A new approach for supplier selection using fuzzy

Int. J. Logistics Systems and Management, Vol. 19, No. 1, 2014

A new approach for supplier selection using fuzzy MCDM Reza Rostamzadeh Department of Management, Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia and Department of Management, East Azarbaijan Science and Research Branch, Islamic Azad University, Tabriz, Iran E-mail: [email protected] E-mail: [email protected] Abstract: The aim of this paper is to propose a new framework for supplier selection using FAHP and TOPSIS methods. As the human decision-making process usually contains fuzziness and vagueness, so linguistic values are used to assess the ratings and weights for criteria. A hierarchy multiple criteria decision-making (MCDM) model based on fuzzy-sets theory including FAHP adopted for finding weights of criteria and its sub-criteria and then for the final ranking of the suppliers TOPSIS method is used in a real industry case. This study concluded that the ranking of the main criteria and sub-criteria in all the suppliers are the same. Drawing on a real case, supplier A was identified to be the best supplier. Also, it can be said that TOPSIS method is a useful additional tool for the problem. More research is definitely called for within the context of studying a more complex supply chain with multiple supply network and nodes. There is also a crucial need for investigating other hybrid methods to find the optimum supplier. The proposed criteria can be applied both in industrial and service organisations with slight modifications. Keywords: supplier selection; multi-criteria decision making; FAHP. Reference to this paper should be made as follows: Rostamzadeh, R. (2014) ‘A new approach for supplier selection using fuzzy MCDM’, Int. J. Logistics Systems and Management, Vol. 19, No. 1, pp.91–114. Biographical notes: Reza Rostamzadeh is currently a Postdoctoral Researcher at Innovation & Commercialization Center (ICC) of the Universiti Teknologi Malaysia (UTM). He received his BA and MA in Industrial Management from IAU of Tabriz, Iran and his PhD degree from UTM. His areas of interest include supply chain management, operation management, lean manufacturing and entrepreneurship.

Copyright © 2014 Inderscience Enterprises Ltd.

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Introduction

Supplier selection is vital to the success of a manufacturing firm. Supplier selection is a multi-criteria decision-making problem (Mahdiloo et al., 2012; Ilangkumaran et al., 2012; Ghosh et al., 2012; Sandeep et al., 2011) and has strategic importance for most companies. It is quite difficult to find an optimal solution and possibly the most important decision made in the purchasing process (Weber et al., 1991; Nydick and Hill, 1992; Mobolurin, 1995). Traditional techniques in operations research mainly deal with quantitative measures, while vagueness and uncertainty, which is described by qualitative measures, exist everywhere within the supply chain. In order to gain competitive advantages in markets, manufacturers must collaborate, not only with component or raw material suppliers, but also with wholesalers/distributors, retailers, and customers, who all participate in a supply chain, directly or indirectly, in order to fulfil customer requests (Ha and Krishnan, 2008; More and Mateen, 2012). Hence, developing a suitable approach for supplier selection seems to be a challenging research task. To build more effective relationships with suppliers, organisations are using supplier selection criteria to strengthen the selection process. Various factors have been used as criteria for supplier selection including price, delivery performance, reputation in the industry, size of enterprise, geographical location, quality, environmental compliance, capacity, services, lead-time, packaging, storage, transportation, and product development. The applicability of these criteria depends on the product or service produced and the market for which these products or services are targeted. To this end, extensive research focuses on developing methods to assist in supplier selection. Nevertheless, relatively little work has been undertaken on rationalising the real industrial applications of many of the supplier selection methods. To rectify this imbalance, this paper applies new approaches for supplier selection using fuzzy AHP and technique based on similarity to ideal solution (TOPSIS) to a well-known Iranian company operating in heavy industries. The remainder of this paper is organised as follows. The next section provides a review of relevant literature. Section 3 briefly discusses FAHP and TOPSIS methodologies. An application of the real industry case and proposed criteria is given in Section 4. Conclusions and managerial implications are presented in the final section.

2

Literature review

Extensive multi-criteria decision making approaches have been proposed for supplier selection, such as the analytic hierarchy process (AHP), analytic network process (ANP), case-based reasoning (CBR), data envelopment analysis (DEA), fuzzy set theory, genetic algorithm (GA), mathematical programming, simple multi-attribute rating technique (SMART), and their hybrids. Narasimahn (1983), Nydick and Hill (1992), Partovi et al. (1989) and Barbarosoglu and Yazgac (1997) were the earliest researches that adopted AHP for supplier selection problems. The major reasons for applying AHP are because AHP can handle both qualitative and quantitative criteria and because it can be easily understood and applied by related human resources. Many factors affect supplier’s performance. Dickson (1966) identified 23 important evaluation criteria for supplier selection. The author concluded that quality, delivery, and performance history are the three most important criteria. Weber et al. (1991) reviewed and classified 74 articles

A new approach for supplier selection using fuzzy MCDM

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addressed the supplier selection problem. They summarised that price was the highest-ranked factor, followed by delivery and quality. Ellram (1990) proposed three principal criteria: 1

the financial statement of the supplier

2

the organisational culture and strategy of the supplier

3

the technological state of the supplier.

An exploration of supplier selection practices across the supply chain provided by Choi and Hartley (1996). They applied Dickson (1966) and Weber et al. (1991) criteria’s and compared supplier-selection practices based on a survey of companies at different levels in the auto industry. Ghodsypour and O’Brien (1998) proposed an integration of an AHP and linear programming to consider both tangible and intangible factors in choosing the best suppliers and giving them optimal order quantities so that the total purchase value is maximised. Akarte et al. (2001) developed a web-based AHP system to evaluate the casting suppliers with respect to 18 criteria. In the system, suppliers had to register, and then input their casting specifications. To evaluate the suppliers, buyers had to determine the relative importance weightings for the criteria based on the casting specifications, and then assigned the performance rating for each criterion using a pairwise comparison. Chan (2003) developed an interactive selection model with AHP to facilitate decision makers in selecting suppliers. The model was so-called because it incorporated a method called chain of interaction, which was deployed to determine the relative importance of evaluating criteria without subjective human judgment. AHP was only applied to generate the overall score for alternative suppliers based on the relative importance ratings. Chan and Chan (2004) applied AHP to evaluate and select suppliers. The AHP hierarchy consists of six evaluating criteria and 20 sub-factors, of which the relative importance ratings were computed based on the customer requirements. Wang et al. (2004) developed an integrated AHP and pre-emptive goal programming (PGP) methodology to take into account both qualitative and quantitative factors in supplier selection. While the AHP process matched product characteristics with supplier characteristics in order to qualitatively determine supply chain strategy, PGP mathematically determined the optimal order quantity from the chosen suppliers. Liu and Hai (2005) applied AHP to evaluate and select suppliers. Similar to Chan (2003), the authors did not apply the AHP’s pairwise comparison to determine the relative importance ratings among the criteria and sub-factors. Instead, the authors used Noguchi’s voting and ranking method, which allowed every manager to vote or to determine the order of criteria instead of the weights. Lin et al. (2009) proposed a method that incorporates the extended association rule algorithm of data mining to find key suppliers. The supplier selection has been viewed as the problem of mining a large database of shipment. The results show that the method is effective and applicable. Data envelopment analytic hierarchy process (DEAHP) applied by Sevkli et al. (2007) for supplier selection. They embedded DEA into AHP methodology. This research concluded that the DEAHP method outperforms the AHP method for supplier selection but Wang et al. (2009) illustrated the weaknesses of the DEAHP and demonstrated the invalidity of their work. Also they stated that extra verification is needed to come to a decision. Mahdiloo et al. (2012) proposed a novel DEA model for solving supplier selection problems whereas the required numerical data for all the inputs

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and outputs for all the suppliers is not available in the real-world problems. The proposed model can measure suppliers’ efficiency in the following problems: the presence of undesirable outputs; the lack of input variables and the presence of zero or negative values in the dataset. More and Mateen (2012) applied a DEA model for suppliers selection and development. The DEA uses an ideal target for each selection criteria and then identifies the best supplier available. Haq and Kannan (2006) presented a structured model for evaluating the supplier selection for the rubber industry using AHP and the model is verified with the fuzzy AHP. Chan et al. (2008) presented fuzzy AHP to efficiently tackle both quantitative and qualitative decision factors involved in the selection of global supplier. Lee (2009) proposed an analytical approach to select suppliers under a fuzzy environment. A (FAHP) model, which incorporates the benefits, opportunities, costs and risks (BOCR) concept, is constructed to evaluate various aspects of suppliers. Sandeep et al. (2012) combined AHP and grey relational analysis (GRA) approach for the supplier selection process. A case study is presented to exemplify the methodology. Ruiz-Torres et al. (2010) presented a new supplier selection model that determines safety stocks based on the supplier delivery reliability. The model includes procurement costs, supplier management costs, inventory carrying costs, and loss costs due to missed deliveries. A sensitivity analysis provided that illustrates how the model can be used to analyse different sourcing strategies under various cost parameters. Jain et al. (2009) provided an overall picture of research on supplier selection process (SSP) and supplier selection practices summarised the different selection criteria, the various problems of suppliers’ selection and the existing methods to solve these problems. In addition, emerging issues and challenges resulting to scope for future works on supply chain procurement activities are identified and some clear guidelines for future research are proposed. Vahdani and Zandieh (2010) suggested the fuzzy balancing and ranking method for selection of suppliers. First, they appraised the performance of alternatives against criteria via linguistic variables which are expressed as triangular fuzzy numbers. The foregoing model obtains the alternative rankings through a four-stage process. Kumar et al. (2011) proposed an integrated model of fuzzy quality function deployment (FQFD) and multiple objective linear programming (MOLP) for supplier selection and order allocation in a global context. Various criteria for global supplier selection are explored through two categories: buyer attributes and supplier attributes. This work helps the supply chain managers/purchasing managers in supplier selection in global markets and allocates the order among them considering all the constraints under fuzzy environment. Bayazi and Karpak (2013) used AHP to aid companies with the decision of selecting the most capable third-party logistic (3PL) service provider for an aerospace company. The methodology enables practitioners to systematically evaluate the trade-offs among multiple factors and therefore helps them in making more informed decisions when evaluating outsourcing logistics services. Ravi (2012) proposed the selection of third-party reverse logistics providers for end-of-life computers using TOPSIS-AHP methods. This study aims to efficiently assist the decision-makers in determining the most appropriate third-party reverse logistics provider. A numerical example from a case company is included to demonstrate the steps of the proposed model. Other works can be considered in Ilangkumaran et al. (2012), Ruiz-Torres et al. (2013), Sawik (2013), Arunkumar et al. (2011), Ghosh et al. (2012) and Shaw et al. (2013). It is indicated that the supplier selection criteria is changing with the new challenge to select suppliers who can add long-term value to the manufacturer. There is no special


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formula to follow for companies to choose their own supplier. Since SSP is a multiple criteria and it is necessary to make trade-off between conflicting tangible and intangible factors to find the best supplier, in this study a new multi criteria approach is proposed to evaluate and prioritise the candidate suppliers.

3

Fuzzy multi-attribute decision-making methods

Fuzzy sets were introduced by Zadeh (1965) to represent/manipulate data and information possessing non-statistical uncertainties. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associated with human cognitive processes, such as thinking and reasoning (Zimmermann, 1991). With different daily decision making problems of diverse intensity, the results can be misleading if the fuzziness of human decision making is not taken into account (Tsaur et al., 2002). Fuzzy set theory providing a more widely frame than classical set theory, has been contributing to the capability of reflecting real world (Ertugrul and Tus, 2007). Figure 1

Triangular fuzzy number M

A tilde ‘~’ will be placed above a symbol if the symbol represents a fuzzy set. A triangular fuzzy number (TFN) M is shown in Figure 1. A TFN is denoted simply as (l | m, m | u) or (l, m, u). The parameters l, m, and u, respectively, denote the smallest possible value, the most promising value, and the largest possible value that describes a fuzzy event. Each TFN has linear representations on its left and right side such that its membership function can be defined as equation (1): ⎧0, ⎪ x −l ⎪ , ⎪m − l μ( x | M ) = ⎨ ⎪u−x , ⎪u − m ⎪0, ⎩

x < l, l ≤ x ≤ m,

(1) m ≤ x ≤ u, x > u.

A fuzzy number can always be given by its corresponding left and right representation of each degree of membership equation (2):

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R. Rostamzadeh M = M l ( y ) , M r ( y ) = ( l + (m − l ) y, u + (m − u ) y ) ,

y ∈ [0, 1],

(2)

where l(y) and r(y) denote the left side representation and the right side representation of a fuzzy number, respectively.

3.1 Methodology of FAHP There are many FAHP methods in literature (Buckley, 1985; Chang, 1996; Van Laarhoven and Pedrcyz, 1983; Mikhailov, 2004). In this study, Chang’s (1992, 1996) extent analysis method is used because of the computational easiness and efficiency of this method. Let X{x1, x2,…,xn} be an object set, and U{u1, u2,…,un}be a goal set. According to the method of Chang’s (1992), each object is taken and extent analysis for each goal, gi is performed, respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs equation (3): M 1gi , M g2i ,… , M gmi , i = 1, 2,… , n,

(3)

where all the M gji ( j = 1, 2,… , m) are TFNs. The steps of Chang’s extent analysis can be

given as in the following: Step 1

The value of fuzzy synthetic extent with respect to the ith object is defined as equation (4): ⎡ n M gji ⊗ ⎢ j =1 ⎣⎢ i =1 m

Si =

∑

⎤ M gji ⎥ j =1 ⎦⎥ m

∑∑

−1

(4)

To obtain [Σin=1Σ nj =1 M gji ]−1 , perform the fuzzy addition operation of m extent analysis values for a particular matrix such that equation (5): ⎛ M gji = ⎜ ⎜ j =1 ⎝ m

∑ n

m

∑∑ M i =1 j =1

m

m

⎞

m

∑ ∑ ∑ u ⎟⎟

j gi

li

j =1

⎛ =⎜ ⎜ ⎝

mi

j =1

m

i

j =1

m

(5)

⎠ ⎞

m

∑ l ∑ m ∑ u ⎟⎟ i

j =1

i

j =1

i

j =1

(6)

⎠

and then compute the inverse of the vector in equation (6) such that equation (7): ⎡ n ⎢ ⎣⎢ i =1

m

∑∑

Step 2

j =1

M gji

⎤ ⎥ ⎦⎥

−1

1 1 ⎞ ⎛ 1 , n , n ⎟ =⎜ n ⎝ Σ i =1ui Σ i =1mi Σ i =1li ⎠

(7)

The degree of possibility of M2 = (l2, m2, u2) ≥ M1 = (l2, m2, u2) is defined as equation (8): V ( M 2 ≥ M1 ) =

SUP y≤x ⎢ ⎣ min

( μM

1

( x), μM 2 ( y ) ) ⎥⎦

(8)


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Can be equivalently expressed as follows equation (9): if m2 ≥ m1 ⎧1 V ( M 2 ≥ M 1 ) = hgt ( M 1 ∩ M 2 ) = μM 2 (d ) = ⎪⎪0 if l1 ≥ u2 (9) ⎨ l1 − u2 ⎪ otherwise ⎪⎩ ( m2 − u2 ) − ( m1 − l1 )

where d is the ordinate of the highest intersection point D between μM1 and μM 2 (see Figure 2). To compare M1 and M2, we need both the values of V(M1 ≥ M2) and V(M2 ≥ M1). Figure 2

Step 3

The intersection between M1 and M2

The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers Mi (i = 1, 2,…,k) can be defined by equation (10): V ( M ≥ M 1 , M 2 ,… , M K ) = V ⎡⎣( M ≥ M 1 ) and ( M ≥ M 2 ) and … and ( M ≥ M K )⎤⎦

(10)

= min V ( M ≥ M i ) , i = 1, 2, 3,… , k .

Assume that equation (11): d ′ ( Ai ) = min V ( Si ≥ Sk ) .

(11)

For k = 1, 2,…n; k ≠ i. Then the weight vector is given by equation (12): W ′ = ( d ′ ( A1 ) , d ′ ( A2 ) ,… , d ′ ( An ) ) , T

(12)

where Ai(i = 1, 2,…,n) are n elements. Step 4

Via normalisation, the normalised weight vectors is given by equation (13): W = ( d ( A1 ) , d ( A1 ) ,… d ( A1 ) ) , T

where W is a non-fuzzy number.

(13)

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3.2 Technique based on similarity to ideal solution Hwang and Yoon (1981) originally proposed the order performance TOPSIS, in which the chosen alternative should not only have the shortest distance from the positive ideal reference point (PIRP), but also have the longest distance from the negative ideal reference point (NIRP), to solve the multiple criteria decision-making (MCDM) problems. Chen et al. (2006) extended the concept of TOPSIS method to develop a methodology for solving supplier selection problems in fuzzy environment. Boran et al. (2009) proposed a multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. TOPSIS method combined with intuitionistic fuzzy to select appropriate suppliers in a group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilised to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Wang and Chang (2007) applied the fuzzy (MCDM) method to determine the importance weights of evaluation criteria and to synthesise the ratings of candidate aircraft then TOPSIS is employed to obtain a crisp overall performance value for each alternative to make a final decision. Wang et al. (2009) used fuzzy hierarchical TOPSIS for supplier selection. In this study TOPSIS method will be used for the final ranking of the candidate suppliers. Other studies can be found in: Ma et al. (2004), Tsao (2003), Wang et al. (2005), You and Fan (2002), Zhang and Fan (2002), Wang and Lee (2009), Chu (2002) and Arabzad et al. (2013). In the following, the steps of TOPSIS is given. Step 1

Decision matrix is normalised via equation (14): rij =

Step 2

wi Σ Jj =1 wij2

Step 4

j = 1, 2, 3,… , J , i = 1, 2, 3,… , n

(14)

The weighted normalised decision matrix is formed by equation (15): vij = wi ∗ rij ,

Step 3

,

j = 1, 2, 3,… , J , i = 1, 2, 3,… , n

(15)

Positive ideal solution (PIS) and negative ideal solution (NIS) will be determined by equations (16) and (17): A+ = {v1+ , v2+ , v3+ ,… , n} max values

(16)

A− = {v1− , v2− , v3− ,… , n} min values

(17)

The distance of each alternative from PIS and NIS will be calculated: n

di+ =

∑ (v

ij

− v +j ) ,

j = 1, 2,… , J

(18)

− v −j ) ,

j = 1, 2,… , J

(19)

2

j =1 n

di− =

∑ (v

ij

j =1

2

A new approach for supplier selection using fuzzy MCDM Step 5

The closeness coefficient of each alternative will be calculated: CCi =

Step 6

4

99

di+

di− , i = 1, 2,… , J + di−

(20)

By comparing CCi values, the ranking of alternatives are determined.

Case study

Supplier selection is the strategy adopted by the manufacturer, to evaluate and select suppliers, which fulfils the requirements of the manufacturer. In general, SCM arises from several corporations that build their own supply chain. They must find more efficient partners to make the chain competitive. Among a variety of available suppliers, manufacturers must choose more collaborative ones who are able to develop long-term relationships (Wise and Morrison, 2000). Regarding to this point that responsibility to the customer needs is known as a basis of sustainability in the marketplace, hence, necessity of attention to factors such as; price, quality, time, … and preparing them in acceptable level are counted as a major function of the organisation. The aim of this research is prioritising proposed criteria in order to choose the best supplier with high performance. First the FAHP was applied and then for the final ranking of suppliers TOPSIS technique was used. Iran Tractor Manufacturing Company (ITMCO) is one of the biggest company in the Middle East. The main activity of the company is producing of the tractor. The firm has a five major suppliers which providing the needed materials of the firm. For making the strategic decisions in the future and having a strong business relationship with the suppliers, the managers and analysts of the company decided to evaluate their supplier’s situation in the market. An interview undertaken with managers and experts of the company from relevant departments including purchasing, manufacturing, quality assurance, and R&D to collect the required criteria. The criteria that cover all needs of the company were noticed. To determine the reliability of the questionnaire, test-retest method was used. In this way, the researcher chose five samples randomly from managers at two different times (at least two weeks) then questionnaires were distributed to them. After that, Spearman rank correlation coefficient analysis and meaningful test of sampling was conducted. Reliability test of the questionnaire was conducted at 96% confidence coefficient level. As the results show, the questionnaire has acceptable reliability. Finally a new multi criteria approach proposed for the problem and was applied for determining the best supplier. Figure 3 shows the structuring of the hierarchy of supplier selection problem, which includes four levels. The top level of the hierarchy represents the ultimate goal of the problem, while the second level of the hierarchy consists of seven main supplier selection criteria, which are namely managerial capabilities, manpower, marketing, material, method, machine and money. At the third level, these criteria are decomposed into various sub-criteria that may affect the buyer’s choice for a particular supplier. Finally, the bottom level of the hierarchy represents the alternative suppliers.

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Figure 3

7Ms approaches for supplier selection

4.1 Application The respondents of this research were managers, assistant managers, analysts and experts of companies. To get the required data of FAHP, a questionnaire was distributed. See Appendix 1 for questionnaire form. For weighting tables, Table 1 is used. Then, the main criteria calculated using FAHP for the all five suppliers. Calculations of sub-criteria were done in the same manner. Here, the calculation for supplier A is shown. The fuzzy evaluation matrix for supplier A is given in Table 2. Table 1

Linguistic scales of importance

Linguistic scale for importance

Triangular fuzzy scale

Triangular fuzzy reciprocal scale

Equal

(1, 1, 1)

(1, 1, 1)

Weak

(1/2, 1, 3/2)

(2/3, 1, 2)

Fairly strong

(3/2, 2, 5/2)

(2/5, 1/2/, 2/3)

Very strong

(5/2, 3, 7/2)

(2/7, 1/3, 2/5)

Absolute

(7/2, 4, 9/2)

(2/9, 1/4, 2/7)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3) (2/3, 1, 2)

Money

Machine

Method

(2/5, 1/2, 2/3)

Marketing

Material

(1, 1, 1)

(2/5, 1/2, 2/3)

Manpower

(1, 1, 1)

Managerial capabilities

Managerial capabilities

(2/3, 1, 2)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3)

(2/3, 1, 2)

(1, 1, 1)

(1, 1, 1)

Manpower

Marketing

(1, 1, 1)

(2/3, 1, 2)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3)

(1, 1, 1)

(1/2, 1, 3/2)

(3/2, 2, 5/2)

Machine

(3/2, 2, 5/2)

(3/2, 2, 5/2)

(1, 1, 1)

(1, 1, 1)

(3/2, 2, 5/2)

(3/2, 2, 5/2)

(3/2, 2, 5/2)

Material

(3/2, 2, 5/2)

(1/2, 1, 3/2)

(1, 1, 1)

(1, 1, 1)

(3/2, 2, 5/2)

(3/2, 2, 5/2)

(3/2, 2, 5/2)

Method

(3/2, 2, 5/2)

(1, 1, 1)

(2/3, 1, 2)

(2/5, 1/2, 2/3)

(1/2, 1, 3/2)

(3/2, 2, 5/2)

(3/2, 2, 5/2)

Money

(1, 1, 1)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3)

(2/5, 1/2, 2/3)

(1, 1, 1)

(1/2, 1, 3/2)

(1/2, 1, 3/2)

Table 2

7M

A new approach for supplier selection using fuzzy MCDM The fuzzy evaluation matrix with respect to the goal for supplier A

101

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R. Rostamzadeh

Step 1 7

∑M j =1

j g1

= (1, 1, 1) ⊕ (1, 1, 1) ⊕ (3/2, 2, 5/2) ⊕ (3/2, 2, 5/2) ⊕ (3/2, 2, 5/2) ⊕ (3/2, 2, 5/2) ⊕ (1/2, 1, 3/2) = (8.5, 11, 13.5)

7

∑M j =1 7

∑ j =1 7

∑ j =1

j g2

7

= (7.5, 10, 12.5)

j =1

M gj4 = (4.27, 4.51, 5.32) M gj6 = (4.85, 6.5, 5.32)

7

7

∑∑ M i =1 j =1

∑M

j gi

7

∑M j =1 7

∑M j =1

j g3

= (6.57, 8.5, 11.16)

j g5

= (4.25, 5.01, 6.66)

j g7

= (7.38, 10, 13.50)

= (8.5, 11, 13.5) ⊕ (7.5, 10, 12.5) ⊕ (6.57, 8.5, 11.16) ⊕ (4.27, 4.51, 5.32) ⊕ (4.25, 5.01, 6.66) ⊕ (4.85, 6.5, 8.89) ⊕ (7.83, 10, 13.50) = (43.77, 55.52, 71.53)

⎡ 7 ⎢ ⎣⎢ i =1

7

∑∑ j =1

M gji

⎤ ⎥ ⎦⎥

−1

1 1 ⎞ ⎛ 1 =⎜ , , ⎟ = (0.013, 0.018, 0.022) ⎝ 71.53 55.52 43.77 ⎠

Managerial capabilities: M 1 = (8.5, 11, 13.5) ⊕ (0.013, 0.018, 0.022) = (0.11, 0.198, 0.297) Manpower: M 2 = (7.5, 10, 12.5) ⊕ (0.013, 0.018, 0.022) = (0.097, 0.18, 0.275) Marketing: M 3 = (6.57, 8.5, 11.16) ⊕ (0.013, 0.018, 0.022) = (0.085, 0.153, 0.245) Machine: M 4 = (4.27, 4.51, 5.32) ⊕ (0.013, 0.018, 0.022) = (0.055, 0.081, 0.117) Material: M 5 = (4.25, 5.01, 6.66) ⊕ (0.013, 0.018, 0.022) = (0.055, 0.09, 0.146) Method: M 6 = (4.85, 6.5, 8.89) ⊕ (0.013, 0.018, 0.022) = (0.063, 0.117, 0.195) Money: M 7 = (7.83, 10, 13.50) ⊕ (0.013, 0.018, 0.022) = (0.101, 0.18, 0.297).

Step 2

These fuzzy values are compared by using equation (9) and these values are obtained: M 1 = (0.11, 0.198, 0.297) ⎫ ⎬ M 2 = (0.097, 0.18, 0.275) ⎭ V ( M 2 ≥ M1 ) =

0.11 − 0.275 = 0.901 (0.18 − 0.275) − (0.198 − 0.11)

A new approach for supplier selection using fuzzy MCDM V ( M1 ≥ M 2 ) = 1 V ( M1 ≥ M 5 ) = 1 V ( M 2 ≥ M8 ) = 1 V (M2 ≥ M7 ) = 1 V (M3 ≥ M4 ) = 1 V ( M 3 ≥ M 7 ) = 0.842 V ( M 4 ≥ M 3 ) = 0.307 V ( M 4 ≥ M 7 ) = 0.139 V ( M 5 ≥ M 3 ) = 0.491 V ( M 5 ≥ M 7 ) = 0.333 V ( M 6 ≥ M 3 ) = 0.753 V ( M 6 ≥ M 7 ) = 0.598 V (M7 ≥ M3 ) = 1 V ( M 7 ≥ M 6 ) = 1.

Step 3

V ( M1 ≥ M 3 ) = 1 V ( M1 ≥ M 6 ) = 1 V (M2 ≥ M5 ) = 1 V ( M 3 ≥ M 1 ) = 0.75 V (M3 ≥ M5 ) = 1 V ( M 4 ≥ M 1 ) = 0.56 V ( M 4 ≥ M 5 ) = 0.873 V ( M 5 ≥ M 1 ) = 0.25 V (M5 ≥ M4 ) = 1 V ( M 6 ≥ M 1 ) = 0.59 V (M6 ≥ M4 ) = 1 V ( M 7 ≥ M 1 ) = 0.912 V (M7 ≥ M4 ) = 1

V ( M1 ≥ M 4 ) = 1 V ( M1 ≥ M 7 ) = 1 V (M2 ≥ M6 ) = 1 V ( M 3 ≥ M 2 ) = 0.845 V (M3 ≥ M6 ) = 1 V ( M 4 ≥ M 2 ) = 0.168 V ( M 4 ≥ M 6 ) = 0.6 V ( M 5 ≥ M 2 ) = 0.325 V ( M 5 ≥ M 6 ) = 0.754 V ( M 6 ≥ M 2 ) = 0.608 V (M6 ≥ M5 ) = 1 V (M7 ≥ M2 ) = 1 V (M7 ≥ M5 ) = 1

Then priority weights are calculated by using equation (10):

(VM1 ≥ M 2 , M 3 , M 4 , M 5 , M 6 , M 7 ) = min (V ( M1 ≥ M 2 ) , V ( M1 ≥ M 3 ) , V ( M1 ≥ M 4 ) , V ( M1 ≥ M 5 ) , V ( M1 ≥ M 6 ) , V ( M1 ≥ M 7 ) ) = 1 V ( M 2 ≥ M 1 , M 3 , M 4 , M 5 , M 6 , M 7 ) = 0.901 V ( M 3 ≥ M 1 , M 2 , M 4 , M 5 , M 6 , M 7 ) = 0.79 V ( M 4 ≥ M 1 , M 2 , M 3 , M 5 , M 6 , M 7 ) = 0.139 V ( M 5 ≥ M 1 , M 2 , M 3 , M 4 , M 6 , M 7 ) = 0.25 V ( M 6 ≥ M 1 , M 2 , M 3 , M 4 , M 5 , M 7 ) = 0.59 V ( M 7 ≥ M 1 , M 2 , M 3 , M 4 , M 5 , M 6 ) = 0.912 W ′ = (1, 0.901, 0.75, 0.139, 0.25, 0.59, 0.912).

Step 4

After the normalisation of these values priority weights with respect to main goal are calculated as:

M3 M4 M5 M6 M7 ⎞ ⎛ M1 M 2 W =⎜ , , , , , , ⎟. ⎝ 0.22 0.198 0.165 0.03 0.05 0.129 0.2 ⎠ Then, weights of sub-criteria are calculated similarly. Final weights of sub-criteria for supplier A are shown in Table 3. The final result of other suppliers presented in Tables 4, 5, 6, and 7 respectively.

103

Controlling (0.11)

Commitment (0.10)

Staffing (0.07)

6

Directing (0.19)

3

5

Organising (0.22)

2

4

Planning (0.31)

Management (0.22)

1

Money (0.2)

Fixed assets (0.10)

Current assets (0.12)

Reputation (0.33)

Product tech (0.45)

Packaging (0.11)

Promotion (0.15)

Place (0.18)

Price (0.25)

Plan (0.31)

Marketing (0.165)

Age (0.08)

Motivation (0.12)

Education (0.35)

Skill (0.16)

Experience (0.29)

Manpower (0.198)

Method (0.129)

Technoware (0.20)

Hardware (0.23)

Infoware (0.25)

Orgaware (0.32)

Material price (0.25)

Delivery time (0.21)

Quality (0.35)

Supply (0.36)

Material (0.05)

Machine (0.03)

Precise (0.05)

Usability (0.10)

Technology (0.2)

Capacity (0.30)

Efficiency (0.35)

Table 3

Rank

104 R. Rostamzadeh

Final weights of criteria and sub-criteria for supplier A using FAHP

Planning (0.25)

Organising (0.22)

Directing (0.15)

Controlling (0.14)

Commitment (0.13)

Staffing (0.11)

2

3

4

5

6

Management (0.31)

1

Money (0.27)

Fixed assets (0.14)


Product tech (0.3)

Reputation (0.38)

Marketing (0.15)

Packaging (0.07)

Place (0.15)

Price (0.25)

Plan (0.28)

Promotion (0.35)

Manpower (0.12)

Age (0.15)

Motivation (0.18)

Education (0.2)

Skill (0.22)

Experience (0.25)

Method (0.07)

Hardware (0.15)

Orgaware (0.25)

Infoware (0.27)

Technoware (0.33)

Material (0.05)


Supply (0.28)

Quality (0.3)


Machine (0.03)

Usability (0.14)

Precise (0.11)

Technology (0.2)

Capacity (0.25)

Efficiency (0.3)

Table 4

Rank

A new approach for supplier selection using fuzzy MCDM Final weights of criteria and sub-criteria for supplier B using FAHP

105

Directing (0.17)

Controlling (0.15)

Commitment (0.11)

Staffing (0.08)

4

5

6

2

3

Planning (0.29)

Organising (0.2)

1

Management (0.33)

Fixed assets (0.1)


Reputation (0.36)

Product tech (0.41)

Money (0.25)

Packaging (0.11)

Promotion (0.15)

Place (0.18)

Price (0.25)

Plan (0.31)

Marketing (0.15)

Age (0.09)

Education (0.15)

Motivation (0.18)

Experience (0.26)

Skill (0.32)

Manpower (0.10)

Technoware (0.15)

Hardware (0.2)

Infoware (0.3)

Orgaware (0.35)

Method (0.07)



Quality (0.3)

Supply (0.39)

Material (0.06)

Precise (0.07)

Usability (0.14)

Capacity (0.15)

Technology(0.29)

Efficiency (0.35)

Machine (0.04)

Table 5

Rank

106 R. Rostamzadeh

Final weights of criteria and sub-criteria for supplier C using FAHP

Controlling (0.13)

Commitment (0.12)

Staffing (0.11)

6

3

5

Directing (0.15)

2

4

Planning (0.27)

Organising (0.21)

1

Management (0.25)

Fixed assets (0.08)


Reputation (0.38)

Product tech (0.42

Money (0.23)

Packaging (0.1)

Place (0.14)

Price (0.21)

Promotion (0.26)

Plan (0.29)

Marketing (0.2)

Age (0.04)

Motivation (0.1)

Education (0.25)

Skill (0.29)

Experience (0.32)

Manpower (0.14)

Technoware (0.16)

Hardware (0.2)

Infoware (0.23)

Orgaware (0.41)

Method (0.08)


Quality (0.2)

Supply (0.33)


Material (0.06)

Precise (0.09)

Usability (0.12)

Technology (0.18)

Capacity (0.29)

Efficiency (0.32)

Machine (0.04)

Table 6

Rank

A new approach for supplier selection using fuzzy MCDM Final weights of criteria and sub-criteria for supplier D using FAHP

107

Controlling (0.16)

Commitment (0.13)

Staffing (0.06)

6

Directing (0.18)

3

5

Organising (0.23)

2

4

Planning (0.24)

Management (0.27)

1

Money (0.2)

Fixed assets (0.13)


Reputation (0.28)

Product tech (0.29)

Packaging (0.11)

Promotion (0.18)

Place (0.2)

Price (0.24)

Plan (0.27)

Marketing (0.16)

Manpower (0.15)

Age (0.08)

Motivation (0.12)

Education (0.35)

Skill (0.16)

Experience (0.29)

Method (0.1)

Technoware (0.1)

Hardware (0.2)

Infoware (0.32)

Orgaware (0.38)


Delivery time (0.2)

Quality (0.31)

Supply (0.33)

Material (0.08)

Machine (0.04)

Precise (0.1)

Usability (0.12)

Technology (0.21)

Capacity (0.27)

Efficiency (0.3)

Table 7

Rank

108 R. Rostamzadeh

Final weights of criteria and sub-criteria for supplier E using FAHP


109

4.2 Application of TOPSIS In this stage researcher has been used TOPSIS for ranking the criteria and sub-criteria. For this reason researchers have grouped the managers and analysts of the company. Decision makers from different backgrounds may define different weight vectors. They usually cause not only the imprecise evaluation but also serious persecution during the decision process. The linguistic evaluation is shown in Table 8. Also, Table 9 shows the decision matrix provided by the managers of the company for the final ranking of the suppliers. Then the normalised decision matrix and weighted normalised decision matrix are constructed. Table 8

Linguistic variables for the criteria weights

Very low (VL)

1

Low (L)

3

Medium (M)

5

High (H)

7

Very high (VH)

9

Table 9

Importance weight of criteria from decision-maker

Criteria Decision-maker

W

M1

M2

M3

M4

M5

M6

M7

Supplier A

9

5

7

1

3

5

9

Supplier B

7

7

7

3

5

7

7

Supplier C

9

5

7

5

5

3

7

Supplier D

7

5

5

1

3

5

7

Supplier E

7

7

5

3

5

5

5

0.276

0.141

0.165

0.036

0.06

0.089

0.184

After normalising via equation (14), R will be obtained. ⎡ 0.511 0.38 0.498 0.149 0.311 ⎢ 0.398 0.532 0.498 0.447 0.518 ⎢ R = ⎢ 0.511 0.38 0.498 0.74 0.518 ⎢ ⎢ 0.398 0.38 0.356 0.149 0.31 ⎢⎣ 0.398 0.532 0.356 0.477 0.518

0.433 0.565 ⎤ 0.606 0.44 ⎥⎥ 0.26 0.44 ⎥ ⎥ 0.433 0.44 ⎥ 0.433 0.314 ⎥⎦

The weights that we obtained from FAHP were used to calculate the weighted decision matrix V. Therefore, weighted normalised decision matrix was formed by equation (15): ⎡ 0.141 ⎢ 0.109 ⎢ V = ⎢ 0.141 ⎢ ⎢ 0.109 ⎢⎣ 0.109

0.053 0.082 0.005 0.018 0.038 0.103 ⎤ 0.08 ⎥⎥ 0.053 0.082 0.026 0.031 0.023 0.08 ⎥ ⎥ 0.053 0.058 0.005 0.018 0.038 0.08 ⎥ 0.075 0.058 0.016 0.031 0.038 0.057 ⎥⎦ 0.075 0.082 0.016 0.031 0.053

110

R. Rostamzadeh

Then the PIS and the NIS will be determined by equations (16) and (17): A+ = {0.141, 0.075, 0.082, 0.026, 0.031, 0.053, 0.103} A− = {0.109, 0.053, 0.058, 0.005, 0.018, 0.023, 0.057}

The distance of each alternative from PIS and NIS were calculated through equations (18) and (19).

d1+ = 0.036 d 2+ = 0.04 d3+ = 0.043 d 4+ = 0.058 d5+ = 0.063 d1− = 0.062 d 2− = 0.053 d3− = 0.052 d 4− = 0.027 d5− = 0.031

The closeness coefficients of each alternative were calculated by equation (20): C1+ =

d1+

d1− 0.062 = = 0.632, + d1− 0.036 + 0.062

0.053 = 0.569, 0.04 + 0.053 0.052 C3+ = 0.547, 0.043 + 0.052 0.027 C4+ = = 0.317, 0.058 + 0.027 0.031 C5+ = = 0.329 0.063 + 0.031 C2+ =

Comparing CCi values, the ranking of suppliers were determined as follows: Supplier A > Supplier B > Supplier C > Supplier E > Supplier D.

5

Conclusions and managerial implications

Most supplier selection decisions are made today in increasingly complex environments where the theory of fuzzy decision making can be of significant use. This paper applied an approach based on the FAHP and TOPSIS for prioritising proposed criteria to supplier selections. In this research, FAHP used for finding weights of 7Ms and its sub-criteria. At the first level there is a main goal which is supplier selection, at second level seven criteria and at third level 32 sub-criteria are located in seven groups. In determining the final weights of criteria and sub-criteria, FAHP and for the final rank of the suppliers, TOPSIS method was used and finally supplier A with (0.63) got the first rank, supplier B (0.56), supplier C (0.54), supplier E (0.32) and supplier D (0.31) received the ranks consequently. Considering the research process and its findings can be pointed out these items: By taking into account of meaning and concept of each criteria which demonstrates the situation of the organisational unit (manufacturing or service), from the viewpoint of managers and analysts of the company, the most important degree has been allocated to managerial capabilities. In the next levels money, marketing, manpower, methods, material and machines have placed. The main criteria in all the suppliers resulted it the


111

same rank. It is true that differences can be seen in some of the sub-criteria but in most cases the rankings and results are the same. In management groups, the most important degree has been allocated to planning (SA: 0.311, SB: 0.25, SC: 0.29, SD: 0.27, SE: 0.24) and the lowest important degree to staffing (SA: 0.07, SB: 0.11, SC: 0.08, SD: 0.11, SE: 0.06). In money groups, the most important degree has been allocated to product technology (SA: 0.45, SC: 0.41, SD: 0.42, SE: 0.29, SB: 0.38 in reputation) and the lowest important degree to fix assets (SA: 0.1, AB:0.14, SC: 0.1, SD: 0.08, SE: 0.13). In marketing groups, the most important degree has been allocated to plan (SA: 0.31, SC: 0.31, SD: 0.29, SE: 0.27, SB: 0.35 in promotion) and the lowest important degree in packaging (SA: 0.11, SB: 0.07, SC: 0.11, SD: 0.1, SE: 0.11). In manpower groups, the most important degree has been allocated to experience (SA: 0.29, SB: 0.25, SD: 0.32, SE: 0.29, SC: 0.32 in skill) and the lowest important degree to the age (SA: 0.08, SB: 0.15, SC: 0.09, SD: 0.04, SE: 0.08). In methods groups, the most important degree has been allocated to the orgaware (SA: 0.32, SC: 0.35, SD: 0.41, SE: 0.38, SB: 0.33 in the technoware) and the lowest important degree to the technoware (SA: 0.2, SC: 0.15, SD: 0.16, SE: 0.1, SB: 0.15 in hardware). In material groups, the most important degree has been allocated to the supply (SA: 0.36, SC: 0.39, SE: 0.33 and SB: 0.38, SD: 0.35 in material price) and the lowest important degree to the material price (SA: 0.25, SC; 0.1, SE: 0.16 and SB: 0.04, SD: 0.12 in delivery time). In machines groups, the most important degree has been allocated to the efficiency (SA: 0.35, SB: 0.3, SC: 0.35, SD: 0.32, SE: 0.3) and the lowest important degree to the precise (S0.05, SC: 0.07, SD: 0.09, SE: 0.1 and SB: 0.14 in usability). Since the human decision-making process usually contains fuzziness and vagueness, so the FAHP is adopted to solve the problem. According to the closeness coefficient, we can determine not only the ranking but also the assessment status of all possible decisionmakers. Therefore the researchers used TOPSIS method for the final ranking of suppliers. TOPSIS method can deal with the ratings of both quantitative as well as qualitative criteria. It appears from the foregoing sections that TOPSIS method is a useful additional tool for the problem. Although the above mentioned approaches can deal with multiple criteria, but in reality, the weightings of supplier evaluating criteria depend a lot on business priorities and strategies. In cases where the weightings are assigned arbitrarily and subjectively without considering the voice of company stakeholders, the suppliers selected may not provide what the company exactly wants. Combining AHP and QFD in fuzzy environment should be developed to select a supplier strategically. The proposed 7Ms in this paper can be easily applied for other managerial application and other multi-attribute evaluation methods such as PROMETHEE, ELECTRE and DEA with slight modification.

Acknowledgements The author would like to deeply thank the anonymous referees for their valuable comments and Editor-in-Chief, Professor Angappa Gunasekaran.

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