ارزیابی و انتخاب تامین کننده بر اساس کیفیت با استفاده از داده های فازی

Since fuzzy quality data are ubiquitous in the real world, under this fuzzy environment, the supplier selection and evaluation on the basis of the quality criterion is proposed in this paper. The CpkCpk index has been the most popular one used to evaluate the quality of supplier’s products. Using fuzzy data collected from q⩾2q⩾2 possible suppliers’ products, fuzzy estimates of q suppliers’ capability indices View the MathML sourceCpki(i=1,2,…,q) are obtained according to the form of resolution identity that is a well-known theorem in fuzzy sets theory. Certain optimization problems are formulated and solved to obtain αα-level sets for the purpose of constructing the membership functions of fuzzy estimates of CpkiCpki. These membership functions are sorted by using a fuzzy ranking method to choose the preferable suppliers. Finally, a numerical example is illustrated to present the possible application by incorporating fuzzy data into the quality-based supplier selection and evaluation.

Nowadays rising customers’ expectations as well as increasing the product quality are becoming an important strategic priority in the pretty competitive global business environment. Manufacturers must produce the correct products at the accurate time and deliver them promptly to customers to sustain their competitive advantage in the marketplace (Hensler, 1994 and Hutt and Speh, 2006). Manufacturers increasingly purchase components from suppliers or hire contract manufacturers to produce necessary parts, and they assemble these parts to deliver finished products to customers. In the automotive industry, the cost of components and parts purchased from outside vendors have increased up to 50%50% of their revenues (Weber, Current, & Benton, 1991). The high technology firms spend more than 80%80% of total product costs on purchasing materials and services (Burton, 1988 and Carr and Pearson, 1999). Obviously, the quality of parts obtained from suppliers determines the quality of the finished products produced by manufacturers as well as the customers’ satisfaction and loyalty. Therefore, the evaluation of supplier performance and selection of suppliers are becoming major challenges faced by the manufacturing and purchasing managers (ASQC, 1981). Assessing a group of suppliers and selecting one or more of them are a complex task because various criteria must be considered in the decision-making process such as quality, cost, goodwill, service, delivery time, and environmental impact (Humphreys, Wong, & Chan, 2003). According to research conducted by Dickson (1966), quality and delivery are two of the most demanded items by component suppliers. Twenty five years after Dickson’s research, Weber et al. (1991) still considered quality to be of “extreme importance” and delivery to be of “considerable importance”. According to Weber’s research on the Just-In-Time (JIT) model, the importance of quality and delivery remains the same. Pearson and Ellram (1995) surveyed 210 members of the National Association of Purchasing Management (NAPM), who were randomly selected from the listings of electronic firms in the two-digit SIC code 38, and they indicated that quality is the most important criterion in the selection and evaluation of suppliers for both the small and large electronic firms that were surveyed. Moreover, according to the survey of current and potential outsourcing end-users by the Outsourcing Institute (2003), the top 10 factors in vendor selection are commitment to quality, price, reference/reputation, flexible contract terms, scope of resources, additional value-added capability, cultural match, existing relationship, location, and others. Quality is still the most important factor for selecting the preferred suppliers. Furthermore, Olhager and Selldin (2004) investigated the strategies and practices in the supply chain management using the sample of 128 Swedish manufacturing firms, and concluded that many aspects are important when companies choose supply chain partners, but quality is the most important criterion. In other words, based on the above works, quality can be seen as a fundamental factor for supplier evaluation among various criteria. Quality affects the productivity and business performance in both industrial and customers’ organizations. Much evidence suggests that high quality has a positive impact upon significantly increasing profitability, through lowering operating costs and improving market share (Garvin, 1988, Maani, 1989, Phillips et al., 1983 and Voehl et al., 1994). Kane (1986) stated that the quantification of the process mean and variation is central to understanding the quality of the components produced from a manufacturing process. This fact brings a issue of quality-based supplier selection and evaluation by process capability indices (PCIs) into the main focus of this research. The first PCI appearing in the literature was the precision index and it was proposed by Juran, 1974 and Kane, 1986 and defined as equation(1) View the MathML sourceCp=USL-LSL6σ, Turn MathJax on where USL stands for the upper specification limit, LSL stands for the lower specification limit, and σσ stands for the process standard deviation. The index CpCp measures process precision (consistency of quality). However, it does not consider whether the process is centered. By considering the magnitude of process variance as well as the location of process mean, the CpkCpk index is defined as equation(2) View the MathML sourceCpk=minUSL-μ3σ,μ-LSL3σ, Turn MathJax on which has been the most popular one used in the manufacturing industry ( Kane, 1986 and Kotz and Lovelace, 1998). Montgomery (2005) recommended some minimum capability requirements for performing the manufacturing processes under some certain designated quality conditions. For example, Cpk⩾1.33Cpk⩾1.33 is for the existing processes, and Cpk⩾1.50Cpk⩾1.50 is for the new processes. On the other hand, Cpk⩾1.50Cpk⩾1.50 is also for the existing processes on safety, strength, or critical parameter, and Cpk⩾1.67Cpk⩾1.67 is for the new processes on safety, strength, or critical parameter. Finley (1992) also found that the required values on all critical supplier processes are 1.33 or higher, and the CpkCpk values of 1.67 or higher are preferred. Many companies have recently adopted criteria for evaluating their processes that include more stringent process capability. Motorola’s “Six Sigma” program essentially requires the process capability to be at least 2.0 to conform the possible 1.5σ1.5σ process shift ( Harry, 1988). The supplier certifications in the manuals of ISO 9000 and QS-9000 include a detailed procedure in evaluating supplier’s products on the basis of the most well-known CpkCpk index. For a purchasing contract, a minimum value of CpkCpk is usually specified. If the prescribed minimum CpkCpk fails to be met, then the supplier is verified to be incapable. Otherwise, the supplier is evaluated to be capable. Naturally, we can investigate the supplier selection and evaluation for the case with q⩾2q⩾2 candidate suppliers’ products by using the CpkCpk index. Let PiPi be the products population of ith supplier with the mean μiμi and variance View the MathML sourceσi2 where i=1,2,…,qi=1,2,…,q. The capability index CpkiCpki indicated the quality of the ith supplier’s products can be defined as equation(3) View the MathML sourceCpki=minUSL-μi3σi,μi-LSL3σi Turn MathJax on for i=1,…,qi=1,…,q. Conceptually, in evaluating a group of suppliers and further selecting one or more of them, the assessment requires knowledge of μiμi and σiσi obtained from each supplier’s products in Eq. (3). However, the μiμi and σiσi are usually unknown. In this case, to assess the appropriate suppliers, sample data must be collected from suppliers in order to estimate CpkiCpki. Let xi1,xi2,…,xinixi1,xi2,…,xini be independent random samples from PiPi for i=1,2,…,qi=1,2,…,q. Generally, the underlying data obtained from the output responses of each supplier’s products are always assumed to be real numbers. Such a situation, Pearn et al., 1992, Pearn and Shu, 2003 and Prasad and Calis, 1999 have used the statistical point estimate View the MathML sourcecˆpki on CpkiCpki by equation(4) View the MathML sourcecˆpki=minUSL-x¯i3si,x¯i-LSL3si, Turn MathJax on where the mean μiμi in Eq. (3) is substituted by the sample mean View the MathML sourcex¯i View the MathML sourcex¯i=1ni∑j=1nixij Turn MathJax on and the standard deviation σiσi in Eq. (3) is substituted by the sample standard deviation sisi View the MathML sourcesi=1ni-1∑j=1ni(xij-x¯i)21/2 Turn MathJax on for i=1,2,…,qi=1,2,…,q. However, in the practical situations, data collected from the key quality characteristic of suppliers’ products are often somewhat imprecise (fuzzy). For example, the data may be given by color intensity of pictures or by the readings on an analogue measurement equipment, as in the studies of Filzmoser and Vertl, 2004 and Viertl and Hareter, 2004. In addition, the imprecise data may be given by scarce sample data, e.g., the observations made with coarse scales, linguistic data, or data collected with vague and incomplete knowledge, as discussed by Gulbay and Kahraman, 2007 and Sugano, 2006. Lee, 2001 and Hong, 2004 indicated that the measurements partly carried out by the decision-makers subjective determination can also be seen to be fuzzy numbers. In their studies, the estimation of CpkCpk index was proposed using fuzzy data. In this paper, we study the quality-based supplier selection and evaluation using fuzzy data, which was not seriously treated by the researchers. The paper is organized as follows. In Section 2, we introduce the basic properties of fuzzy numbers. In Section 3, we discuss the fuzzy estimate of CpkiCpki by considering fuzzy quality data collected from suppliers. Using the form of resolution identity theorem, the membership function of the fuzzy estimate of CpkiCpki for each supplier is obtained. In order to compute the membership degrees, some optimization problems are formulated. In Section 4, we provide computational methods to solve the optimization problems. In Section 5, to select the preferable suppliers, a ranking method proposed by Yuan (1991) is extended to sort the membership functions of fuzzy estimates of suppliers’ CpkiCpki indices. Finally, we summarize our proposed method in a step-by-step procedure. An application of light emitting diodes (LEDs) is illustrated as an example.

The fuzzy set theory is a useful method for modeling the problems with fuzzy (imprecise) information that has been recognized as one of uncertainties in the real world. The main contribution is that the methodology proposed in this paper is capable of selecting the preferable suppliers using fuzzy quality data, which was not seriously treated by the researchers. With the help of resolution identity theorem which is widely used in fuzzy sets theory, computational methods solving certain optimization problems are proposed to construct membership functions of fuzzy estimates of suppliers’ capability indices CpkiCpki with i=1,2,…,qi=1,2,…,q and q⩾2q⩾2. Moreover, using membership functions View the MathML source{cˆ˜pk1,…,cˆ˜pkq} of q suppliers, a fuzzy ranking method proposed by Yuan (1991) is extended to select the preferable suppliers. A step-by-step procedure is developed and a real example taken from the application of light emitting diodes (LEDs) is illustrated the applicability of our proposed methods. It is well-known that there are numerous process capability indices that are available for supplier selection. Although we choose the index CpkiCpki in this paper, we have to remark that the proposed methodology is still applicable to other indices by solving the similar optimization problems.