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Capacity Management in Rental Businesses with Two Customer Bases

Graduate School of Business, Columbia University, 404 Uris Hall, New York, New York 10027
Operations and Information Management Department, The Wharton School, University of Pennsylvania, 3730 Walnut Street, Suite 500, Philadelphia, Pennsylvania 19104
Operations and Information Management Department, The Wharton School, University of Pennsylvania, 3730 Walnut Street, Suite 500, Philadelphia, Pennsylvania 19104
Operations and Information Management Department, The Wharton School, University of Pennsylvania, 3730 Walnut Street, Suite 500, Philadelphia, Pennsylvania 19104
svs30{at}columbia.edu
cohen{at}wharton.upenn.edu
gans{at}wharton.upenn.edu
katalan{at}wharton.upenn.edu

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.

Subject classifications: service systems; queueing control; stochastic knapsack; fluid models.
History: Received September 2000; revision received July 2001; revision received May 2003; accepted March 2004.

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