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Value-At-Risk Optimal Policies for Revenue Management Problems

Author

Listed:
  • Matthias Koenig

    (Department of Management Science, Lancaster University Management School)

  • Joern Meissner

    (Department of Management Science, Lancaster University Management School)

Abstract

Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We state the underlying problem as a Markov decision process and provide a computational method for computing policies, which optimise the value-at-risk for a given confidence level. This is achieved by computing dynamic programming solutions for a set of target revenue values and combining the solutions in order to attain the requested multi-stage risk-averse policy. Numerical examples and comparison with other risk-sensitive approaches are discussed.

Suggested Citation

  • Matthias Koenig & Joern Meissner, 2010. "Value-At-Risk Optimal Policies for Revenue Management Problems," Working Papers MRG/0018, Department of Management Science, Lancaster University, revised Dec 2014.
    • Handle: RePEc:lms:mansci:mrg-0018
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    2. Schlosser, Rainer & Gönsch, Jochen, 2023. "Risk-averse dynamic pricing using mean-semivariance optimization," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1151-1163.
    3. Terciyanlı, Erman & Avṣar, Zeynep Müge, 2019. "Alternative risk-averse approaches for airline network revenue management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 27-46.
    4. Peter Buchholz & Iryna Dohndorf, 2021. "A multi-objective approach for PH-graphs with applications to stochastic shortest paths," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 153-178, February.
    5. Lin, Edward M.H. & Sun, Edward W. & Yu, Min-Teh, 2020. "Behavioral data-driven analysis with Bayesian method for risk management of financial services," International Journal of Production Economics, Elsevier, vol. 228(C).
    6. Sebastian Koch & Jochen Gönsch & Michael Hassler & Robert Klein, 2016. "Practical decision rules for risk-averse revenue management using simulation-based optimization," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(6), pages 468-487, December.
    7. Jochen Gönsch & Michael Hassler & Rouven Schur, 2018. "Optimizing conditional value-at-risk in dynamic pricing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 711-750, July.
    8. Schlosser, Rainer & Gönsch, Jochen, 2025. "Mean-variance optimization in finite horizon Markov decision processes and its application to revenue management," European Journal of Operational Research, Elsevier, vol. 325(3), pages 516-524.
    9. Catherine Cleophas & Daniel Kadatz & Sebastian Vock, 2017. "Resilient revenue management: a literature survey of recent theoretical advances," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 16(5), pages 483-498, October.
    10. Schur, Rouven & Gönsch, Jochen & Hassler, Michael, 2019. "Time-consistent, risk-averse dynamic pricing," European Journal of Operational Research, Elsevier, vol. 277(2), pages 587-603.
    11. Gönsch, Jochen, 2017. "A survey on risk-averse and robust revenue management," European Journal of Operational Research, Elsevier, vol. 263(2), pages 337-348.
    12. Klein, Robert & Koch, Sebastian & Steinhardt, Claudius & Strauss, Arne K., 2020. "A review of revenue management: Recent generalizations and advances in industry applications," European Journal of Operational Research, Elsevier, vol. 284(2), pages 397-412.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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