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A New Compact Linear Programming Formulation for Choice Network Revenue Management

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  • Summit Kunnumkal
  • Kalyan Talluri
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    Abstract

    The choice network revenue management model incorporates customer purchase behavior as a function of the offered products, and is the appropriate model for airline and hotel network revenue management, dynamic sales of bundles, and dynamic assortment optimization. The optimization problem is a stochastic dynamic program and is intractable. A certainty equivalence relaxation of the dynamic program, called the choice deterministic linear program (CDLP) is usually used to generate dynamic controls. Recently, a compact linear programming formulation of this linear program was given for the multi-segment multinomial-logit (MNL) model of customer choice with non-overlapping consideration sets. Our objective is to obtain a tighter bound than this formulation while retaining the appealing properties of a compact linear programming representation. To this end, it is natural to consider the affine relaxation of the dynamic program. We first show that the affine relaxation is NP-complete even for a single-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a new compact linear program that approximates the dynamic programming value function better than CDLP, provably between the CDLP value and the affine relaxation, and often coming close to the latter in our numerical experiments. When the segment consideration sets overlap, we show that some strong equalities called product cuts developed for the CDLP remain valid for our new formulation. Finally we perform extensive numerical comparisons on the various bounds to evaluate their performance.

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    Bibliographic Info

    Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 677.

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    Date of creation: Dec 2012
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    Handle: RePEc:bge:wpaper:677

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    Related research

    Keywords: dynamic programming; network revenue management; approximation algorithms; discrete choice models;

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    References

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    1. Joern Meissner & Arne Strauss & Kalyan Talluri, 2011. "An Enhanced Concave Program Relaxation for Choice Network Revenue Management," Working Papers, Department of Management Science, Lancaster University MRG/0020, Department of Management Science, Lancaster University, revised Jan 2011.
    2. Tudor Bodea & Mark Ferguson & Laurie Garrow, 2009. "Data Set--Choice-Based Revenue Management: Data from a Major Hotel Chain," Manufacturing & Service Operations Management, INFORMS, INFORMS, vol. 11(2), pages 356-361, December.
    3. Qian Liu & Garrett van Ryzin, 2008. "On the Choice-Based Linear Programming Model for Network Revenue Management," Manufacturing & Service Operations Management, INFORMS, INFORMS, vol. 10(2), pages 288-310, October.
    4. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, Elsevier, vol. 216(2), pages 459-468.
    5. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, INFORMS, vol. 50(1), pages 15-33, January.
    6. Arne Strauss & Kalyan Talluri, 2012. "A Tractable Consideration Set Structure for Network Revenue Management," Working Papers 606, Barcelona Graduate School of Economics.
    7. Arne Strauss & Kalyan Talluri, 2012. "A tractable consideration set structure for network revenue management," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1303, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2012.
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    Cited by:
    1. 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.
    2. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1409, Department of Economics and Business, Universitat Pompeu Fabra.

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