A weighted max–min model for fuzzy multi-objective supplier selection in a supply chain A. Amid a,n , S.H. Ghodsypour b , C. O’Brien c a Islamic Azad University, Tehran North Branch, Engineering School, Industrial Engineering Department, Tehran, Iran b Industrial Engineering Department, Amirkabir University of Technology, Tehran, Iran c Nottingham University Business School, Jubilee Campus, NG8 1BB, UK article info Article history: Received 6 July 2008 Accepted 28 April 2010 Available online 4 May 2010 Keywords: Supplier selection Fuzzy multi-objective decision making Weighted max–min model abstract Supplier selection is one of the most important activities of purchasing departments. This importance is increased even more by new strategies in a supply chain. Supplier selection is a multi-criteria decision making problem in which criteria have different relative importance. In practice, for supplier selection problems, many input information are not known precisely. The fuzzy set theories can be employed due to the presence of vagueness and imprecision of information. A weighted max–min fuzzy model is developed to handle effectively the vagueness of input data and different weights of criteria in this problem. Due to this model, the achievement level of objective functions matches the relative importance of the objective functions. In this paper, an analytic hierarchy process (AHP) is used to determine the weights of criteria. The proposed model can help the decision maker (DM) to find out the appropriate order to each supplier, and allows the purchasing manager(s) to manage supply chain performance on cost, quality and service. The model is explained by an illustrative example. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Within new strategies for purchasing and manufacturing, suppliers play a key role in achieving corporate competitiveness. Hence, selecting the right suppliers is a vital component of these strategies. In most industries the cost of raw materials and component parts constitutes the major cost of a product, such that in some cases it can account for up to 70% (Ghobadian et al., 1993). Thus the purchasing department can play a key role in an organization’s efficiency and effectiveness because of the con- tribution of supplier performance on cost, quality, delivery and service in achieving the objectives of a supply chain. Supplier selection is a multiple criteria problem that includes both qualitative and quantitative factors. The relative importance of the criteria and sub-criteria are determined by top management and purchasing managers based upon supply chain strategies. In a real case, decision makers do not have exact and complete information related to decision criteria and constraints. In these cases the theory of fuzzy sets is one of the best tools to handle uncertainty. Fuzzy set theories are employed in the supplier selection problem due to the presence of vagueness and imprecision of information. Amid et al. (2006) developed a weighted additive fuzzy model for supplier selection problems to deal with: imprecise inputs and the basic problem of determining the weights of quantitative/qualitative criteria under conditions of multiple sourcing and capacity constraints. In a weighted additive model, there is no guarantee that the achieve- ment levels of fuzzy goals are consistent with desirable relative weights or the DM’s expectations. When the DM provides the weight of the objective functions, the ratio of membership functions achievement level should be as close as possible to the ratio of objective weights in order to reflect the relative importance of the criteria. However in the weighted additive model, the ratio of achievement levels is not necessarily the same as that of the objective weights. In this paper, a weighted max–min fuzzy multi-objective model has been developed to enable the purchasing managers to assign the order quantities to each supplier based on supply chain strategies. 2. Literature review Dickson (1966) first identified and analyzed the importance of 23 criteria for supplier selection based on a survey of purchasing managers. Weber et al. (1991) reviewed 74 articles discussing supplier selection criteria. They also concluded that supplier selection is a multi-criteria problem and the priority of criteria depends on each purchasing situation. Roa and Kiser (1980) and Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.04.044 n Corresponding author. Tel./fax: + 98 21 88787204. E-mail addresses: a_amid@iau-tnb.ac.ir (A. Amid), ghodsypo@aut.ac.ir (S.H. Ghodsypour), chris.obrien@nottingham.ac.uk (C. O’Brien). Int. J. Production Economics 131 (2011) 139–145