In this article we study a firm that is facing 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 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 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-cost and the infinite-horizon discounted- and average-cost
cases. We compare the integrated inventory policy with the one that
neglects demands from items under warranty.