Priority Allocation in a Rental Model with Decreasing Demand

We analyze a model of rental and return process where limited inventory of a product is rented to two customer classes that differ in their return behavior and penalty costs. The rental demand is a decreasing function of time. We consider two cases: where a demand that is not met is lost and where an unmet demand returns. We show that to minimize penalty cost, the optimal allocation policy may give priority to different classes at different points in time and may decline lower-class demand for some time. Computational results show the benefit of the optimal allocation policy over a priority scheme reportedly used in practice.