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

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 are taken into account in the problem. The problem is formulated as a bi-objective model to minimize annual supply chain costs and to maximize the annual purchasing value. The fuzzy weights of suppliers, which are the output of one of the supplier evaluation methods, are considered in the second objective function. Then, we propose a novel fuzzy multi-objective programming method for obtaining Pareto solutions. The method is the extension of a single-objective method exist in the literature. This method is based on the decision maker's degree of satisfaction from each fuzzy objectives considering the fulfillment level of fuzzy constraints. In the proposed method, the problem remains multi-objective and, unlike existing methods, does not transformed into a single-objective model. At the last stage of proposed method, the fuzzy results are compared with an index, and decision maker 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.