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Approximate Linear Programming in Network Revenue Management with Multiple Modes

Author

Listed:
  • David Sayah

    (Johannes Gutenberg University Mainz)

Abstract
Approximate linear programming has been applied to network revenue management problems under the fundamental modeling assumption that products de?ne combinations of one resource bundle and a fare class. We consider products that can have multiple operational modes allowing companies to select the way they want to serve the purchaser of a multi-mode product. We show that the presence of multi-mode products implies a weaker relation between an a?ne approximate linear program (ALP) and a compact reformulation, known as reduction. Consequently, the upper bound on the maximum expected revenue obtained via the reduction is not necessarily as tight as the upper bound produced via the ALP. We further demonstrate that the gap between these two formulations is bounded in general and zero in a particular class of instances, when multi-mode products are ?exible products. For general instances, we exploit a set-packing structure within the reduction in order to improve the upper bound, i.e., we introduce a cutting plane method that strengthens the reduction by separating valid inequalities. Our computational tests indicate that it is possible to halve the gap in not more than 4% of the time needed to solve the ALP via column generation.

Suggested Citation

  • David Sayah, 2015. "Approximate Linear Programming in Network Revenue Management with Multiple Modes," Working Papers 1518, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1518
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1518.pdf
    File Function: First version, 2015
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    References listed on IDEAS

    as
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    Cited by:

    1. Laumer, Simon & Barz, Christiane, 2023. "Reductions of non-separable approximate linear programs for network revenue management," European Journal of Operational Research, Elsevier, vol. 309(1), pages 252-270.
    2. 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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