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Pricing and Capacity Rationing for Rentals with Uncertain Durations

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  • Noah Gans

    (The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104-6340)

  • Sergei Savin

    (Graduate School of Business, Columbia University, 3022 Broadway at 117th Street, New York, New York 10027)

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.

Suggested Citation

  • Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:3:p:390-407
    DOI: 10.1287/mnsc.1060.0651
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    References listed on IDEAS

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    6. Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    7. Demet Batur & Jennifer K. Ryan & Zhongyuan Zhao & Mehmet C. Vuran, 2019. "Dynamic Pricing of Wireless Internet Based on Usage and Stochastically Changing Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 833-852, October.
    8. Shan Wang & Nan Liu & Guohua Wan, 2020. "Managing Appointment-Based Services in the Presence of Walk-in Customers," Management Science, INFORMS, vol. 66(2), pages 667-686, February.
    9. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    10. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    11. Jiao, Wen & Yan, Hong & Pang, King-Wah, 2016. "Nonlinear pricing for stochastic container leasing system," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 1-18.
    12. Eugene A. Feinberg & Fenghsu Yang, 2016. "Optimal pricing for a GI/M/k/N queue with several customer types and holding costs," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 103-120, February.
    13. Samuel Vercraene & Jean-Philippe Gayon & Fikri Karaesmen, 2018. "Effects of System Parameters on the Optimal Cost and Policy in a Class of Multidimensional Queueing Control Problems," Operations Research, INFORMS, vol. 66(1), pages 150-162, January.
    14. Klein, Robert & Koch, Sebastian & Steinhardt, Claudius & Strauss, Arne K., 2020. "A review of revenue management: Recent generalizations and advances in industry applications," European Journal of Operational Research, Elsevier, vol. 284(2), pages 397-412.
    15. Xufeng Yang & Wen Jiao & Juliang Zhang & Hong Yan, 2022. "Capacity management for a leasing system with different equipment and batch demands," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3004-3020, July.
    16. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    17. Li, Dong & Pang, Zhan, 2017. "Dynamic booking control for car rental revenue management: A decomposition approach," European Journal of Operational Research, Elsevier, vol. 256(3), pages 850-867.
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    19. Manuel A. Nunez & Xue Bai & Linna Du, 2021. "Leveraging Slack Capacity in IaaS Contract Cloud Services," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 883-901, April.

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