Coordination of joint pricing-production decisions in a supply chain

We consider the coordination of dynamic, joint pricing-production/ordering decisions in a decentralized supply chain where a manufacturer outsources her product distribution/retailing function to an independent distributor/retailer. The manufacturer produces and wholesales her product to the distributor who, after some further processing, sells the product to an external market. In a leader-follower setting with convex production/ordering cost functions, both parties make pricing and production/ordering decisions over a discrete, finite-time horizon (a selling season) to maximize their respective profits. For a given manufacturer's (the leader's) wholesale price schedule, we develop a simple forward algorithm to solve the distributor's problem optimally, and prove a planning horizon property of the solution. Our key result is to show the existence of a manufacturer's price schedule that induces distributor to adopt decisions in the decentralized setting to achieve the performance of a centralized supply chain. Based on this channel-optimal pricing policy we then develop an incentive scheme for the manufacturer to achieve channel coordination. A numerical example is provided to compare the performance of different policies and to reinforce key managerial insights generated through analysis.