It is well recognized that suppliers play a crucial role in the production chain and hence in the long term viability of a company. Close working relationships with high performing suppliers are essential in modern production environments. Just-in-time, total quality management, and flexible manufacturing systems have become part of the standard vocabulary in management theory. Supplier selection decisions are an important component of production and logistics management for many firms. Such decisions entail the selection of individual suppliers to employ, and the determination of order quantities to be placed with the selected suppliers. Selecting right suppliers significantly reduces the material purchasing cost and improves corporate competitiveness, which is why many experts believe that the supplier selection is the most important activity of a purchasing department (2005).
Supplier selection is one of the most critical activities of purchasing management in a supply chain, because of the key role of supplier’s performance on cost, quality, delivery and service in achieving the objectives of a supply chain. With increasingly competitive global world markets, companies are under intense pressure to find ways to cut production and material costs to survive and sustain their competitive position in their respective markets. Therefore, an efficient supplier selection process and evaluation of supplier performance are becoming major challenges faced by the manufacturing and purchasing, it needs to be in place and of significant importance for successful supply chain management.
Usually, quality is a critical concern for most manufacturers while purchasing materials. The need of high-quality suppliers has always been an important issue for many manufacturing organizations (1991). With reference to Dickson (1966), quality and delivery are two of the most demanded items by component suppliers. Similarly, Weber, Current, and Benton (1991) considered quality to be of “extreme importance” and delivery to be of “considerable importance”. In additions, Weber’s research on the Just-In-Time (JIT) model, the importance of quality and delivery remains the same. In another study, Pearson and Ellram (1995) surveyed 210 members of the National Association of purchasing management (NAPM), they were randomly selected from the listings of electronic firms, 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. Additionally, there are many researchers studied about the supplier selection topic in the past period. Table 1 summarizes the results from various papers. Obviously, quality can be regarded as a fundamental factor for supplier evaluation among various criteria.
Table 1.
Attributes for supplier selection.
No. Researcher Attributes for supplier selection
1 Gregory (1986) Quality, production plan and control system, amount of past business, purchasing item, price
2 Wagner, Ettenson, and Parrish (1989) Quality is the most important, the second one is delivery, the last one is cost
3 Pacheco (1989) Customer service, product quality, service, delivery, the quality of clerk
4 Houshyar and David (1992) Price, quality, delivery, transportation cost
5 Chaudhry, Forst, and Zydiak (1993) Quality, delivery, price, capacity
6 Lau and Lau (1994) Quality, lead time, price
7 Anderson (1994) Financial status, product quality, geographical location, inventory, facility layout, administration management, technical capability, delivery
8 Wilson (1994) Quality, service, delivery, price
9 Benion and Redmond (1994) Product characteristic is more important then service, supporting, and quality
10 Pearson and Ellram (1995) Quality and cost are the most important. Then goes for supplier design and technical capability
11 Swift (1995) To emphasis on price, product quality. Under single source circumstance, it is needed to evaluate technical supporting from supplier and the reliability of product
12 Patton (1996) Price, quality, delivery, service, equipment & technical, company’s financial status
13 Lambert, Ronald, and Margaret (1997) The most important attributes are including quality, delivery, and service
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Much evidence suggest that high quality has a positive impact upon significantly increasing profitability, through lowing operating costs and improving market share (Chen and Chen, 2009, Garvin, 1988, Maani, 1989, Phillips et al., 1983 and Voehl et al., 1994). Kane (1986) stated that the quantification of the process mean (μ) and variation (σ2)(σ2) is essential to understand the quality of the units produced from a manufacturing process. Taguchi emphasized the loss occurred in a product’s worth when its key quality characteristic deviates from the customers’ target τ=(USL+LSL)/2τ=(USL+LSL)/2, where USL and LSL stand for the upper and lower specification limits, respectively, and the values of USL and LSL are determined by decision-makers. In order to take into account these basic parameters that have been widely used to measure the manufacturing processes performance or supplier potentials, Hsiang and Taguchi (1985) introduced CpmCpm index defined as
equation(1)
View the MathML sourceCpm=USL-LSL6σ2+(μ-τ)2,
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sometimes called the Taguchi index or loss-based capability. Table 1 lists the various values of CpmCpm and its corresponding maximum possible nonconformities in parts per million (PPM). The value of CpmCpm is varied from the lower value of 1.00 to the upper value of 2.00 with increments of 0.05 at each step. For example, if a process has capability with Cpm⩾1.2Cpm⩾1.2, then the production yield would be at least 99.968%. In other words, the number of the nonconformities is less than 318.2 PPM.
CpmCpm PPM CpmCpm PPM CpmCpm PPM CpmCpm PPM
0.95 4371.923 1.30 96.193 1.55 3.319 1.80 0.067
1.00 2699.796 1.35 51.218 1.60 1.587 1.85 0.029
1.10 966.848 1.40 26.691 1.65 0.742 1.90 0.012
1.20 318.217 1.45 13.614 1.70 0.340 1.95 0.005
1.25 176.835 1.50 6.795 1.75 0.152 2.00 0.002
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It is natural to investigate the problem of supplier selection and evaluation for the cases with View the MathML sourceq(q⩾2) candidate suppliers based on the CpmCpm index. Let PiPi be the population of supplier i with the mean μiμi and variance View the MathML sourceσi2 for i=1,2,…,qi=1,2,…,q. The capability index CpmiCpmi of supplier i can be defined as follows:
equation(2)
View the MathML sourceCpmi=USL-LSL6σi2+(μi-τi)2
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for i=1,2,…,qi=1,2,…,q.
Conceptually, in evaluating a group of suppliers, the assessment requires knowledge of μiμi and σiσi of each supplier in Eq. (2). However, μiμi and σiσi usually unknown for i=1,2,…,qi=1,2,…,q. In this case, the sample data must be collected from each supplier which is in order to estimate the value of index CpmiCpmi and to assess/select the appropriate suppliers. Let xi1,xi2,…,xinixi1,xi2,…,xini be the independent random samples from Pi for i=1,2,…,qi=1,2,…,q. Generally, continuous data obtained from the output responses of supplier’s key quality characteristics are always assumed to be real numbers as in the studies by Prasad and Calis, 1999, Shiau et al., 1999, Zimmer et al., 2001, Pearn and Shu, 2003 and Xekalaki and Perakis, 2004 and Hsu and Shu (2008). In this assumption, the statistical point estimate View the MathML sourcecˆpmi of CpmiCpmi is given as
equation(3)
View the MathML sourcecˆpmi=USL-LSL6si2+(x¯i-τ)2,
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where the process mean μiμi in Eq. (2) is switched by the sample mean View the MathML sourcex¯i that is given by
View the MathML sourcex¯i=1ni∑j=1nixij
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and the process standard deviation σiσi in Eq. (2) is replaced by the sample standard deviation sisi that is given by
View the MathML sourcesi=1ni∑j=1ni(xij-x¯i)21/2
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for i=1,2,…,qi=1,2,…,q.
In a practical situation, the output continuous quantities collected from key quality characteristics of suppliers’ products always appear to be somewhat imprecise manner. For example, the data may be given by color intensity 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 come from the insufficient sample data such as the observations made with coarse scales, linguistic data, or data collected with vague and incomplete knowledge, as described by Sugano, 2006, Gulbay and Kahraman, 2007, Zhang and Chu, 2009 and Lee, 2009. In the other study, Hong, 2004 and Lee, 2001 proposed an estimation of single yield-based index by considering fuzzy numbers when the measurement refers to the decision-making’s subjective determination. Since supplier selection problems is usually involved with preferences which are often vague and imprecise. In this paper, we propose a method for the selection and evaluation of supplier using fuzzy data.
The paper is organized as follows. In Section 2, we introduce the basic properties of fuzzy numbers. In Section 3, the fuzzy estimate of CpmiCpmi for each supplier is expressed by using fuzzy data. To obtain the membership function of fuzzy estimate of each supplier, the resolution identity theorem is applied and the membership degree can be obtained by solving optimization problems. In Section 4, we provide a ranking method proposed by Yuan (1991) to sort the fuzzy estimates of CpmiCpmi, which makes decision-makers being capable of selecting the preferable suppliers. In Section 5, we demonstrate the application of the proposed methodology to supplier selection and evaluation using fuzzy data. In Section 6, the conclusions are presented.
