Managing the Inventory of an Item with a Replacement Warranty

In this paper, we study a firm that faces demand from two sources: demand for new items and demand to replace failed items under warranty. We model this setting as a multiperiod single-product inventory problem where the demands for new items in different periods are independent and the demands for replacing failed items depend on the number and ages of the items under warranty. We consider backlogging and emergency supply cases, and study both discounted cost and average cost criteria. We prove the optimality of the w-dependent base-stock ordering policy where the base-stock level is a function of w, the vector representing the number of items at different ages currently under warranty. For the special case where the demand for new products is identically distributed, 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 an optimal w-dependent policy can lead to 69% average improvement in expected costs when compared to a policy that neglects demands from items under warranty.