supply chain coordination with wholesale contract in an uncertain environment

Supply chain coordination is one of the most recently studied fields. one of the coordination contracts is the wholesale contract, which aims to balance the order quantity by offering a reduced price for the large quantity order by the retailer. the goal is to determine the order amount so that both parties in the channel are satisfied with a reasonable profit concerning the proposed price. when a new product is presented to the market, the main challenge would be a sensible demand prediction such that either stock over or shortage stays under a moderate level. there is insufficient sample space in such a new product, or the existing data for similar products does not apply to this new case. these drawbacks prevent one from applying probability theory. referring to an expert would be an appropriate approach in this situation. uncertainty theory is one of the mathematical paradigms which deals with this problem well. using this paradigm, we assume that the demand is an uncertain variable where its uncertainty distribution is presented. we mainly consider the linear uncertain demand and investigate optimal policy for both parties with and without coordination. an illustrative example verifies the appropriateness of the suggested approach. we also compare the results with the case when different scenarios are assumed, and probability theory is the base for the results.