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Solution to the Continuous Time Dynamic Yield Management Model

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  • Yigao Liang

    (USAir Operations Research Group, 2345 Crystal Drive, Arlington, Virginia 22227)

Abstract

We formulate the yield management problem as a continuous time, stochastic, dynamic programming model. We derive an expression for the expected revenue in terms of the stochastic booking processes and the control policies. The solution to the problem is found by maximizing the expected revenue over the possible control decisions. The solution is for an arbitrary number of fare classes and arbitrary booking curves. In particular, it requires no assumptions on the order of arrivals from different fare classes. The solution can be expressed in terms of a double recursion complex. At each node of the complex, the upper limit of a one-dimensional integral is solved to find a critical time for each fare class and for each value of remaining capacity. The critical times are the only values that need to be stored in the reservation control system to achieve optimal real-time control. This simple result is somewhat surprising given the complexity of even the static programming versions of the problem. We derive simple expressions of expected revenues and bid prices, which provide useful information to the user of a yield management system.

Suggested Citation

  • Yigao Liang, 1999. "Solution to the Continuous Time Dynamic Yield Management Model," Transportation Science, INFORMS, vol. 33(1), pages 117-123, February.
    • Handle: RePEc:inm:ortrsc:v:33:y:1999:i:1:p:117-123
    DOI: 10.1287/trsc.33.1.117
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    References listed on IDEAS

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    1. S. L. Brumelle & J. I. McGill, 1993. "Airline Seat Allocation with Multiple Nested Fare Classes," Operations Research, INFORMS, vol. 41(1), pages 127-137, February.
    2. Peter P. Belobaba, 1987. "Survey Paper---Airline Yield Management An Overview of Seat Inventory Control," Transportation Science, INFORMS, vol. 21(2), pages 63-73, May.
    3. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    4. Tak C. Lee & Marvin Hersh, 1993. "A Model for Dynamic Airline Seat Inventory Control with Multiple Seat Bookings," Transportation Science, INFORMS, vol. 27(3), pages 252-265, August.
    5. S. L. Brumelle & J. I. McGill & T. H. Oum & K. Sawaki & M. W. Tretheway, 1990. "Allocation of Airline Seats between Stochastically Dependent Demands," Transportation Science, INFORMS, vol. 24(3), pages 183-192, August.
    6. Peter P. Belobaba, 1989. "OR Practice—Application of a Probabilistic Decision Model to Airline Seat Inventory Control," Operations Research, INFORMS, vol. 37(2), pages 183-197, April.
    7. Lawrence W. Robinson, 1995. "Optimal and Approximate Control Policies for Airline Booking with Sequential Nonmonotonic Fare Classes," Operations Research, INFORMS, vol. 43(2), pages 252-263, April.
    8. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Richard D. Wollmer, 1992. "An Airline Seat Management Model for a Single Leg Route When Lower Fare Classes Book First," Operations Research, INFORMS, vol. 40(1), pages 26-37, February.
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