Elsevier

Information Sciences

Volume 178, Issue 21, 1 November 2008, Pages 4166-4183
Information Sciences

Vendor selection by integrated fuzzy MCDM techniques with independent and interdependent relationships

https://doi.org/10.1016/j.ins.2008.06.003Get rights and content

Abstract

Vendor selection is an evaluation process that is based on many criteria that uses inaccurate or uncertain data. But while the criteria are often numerous and the relationships between higher-level criteria and lower-level sub-criteria are complex, most conventional decision models cannot help us clarify the interrelationships among the sub-criteria. Our proposed integrated fuzzy multiple criteria decision making (MCDM) method addresses this issue within the context of the vendor selection problem. First, we use triangular fuzzy numbers to express the subjective preferences of evaluators. Second, we use interpretive structural modeling (ISM) to map out the relationships among the sub-criteria. Third, we use the fuzzy analytical hierarchy process (AHP) method to compute the relative weights for each criterion, and we use non-additive fuzzy integral to obtain the fuzzy synthetic performance of each common criterion. Fourth, the best vendor is determined according to the overall aggregating score of each vendor using the fuzzy weights with fuzzy synthetic utilities. Fifth, we use an empirical example to show that our proposed method is preferred to the traditional method, especially when the sub-criteria are interdependent. Finally, our results provide valuable suggestions to vendors on how to improve each sub-criterion so that they can bridge the gap between actual and aspired performance values in the future.

Introduction

In today’s highly competitive environment, it is impossible for a company to successfully produce low-cost, high-quality products without satisfactory vendors. The selection of appropriate vendors has long been one of the most important functions of any company’s purchasing department. The vendor selection problem is an unstructured, complicated, and multi-criteria decision problem. Over the past two decades, many studies have pointed out that the key is to set effective evaluation criteria for the vendor selection problem (VSP). Earlier works on vendor selection identified 23 criteria (i.e., price, delivery, quality etc.) for evaluating and selecting appropriate vendors and for deciding on the size of the order to be placed with each vendor [13]. In 47 out of 76 articles, vendor selection used more than one criterion (i.e., multi-criteria) [39].

A vendor selection problem usually involves more than one criterion, and criteria often conflict with each other. In multiple criteria decision making (MCDM), it is usually assumed that the criteria are independent. A considerable number of decision models have been developed based on the MCDM theory, such as preference ranking organization method (PROMETHEE) [2], analytical hierarchy process (AHP) [27], [17], discrete choice analysis (DCA) [35], total cost ownership (TCO) [12], and data envelopment analysis (DEA) [40], [26]. However, in real life the available information in a MCDM process is usually uncertain, vague, or imprecise, and the criteria are not necessarily independent. To tackle the vagueness in information and the essential fuzziness of human judgment/preference, fuzzy set theory was proposed by Zadeh in 1965 [42], and a decision making method in a fuzzy environment was developed by Bellman and Zadeh [1].

A number of subsequent studies used fuzzy set theory to deal with uncertainty in the vendor selection problem. Holt [19] applied seven decision methods to contractor selection. The design process pointed out the advantages and disadvantages in the vendor selection model by Morlacchi in 1999 [25]. De Boer et al. [11] provided a comprehensive review of the literature concerning supplier selection. In these papers, fuzzy set theory was suggested as a way to improve upon the vendor selection problem. Mikhailov [24] proposed the fuzzy AHP method to determine the weight of each criterion and to score each alternative for each criterion. Kumar et al. [22] presented a fuzzy goal programming approach to solve the vendor selection problem with three objectives. In order to select a suitable partner for strategic alliance, fuzzy set theory can also be used to analyze a multiplicity of complex criteria in an MCDM environment [14]. Moreover, Shyur and Shih [30] developed a hybrid MCDM method for strategic vendor selection by using both the ANP and TOPSIS techniques. In order to solve the measurement of qualitative items, an approach was developed using both quantitative and qualitative data for supplier selection [16]. In sum, fuzzy set theory is useful when the purchase situation is full of uncertainty and imprecision due to the subjectivity of human judgment. Likewise, we will use fuzzy set theory in this paper.

An MCDM problem consists of five basic elements: alternatives, criteria, outcomes, preferences, and information (see Table 1). The multiple criteria decision issue focuses mainly on the identification of the evaluation criteria and on the determination of the preference structure (i.e., weights) [33]. Previous researches on the identification of evaluation criteria in vendor selection have usually focused on products, services, and purchase situations [39], [15]. However, there are often too many evaluation criteria in complex problems to determine whether these criteria are dependent on or independent to each other. One solution is to divide a complex system into groups of sub-criteria. We can then use interpretive structural modeling (ISM) to measure the interrelationship among sub-criteria more easily [36], [37], [38]. ISM is based on Boolean operations of one-to-one correspondence between a binary matrix and a graphical representation of a directed network. It is used to help identify the structural relationships among criteria in a system [23]. Here we use ISM to help us build a structural relation map to identify the independence or dependence of the sub-criteria of a criterion. We can then combine MCDM techniques with additive and non-additive models to evaluate vendors.

Furthermore, the weights represent general forms used to represent the preference structure of a decision maker. If the importance of a criterion can be properly captured through the weights, the quality of the decision making will be enhanced. Normally, the methods used to demonstrate the importance of criteria often assume additive weights and independence among criteria. But an additive model is not always suitable due to the varying degrees of interactions among the criteria. Also, decision makers may simply regard the criteria as dependent so that inevitably the decision criteria are correlated to each other. On the other hand, the fuzzy integral model does not need to assume independence among criteria, and it can be used in nonlinear situations. This is why we use the Sugeno integral for λ fuzzy measure and use a non-additive (‘super-additive’) fuzzy integral technique [31], [21] to evaluate the synthetic performance of alternatives. These methods have been successfully applied in various circumstances [18], [5], [6], [7], [8], [32], [34].

We then use AHP [29] to determine the fuzzy weight of each independent criterion. However, fuzzy numbers must first be defuzzified into BNP numbers before they can be used for comparison. Thus, the defuzzification of the fuzzy weight of a criterion is done by calculating the best nonfuzzy performance (BNP) value of the final weights. The three most common defuzzification methods are mean of maximal, Center of Area (COA), and the α-cut methods [43], [41], [28]. But the COA method is simple and does not need to introduce the preferences of any evaluators. So we choose the COA method to transform our fuzzy weights into BNP weights. Finally, the overall score and ranking of each vendor will determine the choice of the best vendor.

We have shown that the MCDM process, particularly in a fuzzy environment, can be used to achieve the goals of practicality, accuracy, and objectivity. Our proposed method establishes an integrated fuzzy MCDM method that incorporates interrelationship and synthetic utility among the sub-criteria of a criterion within the context of the vendor selection problem. This paper is different from previously research in three ways. First, we adopt ISM to build to clarify the interrelations among the sub-criteria of a criterion. Second, we use Sugeno’s fuzzy integral with fuzzy measures, a non-additive method, to calculate the synthetic utility of the weights of the interactive sub-criteria Third, the weights of each criteria can be determined using the fuzzy AHP method. And fourth, the resulting fuzzy weights of each criterion can be defuzzified using the COA method. Finally, once we obtain the overall scores for the criteria of each vendor, we can select the best vendor.

As an empirical example, we use our integrated fuzzy MCDM method to evaluate the performance of the vendors for a well-known high-tech manufacturing company in Taiwan. We show that our proposed method is an effective way for selecting an appropriate vendor, especially when there are interdependent sub-criteria in a complex hierarchy of evaluation criteria.

The rest of this paper is organized as follows. In Section 2, problems in a fuzzy environment are discussed in detail. In Section 3, some fundamentals associated with the proposed approach are addressed. In Section 4, an empirical study of the vendor selection problem in Taiwan is presented to show our proposed method. Our results are discussed and compared with those obtained using the simple additive weight (SAW) method. In Section 5, we conclude this paper with some suggestions for future research.

Section snippets

The vendor selection problem in a fuzzy MCDM environment

Vendor selection has a significant impact on a company’s competitive priorities, such as price, quality, delivery, supporting services, and innovation. The decision making process is complex and usually involves vague information. This is why we study the vendor selection problem in the context of a fuzzy MCDM environment. To achieve a company’s purchasing objective, the vendor selection problem may involve m candidate vendors, each denoted by Vj where j = 1,  , m, from which the best vendor is

Some fundamentals of the integrated fuzzy MCDM method

In this section, some important fundamentals that are used in the proposed method (see Section 4) are addressed. These fundamentals include the methodology used to clarify the interrelationships among the sub-criteria of a criterion, the concept of determining the fuzzy weight for each criterion, and the principle of calculating the synthetic utility with the interactive sub-criteria.

An example of a vendor selection problem in Taiwan

In this section, we use an empirical example of a vendor selection decision to demonstrate that the integrated fuzzy MCDM technique is more appropriate than the traditional method, especially when sub-criteria are interrelated. This section is divided into four subsections: (1) problem descriptions, (2) data collection via questionnaires, (3) results and analyses, and (4) discussions.

Conclusion

Vendor selection is a very complicated multiple criteria problem. The information available for use in multiple criteria decision making is usually uncertain, vague, or imprecise, and the criteria are not necessarily independent. In addition, if a criterion were to contain additional sub-criteria, there would be a stronger possibility of correlation among sub-criteria. However, traditional MCDM methods are based on the assumption of independence among sub-criteria, and the analytical framework

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