Price Discount Subsidy Contract for a Two-Echelon Supply Chain with Random Yield

Abstract

This paper revisits the traditional supplier–buyer integrated production–inventory model which deals with the problem of a manufacturer supplying a product to a retailer serving the end consumer with a known demand. We present two types of price discount subsidy, additional discount subsidy contract, and all units discount subsidy contract to coordinate the supply chain, and analytic solutions for each contract are described. We derived that with yield uncertainty, the manufacturer’s expected profit is concave on the manufacturer’s target production quantity under both contracts, and the discount rate is positively related to the manufacturer’s target production quantity under the all units discount subsidy contract. We derive the constraint condition under which the manufacturer will produce more under the discount subsidy contracts and which contracts are more available to promote the manufacturer’s expected output.