Returns policy in supply chain with fuzzy demand

In a two-stage supply chain composed of one supplier and one retailer, the supply chain models in a fuzzy demand environment is researched. A positive triangular fuzzy number is used to model the external market demand. Using the method of fuzzy cut sets theory, the models of centralized decision-making and returns policy are built, and their optimal policies are also proposed. It shows that the optimal order quantity of the retailer fluctuates at the center of the fuzzy demand and increases with the raise of the retail price; there exists a unique solution of the optimal wholesale price and return price; the coordination of members can be achieved in returns policy with fuzzy demand. Finally, a numerical example is given to illustrate the models and the solution-seeking process.