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A tractable consideration set structure for network revenue management




Models incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular in assortment optimization and revenue management. The dynamic program for these models is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. When there are products that are being considered for purchase by more than one customer segment, CDLP is difficult to solve since column generation is known to be NP-hard. However, recent research indicates that a formulation based on segments with cuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In this paper we investigate the structure of the consideration sets that make the two formulations exactly equal. We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give a counterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation. We derive two classes of valid inequalities called flow and synchronization inequalities to further improve (SDCP+), based on cycles in the consideration set structure. We give a numeric study showing the performance of these cycle-based cuts.

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  • 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.
  • Handle: RePEc:upf:upfgen:1303

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    References listed on IDEAS

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


    discrete-choice models; network revenue management; consideration sets;

    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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