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Reductions of non-separable approximate linear programs for network revenue management

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  • Laumer, Simon
  • Barz, Christiane

Abstract

We suggest a novel choice of non-separable basis functions for an approximate linear programming approach to the well-known network revenue management problem. Considering non-separability is particularly important when interdependencies between resources are large. Such a situation can be illustrated for example by a bus line, where different origin-destination pairs have many overlapping segments. Traditional separable approximation approaches tend to ignore the resulting interactions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:309:y:2023:i:1:p:252-270
    DOI: 10.1016/j.ejor.2023.01.006
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    References listed on IDEAS

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    1. Yuhang Ma & Paat Rusmevichientong & Mika Sumida & Huseyin Topaloglu, 2020. "An Approximation Algorithm for Network Revenue Management Under Nonstationary Arrivals," Operations Research, INFORMS, vol. 68(3), pages 834-855, May.
    2. Arne K. Strauss & Kalyan Talluri, 2017. "Tractable Consideration Set Structures for Assortment Optimization and Network Revenue Management," Production and Operations Management, Production and Operations Management Society, vol. 26(7), pages 1359-1368, July.
    3. Huseyin Topaloglu, 2009. "Using Lagrangian Relaxation to Compute Capacity-Dependent Bid Prices in Network Revenue Management," Operations Research, INFORMS, vol. 57(3), pages 637-649, June.
    4. Guillermo Gallego & Richard Ratliff & Sergey Shebalov, 2015. "A General Attraction Model and Sales-Based Linear Program for Network Revenue Management Under Customer Choice," Operations Research, INFORMS, vol. 63(1), pages 212-232, February.
    5. Sumit Kunnumkal & Kalyan Talluri, 2016. "On a Piecewise-Linear Approximation for Network Revenue Management," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 72-91, February.
    6. J. R. Morrison & P. R. Kumar, 1999. "New Linear Program Performance Bounds for Queueing Networks," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 575-597, March.
    7. Sumit Kunnumkal & Kalyan Talluri, 2019. "Choice Network Revenue Management Based on New Tractable Approximations," Transportation Science, INFORMS, vol. 53(6), pages 1591-1608, November.
    8. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
    9. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    10. Kalyan Talluri & Garrett van Ryzin, 1998. "An Analysis of Bid-Price Controls for Network Revenue Management," Management Science, INFORMS, vol. 44(11-Part-1), pages 1577-1593, November.
    11. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    12. Daniela Pucci de Farias & Benjamin Van Roy, 2004. "On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 462-478, August.
    13. Daniel Adelman & Diego Klabjan, 2012. "Computing Near-Optimal Policies in Generalized Joint Replenishment," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 148-164, February.
    14. Chaoxu Tong & Huseyin Topaloglu, 2014. "On the Approximate Linear Programming Approach for Network Revenue Management Problems," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 121-134, February.
    15. William L. Cooper & Tito Homem-de-Mello, 2007. "Some Decomposition Methods for Revenue Management," Transportation Science, INFORMS, vol. 41(3), pages 332-353, August.
    16. Trick, Michael A. & Zin, Stanley E., 1997. "Spline Approximations To Value Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 255-277, January.
    17. Jiannan Ke & Dan Zhang & Huan Zheng, 2019. "An Approximate Dynamic Programming Approach to Dynamic Pricing for Network Revenue Management," Production and Operations Management, Production and Operations Management Society, vol. 28(11), pages 2719-2737, November.
    18. Daniel Adelman, 2007. "Dynamic Bid Prices in Revenue Management," Operations Research, INFORMS, vol. 55(4), pages 647-661, August.
    19. Sumit Kunnumkal & Kalyan Talluri, 2019. "A strong Lagrangian relaxation for general discrete-choice network revenue management," Computational Optimization and Applications, Springer, vol. 73(1), pages 275-310, May.
    20. Jacob B. Feldman & Huseyin Topaloglu, 2017. "Revenue Management Under the Markov Chain Choice Model," Operations Research, INFORMS, vol. 65(5), pages 1322-1342, October.
    21. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    22. Thomas W. M. Vossen & Dan Zhang, 2015. "Reductions of Approximate Linear Programs for Network Revenue Management," Operations Research, INFORMS, vol. 63(6), pages 1352-1371, December.
    23. Adam Diamant & Joseph Milner & Fayez Quereshy, 2018. "Dynamic Patient Scheduling for Multi†Appointment Health Care Programs," Production and Operations Management, Production and Operations Management Society, vol. 27(1), pages 58-79, January.
    24. Hosseinalifam, M. & Marcotte, P. & Savard, G., 2016. "A new bid price approach to dynamic resource allocation in network revenue management," European Journal of Operational Research, Elsevier, vol. 255(1), pages 142-150.
    25. Wuyang Yuan & Lei Nie & Xin Wu & Huiling Fu, 2018. "A dynamic bid price approach for the seat inventory control problem in railway networks with consideration of passenger transfer," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-23, August.
    26. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    27. Daniel Adelman, 2004. "A Price-Directed Approach to Stochastic Inventory/Routing," Operations Research, INFORMS, vol. 52(4), pages 499-514, August.
    28. Diego Klabjan & Daniel Adelman, 2007. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 528-550, August.
    29. 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.
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