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This study investigates supply chain contracts with a supplier and multiple competing retailers in a fuzzy demand environment. The market demand is considered as a positive triangular fuzzy number. The models of centralized decision, return contract, and revenue-sharing contract are built by the method of fuzzy cut sets theory, and their optimal policies are also proposed. Finally, an example is given to illustrate and validate the models and conclusions. It is shown that the optimal total order quantity of the retailers fluctuates at the center of the fuzzy demand. With the rise of the number of retailers, the optimal order quantity and the fuzzy expected profit for each retailer will decrease, and the fuzzy expected profit for supplier will increase.

In this paper, we consider the revenue sharing contract between supply chain actors in a multi-echelon supply chain, where the demand of the customers and retail price are fuzzy variables. The centralized decision making system and a coordinating contract, namely, the revenue sharing contract with fuzzy demand and asymmetric information are proposed. To derive the optimal solutions, the fuzzy set theory is applied for solving these models. Finally, the optimal results of proposed models are illustrated with three numerical experiments. The effects of the fuzziness of retail price and demand, different contract parameters on the optimal strategies for supply chain actors are also analyzed.