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Overbooking with Bounded Loss

Author

Listed:
  • Daniel Freund

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Jiayu (Kamessi) Zhao

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

Abstract
We study a classic problem in revenue management: quantity-based, single-resource revenue management with no-shows. In this problem, a firm observes a sequence of T customers requesting a service. Each arrival is drawn independently from a known distribution of k different types, and the firm needs to decide irrevocably whether to accept or reject requests in an online fashion. The firm has a capacity of resources B and wants to maximize its profit. Each accepted service request yields a type-dependent revenue and has a type-dependent probability of requiring a resource once all arrivals have occurred (or be a no-show). If the number of accepted arrivals that require a resource at the end of the horizon is greater than B , the firm needs to pay a fixed compensation for each service request that it cannot fulfill. With a clairvoyant that knows all arrivals ahead of time, as a benchmark, we provide an algorithm with a uniform additive loss bound, that is, its expected loss is independent of T . This improves upon prior works achieving Ω ( T ) guarantees.

Suggested Citation

  • Daniel Freund & Jiayu (Kamessi) Zhao, 2023. "Overbooking with Bounded Loss," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1344-1363, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1344-1363
    DOI: 10.1287/moor.2022.1293
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