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On the Choice-Based Linear Programming Model for Network Revenue Management

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  • Qian Liu

    ()
    (Industrial Engineering and Logistics Management Department, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Garrett van Ryzin

    ()
    (Graduate School of Business, Columbia University, New York, New York 10027)

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    Abstract

    Gallego et al. [Gallego, G., G. Iyengar, R. Phillips, A. Dubey. 2004. Managing flexible products on a network. CORC Technical Report TR-2004-01, Department of Industrial Engineering and Operations Research, Columbia University, New York.] recently proposed a choice-based deterministic linear programming model (CDLP) for network revenue management (RM) that parallels the widely used deterministic linear programming (DLP) model. While they focused on analyzing "flexible products"--a situation in which the provider has the flexibility of using a collection of products (e.g., different flight times and/or itineraries) to serve the same market demand (e.g., an origin-destination connection)--their approach has broader implications for understanding choice-based RM on a network. In this paper, we explore the implications in detail. Specifically, we characterize optimal offer sets (sets of available network products) by extending to the network case a notion of "efficiency" developed by Talluri and van Ryzin [Talluri, K. T., G. J. van Ryzin. 2004. Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50 15-33.] for the single-leg, choice-based RM problem. We show that, asymptotically, as demand and capacity are scaled up, only these efficient sets are used in an optimal policy. This analysis suggests that efficiency is a potentially useful approach for identifying "good" offer sets on networks, as it is in the case of single-leg problems. Second, we propose a practical decomposition heuristic for converting the static CDLP solution into a dynamic control policy. The heuristic is quite similar to the familiar displacement-adjusted virtual nesting (DAVN) approximation used in traditional network RM, and it significantly improves on the performance of the static LP solution. We illustrate the heuristic on several numerical examples.

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    Bibliographic Info

    Article provided by INFORMS in its journal Manufacturing & Service Operations Management.

    Volume (Year): 10 (2008)
    Issue (Month): 2 (October)
    Pages: 288-310

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    Handle: RePEc:inm:ormsom:v:10:y:2008:i:2:p:288-310

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    Related research

    Keywords: network revenue management; choice behavior; multinomial logit choice model; dynamic programming; linear programming;

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    Cited by:
    1. Gönsch, Jochen & Koch, Sebastian & Steinhardt, Claudius, 2014. "Revenue management with flexible products: The value of flexibility and its incorporation into DLP-based approaches," International Journal of Production Economics, Elsevier, vol. 153(C), pages 280-294.
    2. Summit Kunnumkal & Kalyan Talluri, 2012. "A New Compact Linear Programming Formulation for Choice Network Revenue Management," Working Papers 677, Barcelona Graduate School of Economics.
    3. Steinhardt, Claudius & Gönsch, Jochen, 2012. "Integrated revenue management approaches for capacity control with planned upgrades," European Journal of Operational Research, Elsevier, vol. 223(2), pages 380-391.
    4. Meissner, Joern & Strauss, Arne, 2012. "Improved bid prices for choice-based network revenue management," European Journal of Operational Research, Elsevier, vol. 217(2), pages 417-427.
    5. Jochen Goensch & Claudius Steinhardt, 2013. "Using Dynamic Programming Decomposition for Revenue Management with Opaque Products," BuR - Business Research, German Academic Association for Business Research, vol. 6(1), pages 94-115, May.
    6. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the Tractability of the Piecewiselinear Approximation for General Discrete-Choice Network Revenue Management," Working Papers 749, Barcelona Graduate School of Economics.
    7. Weaver, Robert D. & Moon, Yongma, 2011. "Pricing Perishables," 2011 International European Forum, February 14-18, 2011, Innsbruck-Igls, Austria 122007, International European Forum on Innovation and System Dynamics in Food Networks.
    8. Joern Meissner & Arne Strauss & Kalyan Talluri, 2011. "An Enhanced Concave Program Relaxation for Choice Network Revenue Management," Working Papers MRG/0020, Department of Management Science, Lancaster University, revised Jan 2011.
    9. 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.
    10. Arne Strauss & Kalyan Talluri, 2012. "A tractable consideration set structure for network revenue management," Economics Working Papers 1303, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2012.
    11. Houyuan Jiang & Zhan Pang, 2011. "Network capacity management under competition," Computational Optimization and Applications, Springer, vol. 50(2), pages 287-326, October.
    12. 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.

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