Coordinating a Three Stage Supply Chain with Fuzzy Demand

In a three stage supply chain composed of one manufacturer, one distributor and one retailer, the supply chain coordination mechanism is studied under a fuzzy demand environment. The market demand is treated as a positive trapezoidal fuzzy number, and the models of centralized decision-making system and spanning revenue sharing (SRS) contract are proposed by the method of the fuzzy set theory. The optimal solutions of the fuzzy models are also proposed. Finally, numerical examples are given to illustrate and validate the models and conclusions. It is shown that the optimal order quantity of the retailer fluctuates at the range of the most possible values of the fuzzy demand, and increases with the raise of the retail price. The coordination of the supply chain members can be achieved by changing the values of contract parameters. In addition, the optimal fuzzy expected profits of the supply chain members will increase with the increasing of the minimum and maximum possible values of the fuzzy demand.