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Continuous-Time Airline Overbooking with Time-Dependent Fares and Refunds

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  • Richard E. Chatwin

    (Applied Decision Analysis LLC, a wholly-owned subsidiary of PricewaterhouseCoopers LLP, Menlo Park, California)

Abstract

We analyze a model of airline overbooking in which customer cancellations and no-shows are explicitly considered. We model the reservations process as a continuous-time birth-and-death process with rewards representing the fares received and refunds paid and a terminal-value function representing the bumping penalty. The airline controls the reservation acceptance (birth) rate by declining reservation requests. Assuming that the fares and refunds are piecewise-constant functions of the time to flight, we demonstrate that a piecewise-constant booking-limit policy is optimal, i.e., at all times, the airline accepts reservation requests up to a booking limit if the current number of reservations is less than that booking limit, and declines reservation requests otherwise. When the fare is constant over time or falls toward flight time, the optimal booking limit falls toward flight-time.

Suggested Citation

  • Richard E. Chatwin, 1999. "Continuous-Time Airline Overbooking with Time-Dependent Fares and Refunds," Transportation Science, INFORMS, vol. 33(2), pages 182-191, May.
    • Handle: RePEc:inm:ortrsc:v:33:y:1999:i:2:p:182-191
    DOI: 10.1287/trsc.33.2.182
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    References listed on IDEAS

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    Cited by:

    1. Ge, Yanming & Xu, Yifan & Dai, Yue, 2010. "Overbooking with bilateral transference in parallel flights," International Journal of Production Economics, Elsevier, vol. 128(2), pages 577-585, December.
    2. Ming Xu & Yan Jiao & Xiaoming Li & Qingfeng Cao & Xiaoyang Wang, 2015. "A Multi-Period Optimization Model for Service Providers Using Online Reservation Systems: An Application to Hotels," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-18, July.
    3. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.
    4. Yingjie Lan & Michael O. Ball & Itir Z. Karaesmen, 2011. "Regret in Overbooking and Fare-Class Allocation for Single Leg," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 194-208, December.
    5. Feng, Youyi & Xiao, Baichun, 2006. "A continuous-time seat control model for single-leg flights with no-shows and optimal overbooking upper bound," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1298-1316, October.
    6. Huseyin Topaloglu & S. Ilker Birbil & J. B. G. Frenk & Nilay Noyan, 2012. "Tractable Open Loop Policies for Joint Overbooking and Capacity Control Over a Single Flight Leg with Multiple Fare Classes," Transportation Science, INFORMS, vol. 46(4), pages 460-481, November.
    7. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    8. Lan, Yingjie & Ball, Michael O. & Karaesmen, Itir Z. & Zhang, Jean X. & Liu, Gloria X., 2015. "Analysis of seat allocation and overbooking decisions with hybrid information," European Journal of Operational Research, Elsevier, vol. 240(2), pages 493-504.
    9. Alexander Erdelyi & Huseyin Topaloglu, 2010. "A Dynamic Programming Decomposition Method for Making Overbooking Decisions Over an Airline Network," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 443-456, August.
    10. Benoit Lardeux & Gabrielle Sabatier & Thierry Delahaye & Mourad Boudia & Odile Tonnet & Pierre Mathieu, 2019. "Yield optimization for airlines from ticket resell," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(3), pages 213-227, June.
    11. Youyi Feng & Baichun Xiao, 2000. "A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes," Management Science, INFORMS, vol. 46(5), pages 644-657, May.
    12. Wei Wang & Darius Walczak, 2016. "Overbooking under dynamic and static policies," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(6), pages 534-553, December.
    13. Feng, Youyi & Xiao, Baichun, 2006. "Integration of pricing and capacity allocation for perishable products," European Journal of Operational Research, Elsevier, vol. 168(1), pages 17-34, January.
    14. Kakuya Matsushima & Kiyoshi Kobayashi, 2012. "Economic Evaluation of Pre- and Post-Discounting Fee Systems," Chapters, in: Charlie Karlsson & Börje Johansson & Roger R. Stough (ed.), The Regional Economics of Knowledge and Talent, chapter 10, Edward Elgar Publishing.
    15. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    16. H Xiong & J Xie & X Deng, 2011. "Risk-averse decision making in overbooking problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1655-1665, September.
    17. Fukui, Hideki & Nagata, Koki, 2020. "How do passengers react to airlines’ overbooking strategies? Evidence from the US airlines," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 242-255.
    18. J. B. G. Frenk & Behrooz Pourghannad & Semih O. Sezer, 2017. "A Static Model in Single Leg Flight Airline Revenue Management," Transportation Science, INFORMS, vol. 51(1), pages 214-232, February.
    19. Guo, Xiaolong & Dong, Yufeng & Ling, Liuyi, 2016. "Customer perspective on overbooking: The failure of customers to enjoy their reserved services, accidental or intended?," Journal of Air Transport Management, Elsevier, vol. 53(C), pages 65-72.
    20. Nurşen Aydın & Ş. İlker Birbil & J. B. G. Frenk & Nilay Noyan, 2013. "Single-Leg Airline Revenue Management with Overbooking," Transportation Science, INFORMS, vol. 47(4), pages 560-583, November.
    21. Alavi Fard, Farzad & Sy, Malick & Ivanov, Dmitry, 2019. "Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 384-399.
    22. Yufeng Dong & Liuyi Ling, 2015. "Hotel Overbooking and Cooperation with Third-Party Websites," Sustainability, MDPI, vol. 7(9), pages 1-17, August.
    23. Itir Karaesmen & Garrett van Ryzin, 2004. "Overbooking with Substitutable Inventory Classes," Operations Research, INFORMS, vol. 52(1), pages 83-104, February.
    24. Scott Fay & Jinhong Xie, 2010. "The Economics of Buyer Uncertainty: Advance Selling vs. Probabilistic Selling," Marketing Science, INFORMS, vol. 29(6), pages 1040-1057, 11-12.

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