Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Improving the Utilization of Front-Line Service Delivery System Personnel

There are two types of work typically performed in services which differ in the degree of control management has over when the work must be done. Serving customers, an activity that can occur only when customers are in the system is, by its nature, uncontrollable work. In contrast, the execution of controllable work does not require the presence of customers, and is work over which management has some degree of temporal control. This paper presents two integer programming models for optimally scheduling controllable work simultaneously with shifts. One model explicitly defines variables for the times at which controllable work may be started, while the other uses implicit modeling to reduce the number of variables. In an initial experiment of 864 test problems, the latter model yielded optimal solutions in approximately 81 percent of the time required by the former model. To evaluate the impact on customer service of having front-line employees perform controllable work, a second experiment was conducted simulating 5,832 service delivery systems. The results show that controllable work offers a useful means of improving labor utilization. Perhaps more important, it was found that having front-line employees perform controllable work did not degrade the desired level of customer service.