A novel fuzzy multi-objective method for supplier selection and order allocation problem using NSGA II

Abstract

This paper introduces a supplier selection and order allocation problem in a single-buyer-multi-supplier supply chain in which appropriate suppliers are selected and orders allocated to them. Transportation costs, quantity discount, fuzzy-type uncertainty, and some practical constraints were taken into account in the problem. The problem was formulated as a bi-objective model to minimize annual supply chain costs and to maximize Annual Purchasing Value (APV). The fuzzy weights of suppliers, which were the output of one of the supplier evaluation methods, were considered in the second objective function. Then, a novel fuzzy multi-objective programming method was formulated for obtaining Pareto solutions. The method is the extension of a single-objective method existing in the literature. It is based on the degree of satisfaction of the Decision Maker (DM) with each fuzzy objective considering the fulfillment level of fuzzy constraints. In the proposed method, the problem remains multi-objective and, unlike in the existing methods, it is not transformed into a single-objective model. At the last stage of the proposed method, the fuzzy results are compared with an index and the DM can identify the appropriate or inappropriate solutions. To solve the problem, Non-dominated Sorting Genetic Algorithm (NSGA II) is designed and computational results are presented using numerical examples.