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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Joern Meissner & Arne Strauss & Kalyan Talluri, 2011.
"An Enhanced Concave Program Relaxation for Choice Network Revenue Management,"
MRG/0020, Department of Management Science, Lancaster University, revised Jan 2011.
- Joern Meissner & Arne Strauss & Kalyan Talluri, 2011. "An Enhanced Concave Program Relaxation for Choice Network Revenue Management," Working Papers 534, Barcelona Graduate School of Economics.
- 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.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:1303. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.