A Max-min fuzzy approach for supplier selection and order allocation problem with transportation costs: Genetic algorithm

In this paper, we study a supplier selection and order allocation problem with in a multi-objective and fuzzy environment. Transportation costs and quantity discount are taken into account in the problem. We assume four common objectives as total costs, on-time delivery rate, defective rate, and purchasing value. We utilize a max-min approach such that the min-operator finds the fuzzy decision that simultaneously satisfies all the fuzzy objectives. Then the maximizing decision is determined to be the maximum degree of membership for the fuzzy decision. We use the non-linear S-shape membership functions to express the vague aspiration levels of the DM’s objective. According to the defined fuzzy membership functions and applying Bellman–Zadeh’s maximization principle, the fuzzy multi objective model is transformed into a single objective model. A genetic algorithm is applied to solve the multi objective fuzzy supplier selection and order allocation problem. Computational results are presented using numerical examples.