یک رویکرد فازی جبرانی برای مشکل انتخاب تامین کننده خطی چندهدفه با چند آیتم

Supplier selection problem is a multi-criteria decision making problem which includes both qualitative and quantitative factors. In the selection process many criteria may conflict with each other, therefore decision-making process becomes complicated. In this paper, we propose a compensatory fuzzy approach to solve multi-objective linear supplier selection problem with multiple-item (MLSSP-MI) by using Werners’ “fuzzy and” (μand) operator. The compromise solutions obtained by using “fuzzy and” (μand) operator are both compensatory and strongly efficient for our MLSSP-MI. To our knowledge, combining compensatory (μand) operator with MLSSP-MI has not been published up to now. Our compensatory fuzzy approach was explained on a case study.

In the context of supply chain management, the supplier selection decision plays a key role. In today’s globally competitive environment; firms give great attention for selecting right suppliers because it helps reduce purchasing costs, improve quality of final products and services, etc. Supplier selection problem is a multi-criteria decision making problem which includes both qualitative and quantitative factors like unit cost, delivery on-time, service quality, etc. In this problem many criteria may conflict with each other, so the selection process becomes complicated and it contains two major problems: (i) which supplier(s) should be chosen? and (ii) how much should be purchased from each selected supplier? These problems encountered in purchasing departments of firms and solving them are very significant. In the last several years, supplier (or vendor) selection problem has gained great importance and is handled by academic researchers and also practitioners in business environment. The literature on this problem exist some researches (i) focused on supplier selection problem criteria, and (ii) proposed methods for supplier selection process. Many researchers identified several criteria for selection process for example Dickson (1966) identified 23 criteria and Dempsey (1978) described 18 criteria. Weber, Current, and Benton (1991) reviewed, annotated and classified 74 related articles which have appeared since 1966 and specific attention is given to the criteria and analytical methods. Weber and Current (1993) presented a multi-objective approach to systematically analyze the inherent tradeoffs involved in multi-criteria supplier selection problems. Barbarosoglu and Yazgac (1997) applied the Analytic Hierarchy Process (AHP) to the supplier selection problem. Ghodsypour and O’Brien (1998) proposed an integration of AHP and linear programming (LP). Karpak, Kumcu, and Kasuganti (1999) used a visual interactive goal programming for supplier selection problem. Ghodsypour and O’Brien (2001) developed a mixed-integer non-linear programming approach to solve the multiple sourcing problem. Erol and ve Ferrell (2003) presented a methodology to assist decision makers in selecting from a finite numbers of alternatives for the problems with multiple conflicting objectives and both qualitative and quantitative criteria. Kumar, Vrat, and Shankar (2006) proposed a fuzzy programming model for vendor selection problem in a supply chain as a “fuzzy multi-objective integer programming vendor selection problem” formulation. Amid, Ghodsypour, and O’Brien (2006) developed a fuzzy multi-objective linear model to overcome the vagueness of the information for supplier selection in a supply chain. Demirtas and Üstün (2008) proposed an integrated approach of Analytic Network Process (ANP) and multi-objective mixed integer linear programming for choosing the best suppliers. Wang, Cheng, and Huang (2009) proposed a fuzzy hierarchical TOPSIS method for supplier selection which simplifies Chen and Cheng (2005)’s metric distance method and proposes an algorithm to modify Chen (2000)’s fuzzy TOPSIS. In this paper, we propose a compensatory fuzzy approach to solve MLSSP-MI by using Werners’ “fuzzy and” (μand) operator. The compromise solutions set obtained by using “fuzzy and” (μand) operator is both compensatory and strongly efficient (Pareto-optimal) for our MLSSP-MI. The paper is organized as follows: Section 2 summarizes the compensatory fuzzy aggregation operators, Section 3 presents the multiple-objective linear supplier selection model, Section 4 explains our methodology using Werners’ compensatory “fuzzy and’’ operator to multi-objective linear supplier selection with multiple-item. Furthermore, giving a theorem and proof, we show that the solutions generated by Werners’ compensatory “fuzzy and” operator do guarantee Pareto-optimality for our problem. Section 5 gives an illustrative numerical example in order to demonstrate the feasibility and efficiency of the proposed method using “fuzzy and’’ operator. Finally Section 6 draws some general conclusions.

In this study, our main objective was to give a compensatory fuzzy method for MLSSP-MI problem to select suppliers for each product and determine how much should be purchased from each selected supplier. In the literature, there are several researches which are handling supplier selection problem with many applications. Researchers mostly used Zimmermann’s min operator for multi-objective supplier selection problem. However, it is known that this operator does not guarantee to generate the strongly-efficient solutions. In this paper, we gave a compensatory method using Werners’ “fuzzy and” operator to solve MLSSP-MI. This operator enables us to search the strongly-efficient solutions, by depending on compensation parameter γ which reflects the decision maker’s preferences. And we gave a theorem and proof that the compensatory solution generated by this operator does guarantee strongly efficiency for our MLSSP-MI. To our knowledge, combining compensatory (μand) operator with MLSSP-MI has not been published up to now. Therefore, μand operator generates a compromise solution which is both compensatory and strongly efficient. Our possible further investigations are multi level version of MLSSP-MI and the usage of nonlinear membership functions for this problem, etc.