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Dynamic Airline Revenue Management with Multiple Semi-Markov Demand

Author

Listed:
  • Shelby Brumelle

    (Deceased. Formerly with the Faculty of Commerce and Business Administration, University of British Columbia)

  • Darius Walczak

    (Pros Revenue Management Inc., 3100 Main Street, Suite 900, Houston, Texas 77002)

Abstract

When a customer requests a discount fare, the airline must decide whether to sell the seat at the requested discount or to hold the seat in hope that a customer will arrive later who will pay more. We model this situation for a single-leg flight with multiple fare classes and customers who arrive according to a semi-Markov process (possibly nonhomogeneous). These customers can request multiple seats (batch requests) and can be overbooked. Under certain conditions, we show that the value function decreases as departure approaches. If each customer only requests a single seat or if the requests can be partially satisfied, then we show that there are optimal booking curves which decrease as departure approaches. We also provide counterexamples to show that this structural property of the optimal policy need not hold for more general arrival processes if the requests can be for more than one seat and must be accepted or rejected as a whole.

Suggested Citation

  • Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:1:p:137-148
    DOI: 10.1287/opre.51.1.137.12796
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    References listed on IDEAS

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    2. Grace Y. Lin & Yingdong Lu & David D. Yao, 2008. "The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing," Operations Research, INFORMS, vol. 56(4), pages 945-957, August.
    3. Jonathan Patrick & Martin L. Puterman & Maurice Queyranne, 2008. "Dynamic Multipriority Patient Scheduling for a Diagnostic Resource," Operations Research, INFORMS, vol. 56(6), pages 1507-1525, December.
    4. Guillermo Gallego & Michael Z. F. Li & Yan Liu, 2020. "Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons," Operations Research, INFORMS, vol. 68(3), pages 655-670, May.
    5. Samii, Amir-Behzad & Pibernik, Richard & Yadav, Prashant & Vereecke, Ann, 2012. "Reservation and allocation policies for influenza vaccines," European Journal of Operational Research, Elsevier, vol. 222(3), pages 495-507.
    6. c{S}. .Ilker Birbil & J. B. G. Frenk & Joaquim A. S. Gromicho & Shuzhong Zhang, 2009. "The Role of Robust Optimization in Single-Leg Airline Revenue Management," Management Science, INFORMS, vol. 55(1), pages 148-163, January.
    7. Mihai Banciu & Fredrik Ødegaard & Alia Stanciu, 2019. "Distribution-free bounds for the expected marginal seat revenue heuristic with dependent demands," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(2), pages 155-163, April.
    8. Alec Morton, 2006. "Structural properties of network revenue management models: An economic perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 748-760, December.
    9. Grace Lin & Yingdong Lu & David Yao, 2007. "Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing," Papers 0708.1146, arXiv.org.
    10. Maclean, K.D.S. & Ødegaard, F., 2020. "Dynamic capacity allocation for group bookings in live entertainment," European Journal of Operational Research, Elsevier, vol. 287(3), pages 975-988.
    11. 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.
    12. Tsai, Wen-Hsien & Hung, Shih-Jieh, 2009. "Dynamic pricing and revenue management process in Internet retailing under uncertainty: An integrated real options approach," Omega, Elsevier, vol. 37(2), pages 471-481, April.
    13. Hyun-Rok Lee & Taesik Lee, 2018. "Markov decision process model for patient admission decision at an emergency department under a surge demand," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 98-122, June.
    14. Yingjie Lan & Huina Gao & Michael O. Ball & Itir Karaesmen, 2008. "Revenue Management with Limited Demand Information," Management Science, INFORMS, vol. 54(9), pages 1594-1609, September.

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