Coordinated Inventory Planning for New and Old Products under Warranty

This paper is motivated by the inventory planning issues faced by a manufacturer of a digital projector. The seller faces demand from two sources: new demand, and demand to replace failed items under warranty. We model this setting as a multi-period single product inventory problem where the new demand in different periods are independent and the demand for replacing failed items under warranty is proportional to the number of items under warranty. We assume linear procurement, penalty and holding costs. We consider backlogging and emergency supply cases, and study both discounted cost and average cost cases. We prove the optimality of the w-dependent base stock ordering policy where the base stock level is a function of w, the number of items currently under warranty. For the special case, where the demand for new products is stationary, we prove the optimality of a stationary w-dependent base stock policy for the finite horizon discounted and the infinite horizon discounted and average cost cases. In our computational study, we find that such an integrated policy can lead to 31% average improvement in expected costs when compared to a policy that neglects warranty repairs. This work is partially supported by NSF Grant DMII-0223117.