Coordination of supply chain with buyer's promotion

In this paper, we develop a model to analyze the coordination of a supply chain with the demand influenced by the buyer's promotion. The supply chain consists of a supplier and a group of homogeneous buyers. The buyers choose inventories ex ante and promotional levels ex post. The annual demand rate depends on the promotional level and the operating cost---including the ordering and inventory holding cost---depends on the promotional level and the order quantity. It is shown that quantity discount alone is not sufficient to guarantee joint profit maximization. Then we propose a contract, discount quantity with transfer profit contract, and show that this contract can coordinate the supply chain. Moreover, it is shown that this policy is robust because it can allocate the supply chain profit arbitrarily between the supplier and the buyer and lead the buyer to choose the joint optimal promotional level and the supplier need not to observe and verify the buyer's promotional level. For the special case that the operating cost is a fixed constant, we show that there is no contract which can coordinate the supply chain if the promotion is unobservable and unverifiable and the discount policy can guarantee the coordination of the supply chain if the promotion is observable and verifiable.