Pricing and Capacity Rationing for Rentals with Uncertain Durations

Authors:
Noah Gans;Sergei Savin
Affiliations:
The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104-6340;Graduate School of Business, Columbia University, 3022 Broadway at 117th Street, New York, New York 10027
Venue:
Management Science
Year:
2007

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Abstract

We consider a rental firm with two types of customers. Contract customers pay fixed, prenegotiated rental fees and expect a high quality of service. Walk-in customers have no contractual relations with the firm and are “shopping for price.” Given multiple contract and walk-in classes, the rental firm has to decide when to offer service to contract customers and what fees to charge walk-in customers for service. We formulate this rental management problem as a problem in stochastic control and characterize optimal policies for managing contract and walk-in customers. We also consider static, myopic controls that are simpler to implement, and we analytically establish conditions under which these policies perform optimally. Complementary numerical tests provide a sense of the range of systems for which myopic policies are effective.