Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version


Publication Source

Operation Research





Start Page


Last Page





We consider the allocation of capacity in a system in which rental equipment is accessed by two classes of customers. We formulate the problem as a continuous-time analogue of the one-shot allocation problems found in the more traditional literature on revenue management, and we analyze a queueing control model that approximates its dynamics. Our investigation yields three sets of results.

First, we use dynamic programming to characterize properties of optimal capacity allocation policies. We identify conditions under which “complete sharing”—in which both classes of customers have unlimited access to the rental fleet—is optimal.

Next, we develop a computationally efficient “aggregate threshold” heuristic that is based on a fluid approximation of the original stochastic model. We obtain closed-form expressions for the heuristic’s control parameters and show that the heuristic performs well in numerical experiments. The closed-form expressions also show that, in the context of the fluid approximation, revenues are concave and increasing in the fleet size.

Finally, we consider the effect of the ability to allocate capacity on optimal fleet size. We show that the optimal fleet size under allocation policies may be lower, the same as, or higher than that under complete sharing. As capacity costs increase, allocation policies allow for larger relative fleet sizes. Numerical results show that, even in cases in which dollar profits under complete sharing may be close to those under allocation policies, the capacity reductions enabled by allocation schemes can help to lift profit margins significantly.


service systems, queueing control, stochastic knapsack, fluid models



Date Posted: 27 November 2017

This document has been peer reviewed.