They use the Dempster-Shafer theory to represent the bias of the decision makers when the information on attributes is incomplete, imprecise or unreliable. Another important contribution is the adoption of parameters such as time,

money and human resources to drive the criteria selection process. However, evaluation of alternative criteria based on these parameters is made using crisp numbers, which is a limitation since the values used are based on estimations arbitrarily judged by decision makers. However, linguistic judgments would be a much more adequate approach to deal with the uncertainty of these judgments (Zadeh, 1973, Wang, 2010, Kilincci & Onal, 2011). Another problem of the study presented by Wu & Barnes (2010) is that despite the fact that the authors propose to use industry oriented criteria, the type of item to be purchased is not considered in this criteria selection process. This is a limitation since the type of item influences the set as well as the weight of the criteria adopted in the supplier selection process (De Boer et al., 2001, Hätönen & Ruokonen, 2010, Park et al., 2010, Osiro et al. 2014). For example, trust and potential for collaboration are important criteria for selection of suppliers of strategic items, whereas technological capability and delivery reliability are criteria more related to bottleneck items (Kraljic, 1983, Hätönen & Ruokonen, 2010). Consequently, the type of item to be purchased should be considered in this criteria selection process. Based on these arguments, this paper proposes a new multicriteria decision making approach to aid the choice and weighting of criteria to be used in the supplier selection process. The criteria selection is initially oriented by a general list of criteria segmented by the type of item to be purchased. The weighting of the criteria is based on their relationship with the buyer´s requirements and the relative importance of these requirements. The fuzzy QFD technique is used for weighting the requirement and criteria since it combines the modeling of linguistic judgments from fuzzy set theory with a technique for prioritization of criteria based on a systematic deployment. The final choice of the criteria is based on a classification procedure that considers both the weight of the criteria and their associated degree of difficulty of data collection. The degree of difficulty of data collection is evaluated based on linguistic judgments related to information availability, human resources and time required and additional resources. A descriptive quantitative approach was adopted as a research method (Bertrand & Fransoo, 2002). The proposed method was implemented in Microsoft Excel©, which facilitates the replication of this proposal. A pilot application was developed in an automotive company so as to evaluate and better discuss the proposal. The paper is organized as follows: Section 2 briefly revises the subject of supplier selection, focusing

specially on criteria definition. Section 3 presents some fundamental concepts on fuzzy set theory and the fuzzy QFD method. Section 4 details the proposal and section 5 presents the pilot application case and discusses its results. Finally, conclusions about this research work and suggestions for further research are made in Section 6.

2. Supplier Selection Supplier selection is a decision-making process comprising of several steps. Based on the studies of Faris et al. (1967) and Kraljic (1983), De Boer et al. (2001) propose a framework for supplier selection that consists of four steps: problem definition, formulation of criteria, qualification and final choice, as illustrated in Figure 1. The first step aims at clearly defining the problem at hand, which may mean searching for new suppliers for a completely new product, replacing current suppliers, or choosing suppliers for new products from the existing pool of suppliers. Especially in the case of selecting new suppliers, depending on the item to be purchased, the number of alternative suppliers may be very large. This situation demands decision making techniques that are able to simultaneously evaluate several alternatives.

Take in Figure 1

In the next step, the buyer should convert its requirements into decision criteria so as to guide the choices. The main objective of the qualification step is to sort the potential suppliers from the initial set of suppliers based on qualifying criteria. Implicit in this qualification step is the non-compensatory rule of the decision making process (Lima Junior et al., 2013). The last step aims at ranking the potential suppliers so as to make the final choice. Sorting and ranking are especially important in decision making for new purchases as well as modified or straight rebuy of routine items, in which there is usually a large set of potential suppliers. Wu & Barnes (2011), based on this framework, proposed an additional step aiming at giving feedback to potential suppliers in their performance in the selection process. Another extension of the De Boer's model, proposed by Igarashi et al. (2013) includes a final step of evaluation of supplier performance. In this regard, Ishizaka and Blakiston (2012) identified factors for a long term relationship split into three types: related to the client, to the service provider and to the interaction of both.

Multicriteria decision making (MCDM) methods for supplier selection include multiattribute techniques, mathematical programming, stochastic programming and artificial intelligence techniques (De Boer et al., 2001, Ho et al., 2010, Wu & Barnes, 2011, Chai et al., 2013). There are several MCDM methods used mostly for outranking such as AHP (Tam & Tummala, 2001, Mani et al., 2014), ANP (Kirytopoulos et al., 2008), DEA (Saen, 2010), fuzzy TOPSIS (Zouggari & Benyoucef, 2012), fuzzy AHP (Kilincci & Onal, 2011), fuzzy ANP (Vinodh et al., 2011), fuzzy ELECTRE (Hatami-Marbini & Tavana, 2011) among others. As shown in Table 1, combined techniques are usually adopted to deal with the problem of supplier selection. Studies on the application of multicriteria techniques for supplier selection generally present their own list of criteria, which are either simply extracted from the literature or determined by judgments of the decision makers of the case presented in the study. Therefore, most of them does not give evidences on how the criteria were identified (Kirytopoulos et al., 2008, Park et al., 2010, Büyüközkan & Çifçi, 2011, Kilincci & Onal, 2011, Amindoust et al., 2012, Lima Junior et al., 2013, Hsu et al., 2014, Mani et al., 2014, Hashemi et al., 2015, Kar, 2015).

Take in Table 1

The use of appropriate techniques can bring effectiveness and efficiency to the selection process (De Boer et al., 1998). To decide which techniques to use one must take into account the alignment of the particularities of the problem at hand with the characteristics of the techniques. For instance, when selecting a new supplier of a routine item with many potential suppliers, techniques that do not limit analysis to only a few alternatives are more adequate than others (De Boer et al., 2001, Lima Junior et al., 2013). Another aspect to be considered to align techniques to the particularities of supplier selection is the adequacy to support group decision making so as to combine different judgments of multiple decision makers from diverse functional areas (De Boer et al., 1998, Kar, 2015).

2.1 Supplier Selection Criteria Defining selection criteria is a very important step in the selection process. The criteria are mostly related to performance requirements or other desired attributes that a supplier should fulfil. Many authors have also pointed out the importance of considering the

long term perspective of buyer-supplier relationship by including criteria such as design and technological capabilities, financial health, ease of communication, willingness to collaborate and share information (Ku et al., 2010, Park et al., 2010, Wang, 2010, Wu & Barnes, 2010, Frödell, 2011). Other authors reinforce the importance of including criteria for evaluating environmental performance of suppliers (Humphreys et al., 2003, Jabbour & Jabbour, 2009, Büyüközkan & Çifçi, 2011, Miemczyk et al., 2012, Kannan et al., 2014, Hashemi et al., 2015). There are a large number of studies that have aimed to identify criteria used by buyers to select suppliers (Dickson, 1966, Germain & Dröge, 1990, Weber et al., 1991, Verma & Pullman, 1998, Kannan & Tan, 2002, Katsikeas et al., 2004, Jabbour & Jabbour, 2009, Ku et al., 2010, Frödell, 2011). A seminal study conducted by Dickson (1966) based on a survey with 170 buyers concluded that out of 23 criteria, quality, delivery and performance history are the three most important ones. In a survey conducted with 139 manufacturing companies in the USA, Verma & Pullman (1998) concluded that although quality is perceived as the most important attribute, cost and on-time delivery are assigned more weight when actually selecting a supplier. Kannan & Tan (2002) also presented an empirical study on the importance of supplier selection criteria and its impact on the performance of the manufacturing companies surveyed. Out of 30 selection criteria, on-time delivery and quality were ranked as the most important. On the other hand, in another study (Frödell, 2011) involving 12 purchasing professionals in the construction industry, cost is placed as the most important criterion, followed by key competencies and the ability to collaborate, indicating the importance given to partnership and collaboration in supply networks. Katsikeas et al. (2004) present the results of a survey of British distributor firms of IT products. In their study, they confirmed a positive relationship among the four supplier selection criteria considered (reliability, price, service and technological capability) and distributors’ performance. Weber et al. (1991) published a study based on the analysis of 74 papers on supplier selection criteria. They pointed price as the most cited criterion, followed by delivery and quality. Also based on literature review, Ku et al. (2010) identified criteria for global supplier selection grouped in: cost or price, quality, service, supplier´s profile, risk, buyer-supplier partnership, cultural and communication barriers and trade restrictions.

Apart from these descriptive studies, there are other studies in the literature that apply quantitative techniques to define a ranking of criteria. Jakowski et al. (2010) present a procedure to determine the rank order of the criteria weights based on the combination of pairwise comparisons, fuzzy set theory and linear programing. Initially, the decision makers compare the relative importance of the criteria based on the conventional AHP scale. These judgments are aggregated and transformed in fuzzy numbers. In the final step, linear programing is applied to calculate the overall criteria weight so as to maximize the satisfaction of the decision making group. Juan et al. (2009) proposed a fuzzy-QFD approach for prioritization of criteria and selection of housing refurbishment contractors. The procedure includes seven steps. The first five steps are used to define the weights of the criteria based on the weights of the requirements and the relationship between them. In the final steps, the global performance of the potential contractors is assessed considering the scores on each criterion. Other studies apply techniques to define a hierarchy of criteria or to analyze the relationships between them. Wu & Barnes (2010) propose the application of non-linear programming to define what they call the optimal configuration hierarchy of criteria. The authors propose first to extract industry oriented criteria from a general list of criteria based on judgments of decision makers. The bias of the decision makers when the information on attributes is incomplete, imprecise or unreliable is modeled according to the Dempster-Shafer theory. Govindan et al. (2010) present a procedure to hierarchize the criteria used for supplier development based on the relationship between them, according to a technique called interpretative structural modeling (ISM). In this technique, the main input is the judgments of the decision makers about pairwise dependence relationship between the criteria, represented in a structural self-interaction matrix. The result of the proposed procedure is a directed graph which is converted into a hierarchy model of the criteria. Chang et al. (2011) presents an approach based on fuzzy DEMATEL aiming at ranking the criteria and analyzing the degree of central role and relation between ten pre-selected criteria so as to design a strategy map and causal diagram. A survey was carried out to evaluate the importance of each criterion as well as the pairwise comparison of the influence of each criterion on each other. Other studies that focus on the relationship between the criteria are based on ANP (Kirytopoulos et al., 2008, Hsu et al., 2014, Hashemi et al., 2015), fuzzy ANP (Vinodh et al., 2011) and fuzzy preference relations (Büyüközkan & Çifçi, 2011).

Apart from Wu & Barnes (2010), all of the other reviewed studies do not define a procedure for initial selection of the criteria to be analyzed. Regarding the final selection procedure, Govindan et al. (2010) propose to hierarchize the criteria based on their relationship but their proposal does not yield an order of importance of the criteria. The methods proposed by Juan et al. (2009), Jakowski et al. (2010) and Chang et al. (2011) generate a rank of criteria but in all of them the ranking procedures are based only on a single factor, which is the weight of the criteria as judged by the decision makers. However, the criteria selection process should also consider the degree of difficulty and amount of resources required to obtain information to evaluate the supplier scores on each alternative criterion. The only multicriteria approach that considers the degree of difficulty is presented by Wu & Barnes (2010). However, they propose the use of crisp values to evaluate the measures of the degree of difficulty such as time, money and human resources, which is a limitation since estimation of these resources is imprecise and uncertain. Few studies on multicriteria decision making for supplier selection found in the literature propose to consider the type of the item in the decision process. Some authors propose multicriteria decision making models in which the type of item is used to categorize the suppliers in the stages of supplier qualification (Wu & Barnes, 2012) and supplier evaluation for development (Osiro et al., 2014). However, despite suggestions that the type of item to be purchased influences the set as well as the weight of the criteria adopted in the supplier selection process (Kraljic, 1983, Wilson, 1994, De Boer et al., 2001, Hätönen & Ruokonen, 2010, Park et al., 2010, Osiro et al. 2014), none of the studies on multicriteria decision making for supplier selection found in the literature propose to consider the type of the item specifically in the early stage of criteria selection and weighting.

3. Fuzzy Set Theory Fuzzy Set Theory (Zadeh, 1965) has been used to support the decision making processes based on imprecise and uncertain information. The values of the variables are expressed qualitatively by linguistic terms and quantitatively by fuzzy sets in the universe of discourse and respective membership functions (Zadeh 1973). Operations between linguistic variables involve the concepts presented next.

3.1 Fundamental Definitions 3.1.1 Definition 1: Fuzzy Set A fuzzy set

in X is defined by: ,

in which

(1)

is the membership function of

pertinence of x in

If

is the degree of

equals zero, x does not belong to the fuzzy set . If

equals 1, x completely belongs to the fuzzy set theory, if

and

. However, unlike the classical set

has a value between zero and 1, x partially belongs to the fuzzy set

That is, the pertinence of x is true with degree of membership given by

.

(Zadeh,

1965, Zimmermann, 1991).

3.1.2 Definition 2: Fuzzy Numbers A fuzzy number is a fuzzy set in which the membership function satisfies the conditions of normality (2) and of convexity (3) for all

,

X and all λ

[0,1].

The triangular fuzzy number is commonly used in decision making due to its intuitive membership function,

, given by:

(4)

in which l, m and u are real numbers with l < m < u (Figure 2). Outside the interval [l, u], the pertinence degree is null, and m represents the point in which the pertinence degree is maximum. Trapezoidal fuzzy numbers are also frequently used in decision making processes (Zimmermann, 1991, Pedrycz & Gomide, 2007).

Take in Figure 2

3.1.3 Algebraic Operations with Fuzzy Numbers Given any real number k and two fuzzy triangular numbers Ã=(l1, m1, u1) and

=(l2, m2,

u2), the main algebraic operations are expressed as follows (Zimmermann, 1991, Pedrycz & Gomide, 2007): 1) Addition of two triangular fuzzy numbers = (l1+l2, m1+m2, u1+u2)

l1

l2

(5)

2) Multiplication of two triangular fuzzy numbers = (l1 l2, m1 m2, u1 u2)

l1

l2

(6)

l1

l2

(7)

l1

l2

(8)

3) Subtraction of two triangular fuzzy numbers = (l1 u2, m1 m2, u1 l2)

4) Division of two triangular fuzzy numbers = (l1 u2, m1 m2, u1 l2)

5) Inverse of a triangular fuzzy number = (1 u1, 1 m1, 1 l1)

l1

(9)

6) Multiplication of a triangular fuzzy number by a constant = (k l1, k m1, k u1)

l1

k

(10)

k

(11)

7) Division of a triangular fuzzy number by a constant = (l1/k, m1/k, u1/k)

l1

3.2 Fuzzy QFD Quality function deployment (QFD) is a quality management technique that is used to convert judgments about degree of importance of requirements into degree of importance of criteria related to those requirements. It has gained wide application to

support decision making problems when the aim is to prioritize a list of objectives (how) based on a list of requirements (what) (Wang, 1999, Bevilacqua et al., 2006, Dursun & Karsak, 2013). The most common application is in product development (Fung et al., 1999, Temponi, 1999, Wang, 1999), although there are several applications of QFD to other purposes of decision making (Amin & Razmi, 2009, Bevilacqua et al., 2006, Juan et al., 2009, Dursun & Karsak, 2013). The House of the Quality is a combination of matrices used to implement this technique (Juan et al., 2009), as illustrated in Figure 3.

Take in Figure 3

The first matrix is the requirement matrix (what). Each row in this matrix corresponds to a selected requirement. In the columns, the input is the judgment of the relative importance of each requirement, given by each decision maker. In the conventional QFD, the requirement importance is judged based on a scale of crisp numbers, varying from 1 (very little important) to 5 (very much important). The second matrix is the relationship matrix made up by the requirements in the rows and the criteria in the columns. The criteria are defined by the decision makers based on a technical evaluation of their relation with the selected requirements. The relationship between a requirement and a criterion is indicated as a score in the corresponding matrix cell. In the conventional QFD, a numeric scale ranging from 1 to 9 is used, where 1 indicates a weak relation, 3 a moderate relation and 9 a strong relation (Wang, 1999). The combination of fuzzy set theory with QFD stands as a suitable approach to modelling imprecise data and uncertainty of decision making problems. Different fuzzy QFD approaches are presented in the literature. Fung et al. (1999) and Temponi (1999) propose the use of fuzzy inference in the evaluation of the relationship between the “what” and the “how”. Wang (1999) presents a fuzzy outranking approach to prioritize the list of “how”. Karsak (2004) proposes the use of fuzzy multi objective programing to prioritize the “how”. Bevilacqua et al. (2006), Amin & Razmi (2009) and Juan et al. (2009) apply triangular fuzzy numbers and algebraic operations to prioritize the “how”. Dursun & Karsak (2013) employ the fuzzy weighted average method to calculate the upper and lower bounds of the weights of supplier selection criteria and the ratings of the suppliers.

In this paper, the fuzzy QFD approach based on triangular fuzzy numbers and algebraic operations (Bevilacqua et al., 2006, Amin & Razmi, 2009, Juan et al., 2009) has been adopted due its modelling and implementation simplicity and low computational complexity. In this approach, fuzzy numbers are applied to model the linguistic judgments of the decision makers. For instance, the degree of importance of a requirement can be evaluated using the linguistic terms very low, low, medium, high and very high. Likewise, the relationship between a requirement and a criterion can be evaluated using the linguistic terms weak, average and strong. Let

be the fuzzy number corresponding to the linguistic judgement of the ith

requirement (i =1, 2, …, n), made by the dth decision maker (d = 1, 2, …, t). The aggregated judgments of the decision makers regarding the ith requirement, represented by

, is given by equation 12. (12)

After aggregation of the judgments, the fuzzy value of the absolute weight

is converted to a crisp number,

, according to the defuzzification procedure specified in equation

13. The defuzzified value of the absolute weight of the ith requirement is converted to the relative weight

according to equation 14. (13)

(14) Let

be the fuzzy number corresponding to the linguistic judgment of the relationship

between the ith requirement (i =1, 2, …, n) and the jth criterion (j =1, 2, …, m), made by the dth decision maker (d = 1, 2, …, t). The aggregated judgments of the decision makers regarding the relationship between the ith requirement and the jth criterion, represented by

, is given by equation 15. (15)

The absolute weight of the jth criterion,

, is calculated by the sum of the product of the

with the value of the relative weight of the ith requirement, as given by

relationship equation 16.

(16) The defuzzified value of the absolute weight of the jth criterion, wj, is given by equation 17. (17) After defuzzification, the absolute weight of the jth criterion is converted to the relative weight

according to equation 18. (18)

4. A Fuzzy QFD Approach to Criteria Selection and Weighting Figure 4 presents the proposed method for criteria selection. It is suggested that the application of this technique should involve the participation of a group of decision makers from different functional areas involved with the process of supplier selection or development (such as quality, logistics, product development and acquisition) and with a good understanding of the competitive priorities of the buyer company. The method is structured in four steps. In step one, the objective is to decide and weigh the requirements for supplier selection based on the judgments of the decision makers. In step two, the objective is to determine the initial set of criteria according to the requirements previously selected and weigh them based on their relationship with the requirements as well as on the weight of the requirements. In these initial steps, in order to define the requirements and the criteria, the decision makers should consider both the type of item to be purchased and the characteristics of the supply chain in which the buyer company is operating. Step three is concerned with the evaluation of the degree of difficulty to gather information needed to evaluate the supplier´s scores on each criterion previously selected. Finally, in step four, each criterion is classified into a twodimensional grid based on the weight and degree of difficulty of data collection for each criterion. These steps are described in detail in the next paragraphs. Take in Figure 4

4.1 Step 1: Requirement selection and weighting In step one, the decision makers have first to decide the set of n requirements for supplier selection. The requirements of the buying company derive from its strategic objectives. They refers to “what” dimensions of performance or performance key areas should be pursued by the supply chain. The criteria are in turn the measures that specify “how” the performance of suppliers should be quantified. In general, requirements related to quality, cost and delivery are relevant for most of the purchasing situations. However, further decision about selection of requirements and criteria should also be driven by the type of item to be purchased, as well as the expected relationship with the potential suppliers and the type of the supply chain. Table 2 presents a list of requirements based on the literature and grouped according to the type of item, following the studies by Kraljic (1983), Hätönen & Ruokonen (2010), Park et al. (2010) and Osiro et al. (2014). The decision makers can choose requirements from the list presented in Table 2. Since the list is not exhaustive, the decision makers can also identify new requirements through brainstorming between them. Take in Table 2 Following the work by Kraljic (1983), Hätönen & Ruokonen (2010) proposed a model that can be used to direct the process of selection of requirements and criteria based on the type of item. As illustrated in Figure 5a, Kraljic (1983) proposes four categories of items based on the combination of the dimensions importance of purchase and complexity of supply market: strategic, bottleneck, leverage and noncritical items. Strategic items are critical as they have a high impact on quality and cost and at the same time there are few suppliers that can attend the specification requirements. Bottleneck items, despite their relatively low profit impact, present supply risks because of scarcity or a monopolistic market (Kraljic 1983, De Boer et al., 2001, Park et al., 2010, Osiro et al., 2014). As illustrated in Figure 5b, Hätönen & Ruokonen (2010) propose that the prevailing requirements and criteria for strategic and bottleneck items are related respectively to supply stability and continuance and technical capabilities. Therefore, for these two categories, the requirements should consider the needs of long term relationship, technological capabilities for product and process development, collaboration, among others. Take in Figure 5

Leverage items, despite having a high impact on the quality and cost of final products, can usually be supplied by several alternative suppliers. Therefore, the dominant requirements and criteria are mostly related to managerial compatibility and transparency in the acquisition process. Finally, routine or noncritical items, are of low importance, as there is no significant possibility of adding value to the component, and there are many suppliers that could supply the items. Consequently, requirements and criteria related to price and cost will be the dominant ones (Kraljic, 1983, De Boer et al., 2001, Park et al., 2010, Osiro et al., 2014). Another important point to be considered is the competitive strategy adopted by the supply chain. Based on these different competitive strategies, Gattorna (2010) proposes four different configurations of supply chains: lean, agile, fully flexible and continuous replenishment. Lean supply chains are set for high volume, low variety and low cost. Therefore, their main requirements and criteria, apart from cost, can include predictable demands and lead times, efficiency, high reliability and low risk. Agile supply chains are designed for responsiveness and for launching new products in the market before competitors. Thus their main requirements and criteria can include rapid response in unpredictable conditions, available capacity, flexible scheduling, fast decision making and delivery, such as new product concept-to launch time. Fully flexible supply chains are designed to meet unplanned or unplannable solutions, with emphasis on finding creative solutions, very fast. Their main requirements and criteria are related to flexibility, ability to problem resolution, speed and measures of innovation. Continuous replenishment supply chains have as main characteristics relationship development, strategic partnerships, mutual trust and long term stability. Their main requirements and criteria can include potential for collaboration, IT infrastructure for information sharing, delivery reliability and quality. A further point is that all the requirements and criteria depend not only on the type of item or the strategy of the supply chain but on the type of industry as well, which will also interfere on the determination of the criteria and their relative weight. Finally, the decision makers have to be careful when determining the requirements and criteria so as to avoid duplication or redundancy. Once the list of the n requirements has been selected, then each decision maker judges the importance of the selected requirements. The degree of importance can be classified

as very low, low, medium, high and very high. Table 3 and Figure 6 present the linguistic terms and corresponding triangular fuzzy numbers used to judge the degree of importance. The aggregated judgments of the t decision makers (d = 1, 2, …, t), regarding the ith requirement (i =1, 2, …, n), are represented by

, given by equation

12. After aggregation of the judgments, the absolute weight

is computed by

defuzzification, according to the procedure specified in equation 13. The value of the absolute weight

is then converted to the relative weight

according to equation 14.

Take in Table 3 Take in Figure 6 4.2 Step 2: Initial criteria selection and weighting In step two, the decision makers have to define a set of m criteria which are related to the requirements selected in step one. As noted in the previous section, the initial selection of the criteria should consider the type of item, the strategy of the supply chain and the type of industry. Table 4 presents a list of criteria based on the studies proposed by Germain and Droge (1990), Kannan and Tan (2002), Humphreys (2003), Katsikeas et al. (2004), Huang and Keskar (2007), Gattorna (2010), Wu and Barnes (2010), Wang (2010), Chang (2011), Kilincci and Onal (2011), Govindan et al. (2013), Rezaei and Ortt (2013), Omurca (2013), Osiro et al. (2014), Mani et al. (2014), Kar (2015) and Rajesh and Ravi (2015). These criteria were also grouped according to the type of item, following the studies by Kraljic (1983), Hätönen & Ruokonen (2010), Park et al. (2010) and Osiro et al. (2014). It is important to note that this list of criteria is just a starting point that can be complemented with other criteria deployed from the needs of the buyers. However, since the cost of evaluation of suppliers increases as a function of the number of criteria, a practical guide is to limit them according to the type of item to be purchased. For instance, while the suppliers of strategic items require a detailed evaluation, taking into account several criteria, suppliers of non-critical items will be evaluated on just a few criteria.

Take in Table 4

The next action after the initial selection of the list of the m criteria is the judgment, by each decision maker, of the relationship between each criterion and each requirement. When there is a relationship between a criterion and a specific requirement, it can be classified as weak, average or strong. Table 5 and Figure 7 present the linguistic terms and corresponding triangular fuzzy numbers used to judge the degrees of relationship. In case there is no relationship between a criterion and a particular requirement, the corresponding fuzzy number will be set to (0.0, 0.0, 0.0).

Take in Table 5 Take in Figure 7 The aggregated judgments of the t decision makers (d = 1, 2, …, t), regarding the relationship between the ith requirement (i =1, 2, …, n) and the jth criterion (j =1, 2, …, m), represented by

, is given by equation 15. The absolute weight of the jth criterion,

, is calculated as in equation 16, by the sum of the product of the aggregated relationship

with the value of the relative weight of the ith requirement,

. The

absolute weight of each criterion is defuzzified as in equation 17 and converted to the relative weight

according to equation 18.

4.3 Step 3: Evaluation of difficulty of data collection The aim of this step is to evaluate the degree of difficulty of data collection regarding the performance of the potential suppliers in respect to each of the m criteria. As illustrated in Figure 4, the evaluation by the decision makers is based on the analysis of three parameters. 

Information availability: the amount of already existing information, either historic data of supply or tacit knowledge of the specialists;



Human resource and time required: the amount of specialists from different functions and the time required for evaluation;



Additional resources: related to any extra resource required such as employing services from consulting firms.

As evaluation of these parameters is imprecise, involving estimation by the decision makers, this work proposes the use of fuzzy variables to represent the parameters information availability ( ), human resource and time required (

) and additional

resource ( ), where j indicates the criterion. Table 6 and Figure 8 present the linguistic terms and their corresponding fuzzy numbers suggested to judge these parameters.

Take in Table 6 Take in Figure 8 After the evaluation by the t decision makers (d = 1, 2, …, t), the judgments regarding each one of these variables should be aggregated using fuzzy arithmetic mean, according to equations 19, 20 and 21. (19)

(20)

(21) Finally, to estimate the degree of difficulty of data collection a fuzzy index,

, is

computed and then defuzzified, as in equations 22 and 23 respectively.

=

(22)

(23)

4.4 Step 4: Criteria classification and final selection In step four the objective is the classification and final selection of the criteria according to their weights,

, and difficulty of data collection,

. These two variables, outputs

of steps two and three should be normalized according to equations 24 and 25 so as to be used in the classification procedure based on the two-dimensional grid illustrated in Figure 9. (24)

(25)

Take in Figure 9

After normalization,

can assume values in the interval [0.0, 1.0] and

values in the interval [

can assume

, 1.0]. As illustrated in Figure 9, for both

variables, values lower than 0.5 are classified as low and values in the range [0.5, 1.0] are classified as high. This classification procedure determines four groups of criteria, as follows: 

Group 1 – Priority criteria: this group includes the criteria that are mostly related to the priority requirements and therefore contribute the most to the fulfilment of these requirements. On top of that, they are preferred since they present a relatively low difficulty of data collection, which contributes to the agility and efficiency of the supplier selection process;



Group 2 – Critical criteria: the criteria in this group are also highly related to the priority requirements and therefore should be considered in the supplier selection process. However, since evaluation of the suppliers on these critical criteria requires a relatively high effort of data collection, it is suggested to choose just the very few vital ones.



Group 3 – Complementary criteria: although the criteria in this group are not the preferred ones as they have a relatively low importance, some of them can be included in the supplier selection process, depending on the number of criteria already selected, since they present a relatively low difficulty of data collection.



Group 4 – Costly criteria: the criteria in this group should not be selected since they are the least important and require a relatively high effort of data collection.

5. Application Case A global first tier manufacturer in the automobile supply chain wishes to revise the criteria used to select suppliers of clutches. In this industry, the main competitive priorities are cost, operation performance and product and process improvement. This

application case was carried out by one of the authors of this study in collaboration with managers of three functional areas of the company. The managers of acquisition, manufacturing and marketing acted as decision makers and are named here, respectively, DM1, DM2 and DM3. These specialists were responsible for proposing the initial lists of requirements and criteria as well as providing the linguistic judgments required in the proposed procedure, as described next. Following the procedure in Figure 4, the list of requirements in Table 2 was analyzed by the decision makers with the purpose of defining the initial set of requirements. Based on the item classification grid in Figure 5a, the item under analysis was consensually considered by the decision makers as a strategic one, since it has high complexity, high cost and few suppliers in the marketplace with technical capabilities. After a brief discussion they agreed on the following: cost (R1), delivery reliability (R2), financial situation (R3), management practices (R4), product development (R5), quality (R6) and relationship (R7). Table 7 presents the judgments in linguistic terms, according to Table 3, made by the decision makers regarding the degree of importance of the requirements. Table 8 presents the triangular fuzzy numbers of these judgments, the aggregated and defuzzified values of the absolute weights (

and

), calculated according to equation

12 and 13. Table 8 also presents the relative weight,

calculated according to

equation 14.

Take in Table 7 Take in Table 8

In the next step, the decision makers were asked to define the initial list of criteria. Table 4 was presented to them as suggestions of criteria depending on the type of item. After a lengthy discussion they agreed on the following initial list of criteria: commitment to cost reduction (C1), competitive price (C2), delivery in full on time (C3), geographical proximity (C4), environmental certification (C5), returns handling capability (C6), solid waste (C7), use of environment friendly material (C8), financial situation (C9), responsiveness to demand change (C10), structure for information sharing (C11), human resource management skill (C12), measurement tools and methods (C13), design capability (C14), commitment to quality improvement (C15), product

conformance (C16), quality certification (C17), ease of communication (C18), honesty (C19), potential for collaboration (C20) and safety programs (C21). Table 9 presents the linguistic judgments made by the three decision makers regarding the degrees of relationship between the requirements and criteria, based on the linguistic terms of Table 5. The corresponding fuzzy numbers of these judgments were aggregated using equation 15. After that, the absolute weight of each criterion ( according to equation 16, which was defuzzified ( weight (

) was calculated

) and converted to the relative

), as in equations 17 and 18 respectively. Table 10 presents these results.

Take in Table 9 Take in Table 10

In step 3, the decision makers had to evaluate the parameters used to calculate the degree of difficulty of data collection. Following the proposed procedure, they evaluated the parameters information availability ( ), human resources and time required (

) and additional resources ( ) using the linguistic terms shown in Table 6

and Figure 8. Table 11 presents the linguistic judgments of these parameters for each criterion made by the three decision makers. Table 12 presents, for each criterion, the fuzzy numbers of the judgments, the fuzzy value of the degree of difficulty (

),

calculated according to equation 22, and the corresponding defuzzified value calculated according to equation 23.

Take in Table 11 Take in Table 12

In step four, the outputs of steps 2 and 3, respectively

and

were normalized

according to equations 24 and 25 (results in Table 13). After normalization, the criteria were classified in groups as a function of their weights (Wj) and their difficulty of data collection (Dj) as shown in Table 13 and in the grid in Figure 10. Table 13 also presents the ranking of the criteria according to Wj and Dj. However, it is worth to note that the final selection discussed next does not consider the ordering but the categorization of the criteria as illustrated in Figure 9.

Take in Table 13 Take in Figure 10

As illustrated in Figure 10, after the proposed procedure, the following criteria were classified in the top quadrants (priority or critical groups): commitment to cost reduction (C1), competitive price (C2), delivery in full on time (C3), financial situation (C9), responsiveness to demand change (C10), commitment to quality improvement (C15), product conformance (C16), quality certification (C17) and potential for collaboration (C20). Since competitive price (C2), delivery in full on time (C3), product conformance (C16) and quality certification (C17) were classified as having low degree of difficulty, these criteria belong to the priority group, meaning that they should be used in the supplier selection process. These results were endorsed by the decision makers as being consistent with the type of the item being studied as well as with the strategic competitive priorities of the supply chain. Besides, commitment to cost reduction (C1), financial situation (C9), responsiveness to demand change (C10), commitment to quality improvement (C15) and potential for collaboration (C20) were classified as critical, meaning that they are important but they require a bigger effort of data collection. Analyzing these results, the decision makers pointed out that these critical criteria are aligned with the needs of supplier evaluation of strategic items imposed by the company. As reported by the decision makers, these criteria are already used by the company except for responsiveness to demand change (C10) and potential for collaboration (C20). Regarding the other criteria, geographical proximity (C4), environmental certification (C5), structure for information sharing (C11), measurement tools and methods (C13), design capability (C14), ease of communication (C18) were classified as complementary criteria. However, although environmental certification (C5) and design capability (C14) are related with just a few of the selected requirements, the decision makers suggested that they should also be considered in the supplier selection process since they are fundamental capabilities to strategic items. Finally, returns handling capability (C6), solid waste (C7), use of environment friendly material (C8), human resource management skill (C12), honesty (C19), and safety programs (C21) were all classified as costly criteria. As suggested by this procedure and validated by the decision makers, these criteria would not be selected since they were evaluated as having low importance and requiring relatively high effort of data collection.

6. Conclusions This paper presented a new approach to aid the choice and weighting of criteria to be used in the supplier selection process. The proposed approach combines the fuzzy QFD procedure for weighting the criteria with a procedure for evaluating the difficulty of data collection so as to portray the criteria in a classification grid. Based on the judgments of three decision makers, the proposed method was applied in an automotive company to revise the criteria used as well as their weighting. The results of the application were considered by the decision makers as consistent and aligned with the strategic competitive priorities of the supply chain. Differently from the majority of studies on supplier management that focus on the problem of supplier selection, this paper explores in detail the problem of criteria definition. The choice for the fuzzy QFD technique based on triangular fuzzy numbers and algebraic operations brings several advantages when compared to other quantitative approaches. Differently from other quantitative techniques such as QFD, AHP (Jakowski et al., 2010) and ANP (Kirytopoulos et al., 2008, Hsu et al., 2014, Hashemi et al., 2015), the applied fuzzy QFD technique enables the use of linguistic terms to judge the importance of the requirements and the relationship between requirements and criteria. The applied fuzzy QFD technique does not require the parameterization of decision rules, as in the fuzzy QFD based on inference, which contributes to its simplicity and agility of the implementation and reviewing of the decision process. Another benefit of using fuzzy QFD is that the number of alternatives (requirements or criteria) simultaneously evaluated is unlimited, unlike comparative approaches such as AHP, ANP and fuzzy AHP, in which the number of alternatives is limited by the human ability to simultaneous comparative judgment. Besides these advantages, the proposed method conveys several genuine contributions, as follows: 

The choice and weighting of the criteria derive from a systematic procedure based on the importance of the related requirements and the intensity of the relationship between requirements and criteria, which is regarded a better option than conventional pairwise comparisons based on relative importance;



Differently from other studies in criteria selection (Juan et al., 2009; Jakowski et al., 2010; Wu & Barnes, 2010; Chang et al., 2011), the type of item as well as

the type of supply chain are formally considered in the determination of the initial list of requirements and criteria; 

It proposes that the final selection of the set of criteria be also dependent on the degree of difficulty of data collection. However, differently from Wu & Barnes, (2010) evaluation is based on linguistic judgments regarding information availability, human resource and time required and other resources;



The method yields as outputs the ordering of the criteria according to the weight and according to the difficulty of data collection. Besides these results, the method classifies the criteria into groups so as to guide the decision in the final selection.

In terms of practical implications, the proposed method helps the decision makers to choose the set of important but not so costly criteria to supplier selection. The proposed method does not add complexity to the process of supplier selection since it would be run only in case a new type of item is to be purchased or a review of the criteria is needed. Moreover, this method can be implemented as an expert system with the external support of IT specialists. However, due its simplicity, it could also be implemented on electronic worksheet by a company interested in its application as long as the developers understand the concepts behind fuzzy variables and their algebraic operations. For using this method, the decision makers need to have a good understanding of the competitive priorities of the buyer company and its supply chain, and how to deploy these priorities in requirements and criteria for supplier selection. They also need to know the importance of the items to be purchased as well as the complexity of the supply market so as to relate the type of item to requirements and criteria. Another important issue is the choice of the values of the fuzzy number vertices for the linguistic terms since it depends on the subjectivity of the decision maker. An approach to support the definition of the membership functions is proposed by Ishizaka and Nguyen (2013). The proposed method can be integrated with other multicriteria decision making techniques so that the selected criteria and respective weights be used as inputs to carry out the supplier selection decision making process. Therefore, further research could explore the integration of this method with multicriteria techniques so as to support the steps in the supplier selection framework proposed by De Boer et al. (2001).

Additional further research can explore the application of this method to the problem of supplier evaluation for development. Finally, a limitation of the proposed method is that it does not deal with the interdependence between the criteria, which could interfere on the choice and weight of the criteria. Therefore, another further study could focuses on the combination of this method with techniques such as fuzzy DEMATEL, ANP and fuzzy ANP so as to try to overcome this limitation.

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Acknowledgments To FAPESP (São Paulo State Science Foundation) and CAPES for supporting this research project. To the anonymous reviewers for their helpful contributions.

Figure 1 - Supplier selection process proposed by De Boer et al. (2001)

Figure 2 - Triangular fuzzy number

Figure 3 – The House of the Quality of QFD (according to Juan et al., 2009).

Figure 4 - The fuzzy QFD approach proposed to support criteria selection.

Figure 5 – (a) Item classification model proposed by Kraljic (1983) and (b) model proposed by Hätönen and Ruokonen (2010).

Figure 6 – Linguistic scale of the degree of importance of requirements.

Figure 7 – Linguistic scale of the degree of relationship between requirements and criteria.

Figure 8 – Linguistic scale of the amount of information availability and resources required.

Figure 9 – Criteria classification grid.

Figure 10 – Results of the criteria classification process.

Table 1 - MCDM methods applied to supplier selection.

Combined method

Single method

Method(s) AHP (Analytic Hierarchy Process)

Scope An application of the AHP in vendor selection of a telecommunications system An AHP based method for sorting problems

Proposed by Tam & Tummala (2001) Ishizaka et al. (2012) Supplier selection considering social Mani et al. sustainability aspects (2014) ANP (Analytic Network An analytic network process approach for Kirytopoulos et Process) supplier selection in pharmaceutical industry al. (2008) ANN (Artificial Neural A method for supplier selection and Aksoy & Öztürk Network) performance evaluation in (2011) just-in-time production environments DEA (Data Envelopment Restricting weights in supplier selection Saen (2010) Analysis) decisions in the presence of dual-role factors Fuzzy Inference A ranking model based on fuzzy inference Amindoust et al. system for sustainable supplier selection (2012) An approach for supplier qualification and Lima Junior et al. selection using compensatory and non(2013) compensatory decision rules Genetic Algorithm Integration of supplier selection, Liao & Rittscher procurement lot sizing and carrier selection (2007) under dynamic demand conditions Grey relational analysis An approach for supplier selection in Rajesh & Ravi resilient supply chains (2015) AHP, fuzzy set theory and A group decision support system for supplier Kar (2015) ANN selection Fuzzy logic, AHP, fuzzy AHP A comparison of fuzzy logic, AHP, fuzzy AHP Ishizaka (2014) and hybrid fuzzy AHP and hybrid fuzzy AHP for supplier selection A multi-criteria decision-making approach Hsu et al. (2014) ANP and VIKOR (Serbian for evaluating carbon performance of abbreviation that means suppliers in the electronics industry multicriteria optimization and compromise solution) ANP and improved grey An integrated approach for green supplier Hashemi et al. selection based on economic and relational analysis (2015) environmental criteria Fuzzy ART (Adaptive A categorization method for supplier Keskin et al. Resonance Theory) evaluation and selection (2010) Fuzzy AHP An approach for supplier selection in a Kilinci & Onal washing machine company (2011) Fuzzy ANP Application of fuzzy analytic network process Vinodh et al. for supplier selection in a manufacturing (2011) organization Fuzzy ANP and fuzzy A framework for sustainable supplier Büyüközkan & preference relation selection with incomplete information Çifçi (2011) Fuzzy c-means and Rough An intelligent supplier evaluation, selection Omurca (2013) Set Theory and development system Fuzzy QFD A fuzzy QFD-based approach for supplier Dursun & Karsak

selection Fuzzy ELECTRE (Elimination An extension of the ELECTRE I method for and Choice Translating group decision making under a fuzzy Reality) environment Fuzzy multi objective linear A fuzzy approach for multi objective supplier programming selection Fuzzy TOPSIS (Technique A fuzzy TOPSIS approach for supplier for Order Preference by selection considering group of decision Similarity to Ideal makers Solution) Fuzzy Two-Tupple A fuzzy linguistic computing approach to supplier evaluation Fuzzy VIKOR A method for supplier selection based on entropy measure for objective weight

(2013) Hatami-Marbini & Tavana (2011) Arikan (2013) Zouggari & Benyoucef (2012) Wang (2010) Shemshadi et al. (2011)

Table 2 - List of requirements suggested for supplier selection according to the type of item. Strategic item Cost (Govindan et al., 2013)

Bottleneck item Cost (Govindan et al., 2013)

Leverage item Cost (Govindan et al., 2013)

Non critical item Cost (Govindan et al., 2013)

Delivery reliability (Chang, 2011)

Delivery reliability (Chang, 2011)

Delivery reliability (Chang, 2011)

Delivery reliability (Chang, 2011)

Environmental aspects (Huang & Keskar, 2007)

Environmental aspects (Huang & Keskar, 2007)

Environmental aspects (Huang & Keskar, 2007)

Environmental aspects (Huang & Keskar, 2007)

Flexibility (Huang & Keskar, 2007)

Flexibility (Huang & Keskar, 2007)

Flexibility (Huang & Keskar, 2007)

Health and security (Govindan et al., 2013)

Health and security (Govindan et al., 2013)

Health and security (Govindan et al., 2013)

Health and security (Govindan et al., 2013)

Information technology (Katsikeas et al., 2004)

Information technology (Katsikeas et al., 2004)

Information technology (Katsikeas et al., 2004)

Innovation (Kar, 2015)

Management practices (Kilincci & Onal, 2011)

Management practices (Kilincci & Onal, 2011)

Product development (Osiro et al. 2014)

Product development (Osiro et al. 2014)

Quality (Govindan et al., 2013)

Quality (Govindan et al., 2013)

Quality (Govindan et al., 2013)

Relationship (Rezaei & Ortt, 2013)

Relationship (Rezaei & Ortt, 2013)

Relationship (Rezaei & Ortt, 2013)

Stability / continuity (Kar, 2015)

Management practices (Kilincci & Onal, 2011) Product development (Osiro et al. 2014)

Social responsibility (Mani et al., 2014) Stability / continuity (Kar, 2015)

Table 3 – Linguistic terms of the importance of requirements. Linguistic terms

Fuzzy triangular number

Quality (Govindan et al., 2013)

Very Low (VL) Low (L) Medium (M) High (H) Very High (VH)

(1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00)

Table 4 - List of alternative criteria for supplier selection. Type of item

Alternative criteria suggested

Non critical item

Order fulfilment cost (Huang & Keskar, 2007) Competitive price (Katsikeas et al., 2004) Delivery capacity (Wu & Barnes, 2010) Delivery in full on time (Wu & Barnes, 2010) Delivery lead-time (Govindan et al., 2013) Service level (Wu & Barnes, 2010) Environmental certification (Humphreys, 2003)

Recycling (Humphreys, 2003) Returns handling capability (Humphreys, 2003) Reuse of packaging (Humphreys, 2003) Use of environment friendly material (Humphreys, 2003) Bargaining power (Wu & Barnes, 2010) Capacity utilization (Huang & Keskar, 2007)

Leverage item

Attractive discounts (Katsikeas et al., 2004) Returns handling capability (Humphreys, 2003) Commitment to cost reduction (Osiro et al., Reuse of packaging (Humphreys, 2003) 2014) Use of environment friendly material Competitive price (Katsikeas et al., 2004) (Humphreys, 2003) Order fulfilment cost (Huang & Keskar, 2007) Bargaining power (Wu & Barnes, 2010) Payment term (Huang & Keskar, 2007) Financial power (Wang, 2010) Communication with external logistics Resilience (Rajesh & Ravi, 2015) service suppliers (Germain & Dröge, 1990) Capacity utilization (Huang & Keskar, 2007)

Speed of problem resolution (Gattorna, 2010) Communication channels (Kar, 2015) After sale & warranty (Wang, 2010) Product conformance (Govindan et al., 2013) Health programs (Mani et al., 2014) Safety programs (Mani et al., 2014) Working conditions (Govindan et al., 2013) Measurement tools and methods (Germain & Dröge, 1990) Staff training (Humphreys, 2003) Strategic orientation (Wu & Barnes, 2010) Elapsed time from concept to launch of new products (Gattorna, 2010) Technical know-how (Katsikeas et al., 2004) After sale and warranty (Wang, 2010)

Bottleneck item

Delivery capacity (Wu & Barnes, 2010) Inventory turnover (Wu & Barnes, 2010) Delivery in full on time (Wu & Barnes, 2010) Responsiveness to demand change (Chang, Delivery lead-time (Govindan et al., 2013) 2011) Geographical proximity (Kannan & Tan, Speed of problem resolution (Gattorna, 2010) 2002) Communication channels (Kar, 2015) Reliability of service (Katsikeas et al., 2004) Structure for information sharing (Rezaei & Service level (Wu & Barnes, 2010) Ortt, 2013) Chemical waste (Humphreys, 2003) Timely information (Germain & Dröge, 1990) Clean technology availability (Humphreys, R&D capabilities (Katsikeas et al., 2004) 2003) Technological structure (Rajesh & Ravi, 2015) Environmental certification (Humphreys, 2003) Recycling (Humphreys, 2003)

Product conformance (Govindan et al., 2013) Ease of communication (Wang, 2010) Influence on industry (Rezaei & Ortt, 2013) Reputation (Wu & Barnes, 2010) Strategic position in the marketplace (Wu & Barnes, 2010) Process capability (Omurca, 2013) Refund policy (Katsikeas et al., 2004) Health programs (Mani et al., 2014) Safety programs (Mani et al., 2014) Working conditions (Govindan et al., 2013)

Order fulfilment cost (Huang & Keskar, 2007) Payment term (Huang & Keskar, 2007) Competitive price (Katsikeas et al., 2004) Transportation cost (Wu & Barnes, 2010) Communication with external logistics service suppliers (Germain & Dröge, 1990) Delivery capacity (Wu & Barnes, 2010) Delivery in full on time (Wu & Barnes, 2010) Delivery lead-time (Govindan et al., 2013) Reliability of service (Katsikeas et al., 2004) Service level (Wu & Barnes, 2010) Chemical waste (Humphreys, 2003) Clean technology availability (Humphreys,

Measurement tools and methods (Germain & Dröge, 1990) Staff training (Humphreys, 2003) Ability to co-design (Wang, 2010) Elapsed time from concept to launch of new products (Gattorna, 2010) Technical know-how (Katsikeas et al., 2004) Ability to problem resolution (Osiro et al., 2014) After sale and warranty (Wang, 2010) Product conformance (Govindan et al., 2013) Ease of communication (Wang, 2010)

Use of environment friendly material (Humphreys, 2003) Bargaining power (Wu & Barnes, 2010) Financial power (Wang, 2010) Financial situation (Chang, 2011) Resilience (Rajesh & Ravi, 2015) Capacity utilization (Huang & Keskar, 2007) Responsiveness to demand change (Chang, 2011) Speed of problem resolution (Gattorna, 2010) Communication channels (Kar, 2015) Information systems (Wu & Barnes, 2010) Structure for information sharing (Rezaei &

Strategic item

2003) Environmental certification (Humphreys, 2003) Recycling (Humphreys, 2003) Returns handling capability (Humphreys, 2003) Reuse of packaging (Humphreys, 2003)

Ortt, 2013) Timely information (Germain & Dröge, 1990) R&D capabilities (Katsikeas et al., 2004) Technological structure (Rajesh & Ravi, 2015)

Potential for collaboration (Rezaei & Ortt, 2013) Reputation (Wu & Barnes, 2010) Process capability (Omurca, 2013) Health programs (Mani et al., 2014) Safety programs (Mani et al., 2014) Working conditions (Govindan et al., 2013)

Attractive discounts (Katsikeas et al., 2004) Commitment to cost reduction (Osiro et al., 2014) Competitive price (Katsikeas et al., 2004) Order fulfilment cost (Huang & Keskar, 2007) Payment term (Huang & Keskar, 2007) Transportation cost (Wu & Barnes, 2010) Variation in price (Wu & Barnes, 2010) Communication with external logistics service suppliers (Germain & Dröge, 1990) Delivery capacity (Wu & Barnes, 2010) Delivery in full on time (Wu & Barnes, 2010) Delivery lead-time (Govindan et al., 2013) Geographical proximity (Kannan & Tan, 2002) Reliability of service (Katsikeas et al., 2004) Service level (Wu & Barnes, 2010) Average volume of air emission pollutant (Humphreys, 2003)

Bargaining power (Wu & Barnes, 2010) Financial power (Wang, 2010) Financial situation (Chang, 2011) Resilience (Rajesh & Ravi, 2015) Capacity utilization (Huang & Keskar, 2007) Inventory turnover (Wu & Barnes, 2010) Responsiveness to demand change (Chang, 2011) Speed of problem resolution (Gattorna, 2010) Communication channels (Kar, 2015) Information systems (Wu & Barnes, 2010) Structure for information sharing (Rezaei & Ortt, 2013) Timely information (Germain & Dröge, 1990) R&D capabilities (Katsikeas et al., 2004) Technological structure (Rajesh & Ravi, 2015) Unique competencies (Wu & Barnes, 2010) Human resource management skill (Wu & Barnes, 2010)

Ability to problem resolution (Osiro et al., 2014) After sale and warranty (Wang, 2010) Commitment to quality improvement (Kannan & Tan, 2002) Product conformance (Govindan et al., 2013) Quality certification (Huang & Keskar, 2007) Ease of communication (Wang, 2010) Government relationships (Wu & Barnes, 2010) Honesty (Kannan & Tan, 2002) Influence on industry (Rezaei & Ortt, 2013) Organizational culture (Wu & Barnes, 2010) Potential for collaboration (Rezaei & Ortt, 2013) Regular communications (Kannan & Tan, 2002) Reputation (Wu & Barnes, 2010)

Carbon emission (Humphreys, 2003) Chemical waste (Humphreys, 2003) Clean technology availability (Humphreys, 2003) Environmental certification (Humphreys, 2003) Environmental policies (Humphreys, 2003) Recycling (Humphreys, 2003) Resource consumption (Huang & Keskar, 2007) Returns handling capability (Humphreys, 2003) Reuse of packaging (Humphreys, 2003) Solid waste (Humphreys, 2003) Use of environment friendly material (Humphreys, 2003) Assets (Huang & Keskar, 2007)

Inventory reduction programs (Germain & Droge, 1990) Measurement tools and methods (Germain & Dröge, 1990) Staff training (Humphreys, 2003) Stakeholders relationship (Humphreys, 2003) Strategic orientation (Wu & Barnes, 2010) Ability to co-design (Wang, 2010) Design capability (Huang & Keskar, 2007) Elapsed time from concept to launch of new products (Gattorna, 2010) Product familiarity (Wu & Barnes, 2010) Senior management support (Humphreys, 2003) Technical know-how (Katsikeas et al., 2004)

Strategic position in the marketplace (Wu & Barnes, 2010) Process capability (Omurca, 2013) Refund policy (Katsikeas et al., 2004) Accidents (Rajesh & Ravi, 2015) Health programs (Mani et al., 2014) Safety audits (Huang & Keskar, 2007) Safety programs (Mani et al., 2014) Safety training (Huang & Keskar, 2007) Child labor (Mani et al., 2014) Coordination of social projects (Govindan et al., 2013) Educational institutions (Govindan et al., 2013) Working conditions (Govindan et al., 2013) Supporting community projects (Govindan et al., 2013)

Table 5 – Linguistic terms of the degree of relationship between criteria and requirements. Linguistic terms Fuzzy triangular number No relationship (0.00, 0.00, 0.00) (NR) Weak (W) (1.00, 1.00, 3.00) Average (A) (1.00, 3.00, 5.00) Strong (S) (5.00, 9.00, 9.00) Table 6 – Linguistic terms of information availability and resources required. Fuzzy triangular Linguistic Terms number Very few (VF) (1.00, 1.00, 2.00) Few (FE) (1.00, 2.00, 3.00) Fair (FA) (2.00, 3.00, 4.00) Many (MA) (3.00, 4.00, 5.00) A lot of (AL) (4.00, 5.00, 5.00) Table 7 – Linguistic judgments of the priorities of requirements. Requirements

DM1

DM2

DM3

R1 R2 R3 R4 R5 R6 R7

VH VH VH H H VH H

VH VH H H VH VH H

VH VH VH M H VH M

Table 8 – Fuzzy numbers of the priorities of requirements and values of the absolute and relative importance of requirements. Requirements R1 R2 R3 R4 R5 R6 R7

DM1 (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00)

DM2 (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00)

DM3 (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00)

(4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.67, 4.67, 5.00) (2.67, 3.67. 4.67) (3.33, 4.33, 5.00) (4.00, 5.00, 5.00) (2.67, 3.67. 4.67)

4.75 4.75 4.50 3.67 4.25 4.75 3.67

0.16 0.16 0.15 0.12 0.14 0.16 0.12

Table 9 - Linguistic judgments of the degree of relationship between requirements and criteria. DM1

DM2

DM3

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

R1

S

S

A

S

NR

W

W

A

NR

W

NR

W

NR

NR

A

A

NR

NR

NR

NR

NR

R2

NR

NR

S

S

NR

NR

NR

NR

NR

A

NR

W

NR

NR

W

W

W

NR

NR

NR

NR

R3

W

NR

NR

NR

NR

NR

NR

NR

S

NR

NR

NR

NR

NR

NR

NR

NR

NR

W

NR

NR

R4

W

NR

A

NR

A

W

W

NR

NR

W

NR

W

W

NR

S

NR

A

NR

NR

NR

W

R5

NR

NR

NR

NR

W

W

NR

A

NR

NR

NR

NR

W

A

NR

NR

NR

NR

NR

S

NR

R6

A

A

W

NR

NR

NR

NR

NR

NR

W

NR

W

W

NR

S

S

S

W

NR

A

NR

R7

W

W

A

A

NR

NR

NR

NR

NR

S

S

NR

NR

NR

A

NR

A

S

S

S

NR

R1 R2 R3 R4 R5 R6 R7

S NR

S NR

W S

A A

W NR

W NR

A NR

A NR

NR NR

A S

NR NR

W A

W W

A NR

S A

S S

W A

NR NR

NR NR

NR W

W W

W A NR S NR

NR A NR S NR

NR S NR S NR

NR NR NR NR NR

NR A S W W

NR A S NR NR

NR A NR W NR

NR NR S A NR

S W W A NR

NR S NR S W

NR NR NR NR S

NR S W A W

NR S W S NR

NR W S A W

NR S W S A

NR A NR S NR

W S W S W

NR NR W W S

NR NR NR NR S

NR NR S S S

NR A NR W W

R1 R2 R3 R4 R5 R6 R7

A NR NR A NR W

S NR NR W NR A

W S NR A NR A

W S NR NR NR NR

NR NR NR W A W

W NR NR A A NR

NR NR NR NR NR NR

A NR NR NR S W

NR NR S NR W S

W S NR A NR S

NR NR NR NR NR NR

W W W A W W

NR W NR A W A

W NR NR NR S W

A W NR S W S

S S NR A NR S

W W NR S W S

NR NR NR NR NR W

NR NR NR NR NR NR

W NR NR NR S A

W W NR W NR W

W

NR

W

W

W

NR

NR

NR

NR

W

A

W

NR

NR

W

NR

W

S

S

S

W

C20

C21

Table 10 - Fuzzy numbers of the aggregated degrees of relationship and values of the absolute and relative weights of the criteria. C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

R1 (3.67, 7.00, 7.67) R2 (0.00, 0.00, 0.00) R3 (0.67, 0.67, 2.00) R4 (1.00, 2.33, 4.33) R5 (0.00, 0.00, 0.00) R6 (2.33, 4.33, 5.67) R7 (0.67, 0.67, 2.00) (1.24, 2.24, 3.15)

(5.00, 9.00, 9.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.67, 1.33, 2.67) (0.00, 0.00, 0.00) (2.33, 5.00, 6.33) (0.33, 0.33, 1.00) (1.27, 2.39, 2.84)

(1.00, 1.67, 3.67) (5.00, 9.00, 9.00) (0.00, 0.00, 0.00) (2.33, 5.00, 6.33) (0.00, 0.00, 0.00) (2.33, 4.33, 5.67) (0.67, 1.33, 2.67) (1.67, 3.11, 3.96)

(2.33, 4.00, 5.67) (3.67, 7.00, 7.67) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.67, 1.33, 2.67) (1.02, 1.88, 2.41)

(0.33, 0.00, 1.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (1.00, 2.33, 4.33) (2.33, 4.33, 5.67) (0.67, 0.67, 2.00) (0.67, 0.67, 2.00) (0.68, 1.07, 2.03)

(1.00, 1.00, 3.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (1.00, 2.33, 4.33) (2.33, 4.33, 5.67) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.60, 1.05, 1.79)

(0.67, 1.33, 2.67) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.67, 1.33, 2.67) (0.00, 0.00, 0.00) (0.33, 0.33, 1.00) (0.00, 0.00, 0.00) (0.24, 0.42, 0.90)

(1.00, 3.00, 5.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (3.67, 7.00, 7.67) (0.67, 1.33, 2.67) (0.00, 0.00, 0.00) (0.77, 1.66, 2.27)

(0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (5.00, 9.00, 9.00) (0.33, 0.33, 1.00) (0.67, 0.67, 2.00) (2.00, 4.00, 4.67) (0.00, 0.00, 0.00) (1.19, 2.10, 2.47)

(1.00, 1.67, 3.67) (3.67, 7.00, 7.67) (0.00, 0.00, 0.00) (2.33, 4.33, 5.67) (0.00, 0.00, 0.00) (3.67, 6.33, 7.00) (2.33, 3.67, 5.00) (1.87, 3.32, 4.16)

(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) (3.67, 7.00, 7.67) (0.44, 0.85, 0.93)

(1.00, 1.00, 3.00) (1.00, 1.67, 3.67) (0.33, 0.33, 1.00) (2.33, 4.33, 5.67) (0.67, 0.67, 2.00) (1.00, 1.67, 3.67) (0.67, 0.67, 2.00) (0.98, 1.43, 2.97)

(0.33, 0.33, 1.00) (0.67, 0.67, 2.00) (0.00, 0.00, 0.00) (2.33, 4.33, 5.67) (1.00, 1.00, 3.00) (2.33, 4.33, 5.67) (0.00, 0.00, 0.00) (0.94, 1.50, 2.46)

(0.67, 1.33, 2.67) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.33, 0.33, 1.00) (3.67, 7.00, 7.67) (0.67, 1.33, 2.67) (0.33, 0.33, 1.00) (0.80, 1.48, 2.15)

(2.33, 5.00, 6.33) (1.00, 1.67, 3.67) (0.00, 0.00, 0.00) (5.00, 9.00, 9.00) (0.67, 0.67, 2.00) (5.00, 9.00, 9.00) (1.00, 2.33, 4.33) (2.12, 3.92, 4.87)

(3.67, 7.00, 7.67) (3.67, 6.33, 7.00) (0.00, 0.00, 0.00) (0.67, 2.00, 3.33) (0.00, 0.00, 0.00) (5.00, 9.00, 9.00) (0.00, 0.00, 0.00) (2.01, 3.74, 4.11)

(0.67, 0.67, 2.00) (1.00, 1.67, 3.67) (0.33, 0.33, 1.00) (3.67, 7.00, 7.67) (0.67, 0.67, 2.00) (5.00, 9.00, 9.00) (1.00, 1.67, 3.67) (1.75, 2.97, 4.10)

(0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.33, 0.33, 1.00) (1.00, 1.00, 3.00) (5.00, 9.00, 9.00) (0.81, 1.29, 1.70)

(0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.33, 0.33, 1.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (5.00, 9.00, 9.00) (0.65, 1.14, 1.24)

(0.33, 0.33, 1.00) (0.33, 0.33, 1.00) (0.00, 0.00, 0.00) (0.00, 0.00, 0.00) (5.00, 9.00, 9.00) (2.33, 5.00, 6.33) (5.00, 9.00, 9.00) (1.77, 3.24, 3.65)

(0.67, 0.67, 2.00) (0.67, 0.67, 2.00) (0.00, 0.00, 0.00) (1.00, 1.67, 3.67) (0.00, 0.00, 0.00) (0.67, 0.67, 2.00) (0.67, 0.67, 2.00) (0.51, 0.60, 1.62)

2.22

2.23

2.96

1.80

1.22

1.12

0.49

1.59

1.96

3.17

0.77

1.70

1.60

1.48

3.71

3.40

2.94

1.27

1.04

2.98

0.83

0.05

0.05

0.07

0.04

0.03

0.03

0.01

0.04

0.05

0.08

0.02

0.04

0.04

0.04

0.09

0.08

0.07

0.03

0.03

0.07

0.02

0.16

0.16

0.15

0.12

0.14

0.16

0.12

Table 11 - Linguistic judgments of the parameters used to evaluate the degree of difficulty of data collection. Information availability ( )

Human resource and time ( )

Additional resource required ( )

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

C2

MA AL

MA AL

FA AL

MA FE

FE VF

FE VF

FE VF

VF VF

VF VF

C3

AL

AL

AL

FE

FE

VF

VF

VF

VF

C4

AL

AL

AL

MA

AL

MA

FE VF

VF VF

VF VF

VF VF

VF

C5

FE VF

C6

MA

FA

FA

MA

MA

FE

VF

VF

VF

C7

FA

MA

FE

MA

FA

FA

FA

FE

FA

C8

FA

FA

FA

MA

FA

FE

FA

FE

VF

C9

FA

MA

FA

FE

VF

VF

FA

FA

FE

C10

MA

MA

MA

FE

FA

FE

FE

FE

VF

C11

AL

AL

AL

FE

VF

FE

VF

VF

VF

C12

FA

MA

FE

MA

FA

FE

MA

FE

VF

C13

AL

AL

AL

VF

FA

FE

FE

FE

VF

C14

MA

AL

MA

FE

FE

FE

VF

VF

VF

C15

FE

MA

FA

FE

FE

FE

FE

FA

VF

C16

MA

FA

MA

MA

AL

MA

FE VF

VF VF

VF VF

VF VF

VF

C17

FE VF

C18

MA

AL

AL

FE

VF

VF

VF

VF

VF

C19

FA

FA

FA

MA

FA

FE

MA

FE

FE

C20

MA

MA

MA

FE

MA

FE

VF

FE

VF

C21

FA

MA

FA

MA

FE

FE

VF

VF

VF

C1

VF

VF

Table 12 – Fuzzy numbers of the judgments of the parameters of difficulty of data collection, fuzzy values of degree of difficulty and defuzzified values. Information availability ( ) C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13

DM1 (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (2.00, 3.00, 4.00) (4.00, 5.00, 5.00)

DM2 (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00)

DM3 (2.00, 3.00, 4.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (1.00, 2.00, 3.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (1.00, 2.00, 3.00) (4.00, 5.00, 5.00)

Human resource and time ( DM1 (3.00, 4.00, 5.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (3.00, 4.00, 5.00) (1.00, 1.00, 2.00)

DM2 (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00)

)

DM3 (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (2.00, 3.00, 4.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00)

Additional resource required ( ) DM1 (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (3.00, 4.00, 5.00) (1.00, 2.00, 3.00)

DM2 (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (2.00, 3.00, 4.00) (2.00, 3.00, 4.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00)

DM3 (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00)

(0.29, 0.55, 1.13) (0.20, 0.23, 0.54) (0.20, 0.27, 0.58) (0.20, 0.27, 0.58) (0.20, 0.23, 0.60) (0.46, 0.90, 1.71) (0.46, 0.89, 1.83) (0.46, 0.94, 1.92) (0.31, 0.55, 1.21) (0.23, 0.50, 1.00) (0.20, 0.27, 0.58) (0.46, 0.89, 1.83) (0.23, 0.37, 0.71)

0.63 0.30 0.33 0.33 0.32 0.99 1.02 1.07 0.66 0.56 0.33 1.02 0.42

C14 C15 C16 C17 C18 C19 C20 C21

(3.00, 4.00, 5.00) (1.00, 2.00, 3.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00)

(4.00, 5.00, 5.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (4.00, 5.00, 5.00) (4.00, 5.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00)

(3.00, 4.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (3.00, 4.00, 5.00) (4.00, 5.00, 5.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (2.00, 3.00, 4.00)

(1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (3.00, 4.00, 5.00) (1.00, 2.00, 3.00) (3.00, 4.00, 5.00)

(1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (3.00, 4.00, 5.00) (1.00, 2.00, 3.00)

(1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00)

(1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (3.00, 4.00, 5.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00)

(1.00, 1.00, 2.00) (2.00, 3.00, 4.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00)

(1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00) (1.00, 2.00, 3.00) (1.00, 1.00, 2.00) (1.00, 1.00, 2.00)

(0.20, 0.35, 0.75) (0.29, 0.67, 1.50) (0.21, 0.36, 0.88) (0.20, 0.23, 0.60) (0.20, 0.25, 0.59) (0.46, 0.94, 1.92) (0.27, 0.50, 1.00) (0.31, 0.55, 1.21)

0.41 0.78 0.45 0.32 0.32 1.07 0.57 0.66

Table 13 – Normalized values of weights (Wj) and difficulty of data collection (Dj) and results of classification according to the grid in Figure 9. Ranking according to C1 C2

0.60

8st

0.60

st

7

st

0.59 0.28

Ranking according to

Classification of

Classification of

Classification of Cj

13st

High

High

Critical

st

High

Low

Priority

st

1

C3

0.80

5

0.31

5

High

Low

Priority

C4

0.49

10st

0.31

6st

Low

Low

Complementary

0.33

st

0.30

nd

Low

Low

Complementary

st

Low

High

Costly

st

Low

High

Costly

st

Low

High

Costly

st

High

High

Critical

st

High

High

Critical

Low

Low

Complementary

C5 C6 C7 C8 C9 C10 C11 C12 C13

0.30 0.13 0.43 0.53 0.85 0.21 0.46 0.43

16

st

17

st

21

st

12

st

9

rd

3

st

20

st

11

st

13

st

0.93 0.95 1.00 0.61 0.52 0.31 0.95 0.39

2

17 18 20 14 11

st

7

st

19

Low

High

Costly

st

Low

Low

Complementary

st

Low

Low

Complementary

8

C14

0.40

14

0.39

9

C15

1.00

1st

0.73

16st

High

High

Critical

0.92

nd

0.43

st

C16 C17 C18 C19 C20 C21

0.79 0.34 0.28 0.80 0.22

2

st

6

st

15

st

18

st

4

st

19

0.30 0.30 1.00 0.53 0.61

10

High

Low

Priority

rd

High

Low

Priority

st

3

4

Low

Low

Complementary

st

Low

High

Costly

st

High

High

Critical

st

Low

High

Costly

21 12 15

Graphical abstract

Highlights 

 

Proposes a method to aid the choice and weighting of criteria to supplier selection. Combines fuzzy QFD with a classification procedure based on a two dimensional grid. Assesses the difficulty to get data to evaluate the suppliers on each criterion. The type of item is considered to define of the list of requirements and criteria.



The method classifies the criteria into groups so as to guide the final selection.

