Mathematical Methods of Operations Research

, Volume 65, Issue 3, pp 565–579 | Cite as

Risk-sensitive capacity control in revenue management

Original Article


Both the static and the dynamic single-leg revenue management problem are studied from the perspective of a risk-averse decision maker. Structural results well-known from the risk-neutral case are extended to the risk-averse case on the basis of an exponential utility function. In particular, using the closure properties of log-convex functions, it is shown that an optimal booking policy can be characterized by protection levels, depending on the actual booking class and the remaining time. Moreover, monotonicity of the protection levels with respect to the booking class and the remaining time are proven.


Markov decision processes Revenue management Exponential utility Risk-sensitivity Log-convex functions 


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  1. Agrawal V, Seshadri S (2000) Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem. Manuf Serv Oper Manage 2(4):410–423CrossRefGoogle Scholar
  2. Barz C (2006) How does risk aversion affect optimal revenue management policies? A simulation study. In: Mattfeld D, Suhl L (eds) DSOR contributions to information systems, vol 4, pp 161–172Google Scholar
  3. Barz C, Waldmann K-H (2006) An application of Markov decision processes to the seat inventory control problem. In: Morlock M, Schwindt C, Trautmann N, Zimmermann J (eds) Perspectives on operations research—essays in honor of Klaus Neumann. Deutscher Universitäts-Verlag, Wiesbaden, pp 113–128Google Scholar
  4. Belobaba PP (1987a) Airline yield management. Transp Sci 21(2):63–73Google Scholar
  5. Belobaba PP (1987b) Air travel demand and airline seat inventory management. PhD Thesis, Massachusetts Institute of TechnologyGoogle Scholar
  6. Belobaba PP, Weatherford LR (1996) Comparing decision rules that incorporate customer diversion in perishable asset revenue management situations. Decis Anal 27:343–363Google Scholar
  7. Bitran GR, Caldentey R (2003) An overview of pricing models for revenue management. Manuf Serv Oper Manage 5(3):203–229CrossRefGoogle Scholar
  8. Bouakiz M, Sobel MJ (1992) Inventory control with an exponential utility criterion. Oper Res 40(3):603–608MATHMathSciNetGoogle Scholar
  9. Brumelle SL, McGill JI (1993) Airline seat allocation with multiple nested fare classes. Oper Res 41(1):127–137MATHGoogle Scholar
  10. Chen X, Sim M, Simchi-Levi D, Sun P (2005) Risk aversion in inventory management. Working paper, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
  11. Coraluppi SP (1997) Optimal control of Markov decision processes for performance and robustness. PhD Thesis, University of MarylandGoogle Scholar
  12. Curry RE (1990) Optimal airline seat allocation with fare classes nested by origins and destinations. Transp Sci 24(3):193–204MathSciNetGoogle Scholar
  13. Feng Y, Xiao B (1999) Maximizing revenues of perishable assets with a risk factor. Oper Res 47(2):337–341MATHGoogle Scholar
  14. Howard R (1988) Decision analysis: practice and promise. Manage Sci 34(6):679–695Google Scholar
  15. Howard R, Matheson JE (1972) Risk-sensitive Markov decision processes. Manage Sci 18(7):356–369MathSciNetMATHGoogle Scholar
  16. Kirkwood CW (2004) Approximating risk aversion in decision analysis applications. Decis Anal 1(1):55–72CrossRefGoogle Scholar
  17. Lancaster J (2003) The financial risk of airline revenue management. J Revenue Pricing Manage 2:158–165CrossRefGoogle Scholar
  18. Lautenbacher CJ, Stidham S Jr (1999) The underlying Markov decision process in the single-leg airline yield management problem. Transp Sci 33(2):136–146MATHGoogle Scholar
  19. Lee TC, Hersh M (1993) A model for dynamic airline seat inventory control with multiple seat bookings. Transp Sci 27(3):252–265Google Scholar
  20. Li MZF, Oum TH (2002) A note on the single leg, multifare seat allocation problem. Transp Sci 36(3):349–353MATHCrossRefGoogle Scholar
  21. Liang Y (1999) Solution to the continuous time dynamic yield management model. Transp Sci 33(1):117–123MATHGoogle Scholar
  22. Littlewood K (1972) Forecasting and control of passangers. In: 12th AGIFORS symposium proceedings, pp 95–117Google Scholar
  23. Mitra D, Wang Q (2003) Stochastic traffic engineering, ith applications to network revenue management. In: IEEE INFOCOM 2003—the conference on computer communications, vol 22(1), pp 396–405Google Scholar
  24. Mitra D, Wang Q (2005) Stochastic traffic engineering for demand uncertainty and risk-aware network revenue management. IEEE/ACM Trans Netw 13(2):221–233CrossRefGoogle Scholar
  25. Müller A (2000) Expected utility maximization of optimal stopping problems. Eur J Oper Res 122(1):101–114MATHCrossRefGoogle Scholar
  26. Phillips RL (2005) Pricing and revenue optimization. Stanford Business Books, StanfordGoogle Scholar
  27. Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32(1/2):122–136MATHCrossRefGoogle Scholar
  28. Roberts AW, Varberg DE (1973) Convex functions. Academic, LondonMATHGoogle Scholar
  29. Robinson LW (1995) Optimal and approximate control policies for airline booking with sequential nonmonotonic fare classes. Oper Res 43(2):252–263MATHGoogle Scholar
  30. Stidham S Jr (1978) Socially and individually optimal control of arrivals to a GI/M/1 queue. Manage Sci 24(15):1598–1610MATHMathSciNetGoogle Scholar
  31. Talluri KT, van Ryzin GJ (2004b) The theory and practice of revenue management. Kluwer Academic Publishers, DordrechtMATHGoogle Scholar
  32. Weatherford LR (2004) EMSR versus EMSU: revenue or utility? J Revenue Pricing Manage 3(3):277–284CrossRefGoogle Scholar
  33. Wollmer RD (1992) An airline management model for a single leg route when lower fare classes book first. Oper Res 40(1):26–37MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institut für Wirtschaftstheorie und Operations ResearchUniversität KarlsruheKarlsruheGermany

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