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An Enhanced Concave Program Relaxation for Choice Network Revenue Management

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Author Info

  • Joern Meissner

    (Department of Management Science, Lancaster University Management School)

  • Arne Strauss

    (Department of Management Science, Lancaster University Management School)

  • Kalyan Talluri

    (ICREA & Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain)

Abstract

The network choice revenue management problem models customers as choosing from an offerset, 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 valid inequalities called product cuts, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called kSDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product cuts and the kSDCP method are very simple and easy to implement, work with general discrete choice models and are applicable to the case of overlapping segment consideration sets. In our computational testing SDCP with product cuts achieves the CDLP value at a fraction of the CPU time taken by column generation and hence has the potential to be scalable to industrial-size problems.

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Bibliographic Info

Paper provided by Department of Management Science, Lancaster University in its series Working Papers with number MRG/0020.

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Length: 20 pages
Date of creation: Jan 2011
Date of revision: Jan 2011
Handle: RePEc:lms:mansci:mrg-0020

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Postal: LANCASTER LA1 4YX
Web page: http://www.lums.lancs.ac.uk/departments/ManSci/
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Related research

Keywords: operations research; marketing; bid prices; yield management; heuristics; discrete-choice; network revenue management;

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References

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  1. Joern Meissner & Arne Strauss, 2008. "Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice," Working Papers MRG/0008, Department of Management Science, Lancaster University, revised Apr 2010.
  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. Summit 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.
  3. Joern Meissner & Arne Strauss, 2008. "Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice," Working Papers MRG/0008, Department of Management Science, Lancaster University, revised Apr 2010.
  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. Arne Strauss & Kalyan Talluri, 2012. "A Tractable Consideration Set Structure for Network Revenue Management," Working Papers 606, Barcelona Graduate School of Economics.

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