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An enhanced concave program relaxation for choice network revenue management

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Abstract

The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.

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  • Joern Meissner & Arne Strauss & Kalyan Talluri, 2011. "An enhanced concave program relaxation for choice network revenue management," Economics Working Papers 1259, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2011.
  • Handle: RePEc:upf:upfgen:1259
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. Arne Strauss & Kalyan Talluri, 2012. "A Tractable Consideration Set Structure for Network Revenue Management," Working Papers 606, Barcelona Graduate School of Economics.
    3. Sumit Kunnumkal & Kalyan Talluri, 2012. "A New Compact Linear Programming Formulation for Choice Network Revenue Management," Working Papers 677, Barcelona Graduate School of Economics.
    4. 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.
    5. 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.

    More about this item

    Keywords

    discrete-choice models; network revenue management; optimization;

    JEL classification:

    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing
    • L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

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