A weighted additive fuzzy multiobjective model for the supplier selection problem under price breaks in a supply Chain

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. Supplier selection is a multiple-criteria decision-making (MCDM) problem that is affected by several conflicting factors. Depending on the purchasing situations, criteria have varying importance and there is a need to weight criteria. In practice, for supplier selection problems, most of the input information is not known precisely. In these cases, the theory of fuzzy sets is one of the best tools for handling uncertainty. The fuzzy multiobjective model is formulated in such a way as to simultaneously consider the imprecision of information and determine the order quantities to each supplier based on price breaks. The problem includes the three objective functions: minimizing the net cost, minimizing the net rejected items and minimizing the net late deliveries, while satisfying capacity and demand requirement constraints. In order to solve the problem, a fuzzy weighted additive and mixed integer linear programming is developed. The model aggregates weighted membership functions of objectives to construct the relevant decision functions, in which objectives have different relative importance. A numerical example is given to illustrate how the model is applied. Finally, the conclusions and recommendations are presented.