Competing Suppliers under Sales-Rebate Contract and Price Sensitive Demand in a Decentralized Supply Chain

This paper studies a competition in a decentralized supply chain between two independent suppliers who sell their products to a common retailer, under sales-rebate contract, and wherein the demand is sensitive to retail prices. The inventory related operational costs are included in the chain based on the economic order quantity model. The conditions of existence and uniqueness of the retailer’s optimal solution are discussed and found to be satisfied under symmetric chain parameters. However, the optimal wholesale price is found to exist and unique under symmetric optimal demand rates. In addition, due to the non-linearity of the inventory related costs, it is difficult to obtain a close theoretical solution form. The optimal demand rates and wholesale prices of the model are calculated numerically. The profit functions of the retailers and the suppliers are evaluated and the total Nash profit is compared to that of the integrated system. Furthermore, the impact of the inventory related costs is investigated numerically.