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Motivated by innovative rental business models, we study a rental system with random loss of inventory due to use. We utilize a discrete-time model in which the inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Demand, rental durations, and rental unit lifetimes are stochastic; sample path coupling allows us to derive structural results that hold under limited distributional assumptions. Considering different “recirculation” rules (i.e., which unit to select to meet a demand), we prove the concavity of the expected profit function and identify the optimal recirculation rule under two different models of a rental unit’s state: the number of times rented out or its condition. We develop two upper bounds on the number of lost rental units and two heuristics for the inventory decision. Numerical study shows the following: (1) accounting for rental unit loss can increase the expected profit by 7% for a single season; (2) the optimal inventory level in response to increasing loss probability is nonmonotonic; (3) both heuristics perform well; and (4) choosing the optimal recirculation rule over a commonly used policy can increase the profit-maximizing service level by up to six percentage points.
Slaugh et al. (Wed,) studied this question.