Optimal procurement, disposal and pricing policies for managing rental goods

Consider a video rental retailer who procures DVDs or video cassettes from a distributor and rents them to the customers. To meet the time-varying rental demand, the retailer needs to develop cost-effective procurement and disposal policies. In this paper, we first present a base model in which the underlying rental demand is decreasing over time, backorders are not allowed and the disposal price is exogenous. For this base model, we show that the optimal procurement quantity is equal to the sum of effective demands (rental demand net of returns) over an integral number of periods, and the optimal disposal policy can be determined by solving a simple dynamic program with polynomial complexity. We then analyze the case of endogenous disposal prices and derive optimal disposal policies by solving a quadratic optimization problem with tree constraints. We also extend the base model to allow for backorders and to cases where the retailer has multiple procurement opportunities and a contractual period where disposals are not allowed. We show that the qualitative nature of the procurement policy is preserved in these cases and the optimal procurement and selling policies can be determined using similar dynamic programming algorithms.