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An Application of Markov Decision Processes to the Seat Inventory Control Problem

  • Christiane Barz
  • Karl-Heinz Waldmann

Abstract

Airlines typically divide a pool of identical seats into several booking classes that represent e.g. different discount levels with differentiated sale conditions and restrictions. Assuming perfect market segmentation, mixing discount and higher-fare passengers in the same aircraft compartment offers the airline the potential of gaining revenue from seats that would otherwise fly empty. If too many seats are sold at a discount price, however, the airline company would loose full-fare passengers. If too many seats are protected for higher-fare demand, the flight would depart with vacant seats. Seat inventory control deals with the optimal allocation of capacity to these different classes of demand, forming a substantial part of a revenue management system.

Keywords

Markov Decision Process Revenue Management External Process Optimal Decision Rule Terminal Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Aviv Y, Pazgal A (2005) A partially observed Markov decision process for dynamic pricing. Management Science 49(9):1400–1416CrossRefGoogle Scholar
  2. [2]
    Belobaba PP (1987) Airline yield management. Transportation Science 21(2):63–73Google Scholar
  3. [3]
    Belobaba PP (1989) Application of a probabilistic decision model to airline seat inventory control. Operations Research 37(2):183–197Google Scholar
  4. [4]
    Brumelle SL, McGill JI (1993) Airline seat allocation with multiple nested fare classes. Operations Research 41(1):127–137Google Scholar
  5. [5]
    Brumelle SL, McGill JI, Oum TH, Sawaki K, Thretheway MW (1990) Allocation of airline seat between stochastically dependent demands. Transportation Science 24(3):183–192Google Scholar
  6. [6]
    Brumelle SL, Walczak D (2003) Dynamic airline revenue management with multiple semi-Markov demand. Operations Research 51(1):137–148CrossRefGoogle Scholar
  7. [7]
    Curry RE (1990) Optimal airline seat allocation with fare classes nested by origins and destinations. Transportation Science 24(3):193–204Google Scholar
  8. [8]
    Helm WE, Waldmann KH (1984) Optimal control of arrivals to multi-server queues in a random environment. Journal of Applied Probability 21(3):602–615CrossRefGoogle Scholar
  9. [9]
    Hinderer K, Waldmann KH (2005) Algorithms for countable state Markov decision models with an absorbing set. SIAM J. Control and Optimization 43(6):2109–2131CrossRefGoogle Scholar
  10. [10]
    Kleywegt AJ, Papastavrou JD (1998) The dynamic and stochastic Knapsack problem. Operations Research 46(1):17–35Google Scholar
  11. [11]
    Lautenbacher CJ, Stidham S Jr (1999) The underlying Markov decision process in the single-leg airline yield management problem. Transportation Science 33(2):136–146Google Scholar
  12. [12]
    Lee TC, Hersh M (1993) A model for dynamic airline seat inventory control with multiple seat bookings. Transportation Science 27(3):252–265Google Scholar
  13. [13]
    Liang Y (1999) Solution to the continuous time dynamic yield management model. Transportation Science 33(1):117–123Google Scholar
  14. [14]
    Littlewood K (1972) Forecasting and control of passengers. 12th AG-IFORS Symposium Proceedings, pp. 95–117Google Scholar
  15. [15]
    Robinson LW (1995) Optimal and approximate control policies for airline booking with sequential nonmonotonic fare classes. Operations Research 43(2):252–263Google Scholar
  16. [16]
    Schäl M (1975) Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32:179–196CrossRefGoogle Scholar
  17. [17]
    Shaked M, Shanthikumar JG (1988) Stochastic convexity and its applications. Advances in applied probabilities 20(2):427–446CrossRefGoogle Scholar
  18. [18]
    van Slyke R, Young Y (2000) Finite horizon stochastic Knapsacks with applications to yield management. Operations Research 48(1):155–172CrossRefGoogle Scholar
  19. [19]
    Stidham S Jr (1978) Socially and individually optimal control of arrivals to a GI/GI/1 queue. Management Science 24(15):1598–1610Google Scholar
  20. [20]
    Subramanian J, Stidham S Jr, Lautenbacher CJ (1999) Airline yield management with overbooking, cancellations, and no-shows. Transportation Science 33(2):147–167CrossRefGoogle Scholar
  21. [21]
    Talluri KT, van Ryzin GJ (2004) The Theory and Practice of Revenue Management. Kluwer Academic Publishers, DordrechtGoogle Scholar
  22. [22]
    Walczak D (2001) Dynamic modelling approaches to airline revenue management. Ph.D. thesis at the Centre for Transportation Studies, University of British ColumbiaGoogle Scholar
  23. [23]
    Wollmer RD (1992) An airline management model for a single leg route when lower fare classes book first. Operations Research 40(1):26–37Google Scholar

Copyright information

© Deutscher Universitäts-Verlag/GWV Fachverlage GmbH, Wiesbaden 2006

Authors and Affiliations

  • Christiane Barz
    • 1
  • Karl-Heinz Waldmann
    • 1
  1. 1.Institut für Wirtschaftstheorie und Operations ResearchUniversität KarlsruheKarlsruhe

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