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On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

Author

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  • Sumit Kunnumkal
  • Kalyan Talluri
Abstract
The choice network revenue management (RM) model incorporates customer purchase behavior as customers purchasing products with certain probabilities that are a function of the offered assortment of products, and is the appropriate model for airline and hotel network revenue management, dynamic sales of bundles, and dynamic assortment optimization. The underlying stochastic dynamic program is intractable and even its certainty-equivalence approximation, in the form of a linear program called Choice Deterministic Linear Program (CDLP) is difficult to solve in most cases. The separation problem for CDLP is NP-complete for MNL with just two segments when their consideration sets overlap; the affine approximation of the dynamic program is NP-complete for even a single-segment MNL. This is in contrast to the independentclass (perfect-segmentation) case where even the piecewise-linear approximation has been shown to be tractable. In this paper we investigate the piecewise-linear approximation for network RM under a general discrete-choice model of demand. We show that the gap between the CDLP and the piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinear approximation is polynomially-time solvable for a fixed consideration set size, bringing it into the realm of tractability for small consideration sets; small consideration sets are a reasonable modeling tradeoff in many practical applications. Our solution relies on showing that for any discrete-choice model the separation problem for the linear program of the piecewise-linear approximation can be solved exactly by a Lagrangian relaxation. We give modeling extensions and show by numerical experiments the improvements from using piecewise-linear approximation functions.

Suggested Citation

  • Sumit Kunnumkal & Kalyan Talluri, 2014. "On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management," Economics Working Papers 1409, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1409
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    References listed on IDEAS

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    1. Tudor Bodea & Mark Ferguson & Laurie Garrow, 2009. "Data Set--Choice-Based Revenue Management: Data from a Major Hotel Chain," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 356-361, December.
    2. 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.
    3. 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.
    4. Qian Liu & Garrett van Ryzin, 2008. "On the Choice-Based Linear Programming Model for Network Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 288-310, October.
    5. Dan Zhang & Daniel Adelman, 2009. "An Approximate Dynamic Programming Approach to Network Revenue Management with Customer Choice," Transportation Science, INFORMS, vol. 43(3), pages 381-394, August.
    6. 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.
    7. Sumit Kunnumkal & Kalyan Talluri, 2012. "A new compact linear programming formulation for choice network revenue management," Economics Working Papers 1349, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Hauser, John R & Wernerfelt, Birger, 1990. "An Evaluation Cost Model of Consideration Sets," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 16(4), pages 393-408, March.
    9. Gustavo Vulcano & Garrett van Ryzin & Wassim Chaar, 2010. "OM Practice--Choice-Based Revenue Management: An Empirical Study of Estimation and Optimization," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 371-392, February.
    10. Paat Rusmevichientong & David Shmoys & Chaoxu Tong & Huseyin Topaloglu, 2014. "Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters," Production and Operations Management, Production and Operations Management Society, vol. 23(11), pages 2023-2039, November.
    11. Sumit Kunnumkal & Kalyan Talluri, 2011. "Equivalence of Piecewise-Linear Approximation and Lagrangian Relaxation for Network Revenue Management," Working Papers 608, Barcelona School of Economics.
    12. Kalyan Talluri, 2009. "A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters," Economics Working Papers 1141, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Sumit Kunnumkal & Kalyan Talluri, 2012. "A New Compact Linear Programming Formulation for Choice Network Revenue Management," Working Papers 677, Barcelona School of Economics.
    14. Constantinos Maglaras & Joern Meissner, 2006. "Dynamic Pricing Strategies for Multiproduct Revenue Management Problems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 136-148, July.
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    Cited by:

    1. 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.
    2. 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.

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    More about this item

    Keywords

    Optimization Techniques; Programming Models; Dynamic Analysis; Air Transportation ; Sports; Gambling; Recreation; Tourism; Production Management;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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