×

A refined deterministic linear program for the network revenue management problem with customer choice behavior. (English) Zbl 1152.90488

Summary: We present a new deterministic linear program for the network revenue management problem with customer choice behavior. The novel aspect of our linear program is that it naturally generates bid prices that depend on how much time is left until the time of departure. Similar to the earlier linear program used by G. van Ryzin and Q. Liu [M & SOM 10, 288–310 (2008)], the optimal objective value of our linear program provides an upper bound on the optimal total expected revenue over the planning horizon. In addition, the percent gap between the optimal objective value of our linear program and the optimal total expected revenue diminishes in an asymptotic regime where the leg capacities and the number of time periods in the planning horizon increase linearly with the same rate. Computational experiments indicate that when compared with the linear program that appears in the existing literature, our linear program can provide tighter upper bounds, and the control policies that are based on our linear program can obtain higher total expected revenues.

MSC:

90B50 Management decision making, including multiple objectives
90C05 Linear programming
91B42 Consumer behavior, demand theory
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] P. P.Belobaba, Air travel demand and airline seat inventory management, Technical Report FTL-R87-8, Flight Trans Lab, Massachusetts Institute of Technology, Cambridge, MA, 1987.
[2] Belobaba, Comparing decis rules that incorporate customer diversion in perishable asset revenue management situations, Decis Sci 27 pp 343– (1996) · doi:10.1111/j.1540-5915.1996.tb00856.x
[3] Bront, A column generation algorithm for choice-based network revenue management, Oper Res (2007)
[4] G.Gallego,G.Iyengar,R.Phillips, and A.Dubey, Managing flexible products on a network CORC, Technical Report TR-2004-01, Columbia University, 2004.
[5] S.Kunnumkal and H.Topaloglu, An alternative to Clark and Scarf’s balance assumption for inventory distribution systems, Technical Report, Cornell University, School of Operations Research and Industrial Engineering, 2006, Available at http://legacy.orie.cornell.edu/huseyin/publications/publications.html. · Zbl 1141.90330
[6] Talluri, An analysis of bid-price controls for network revenue management, Management Sci 44 pp 1577– (1998) · Zbl 1004.90042
[7] Talluri, Revenue management under a general discrete choice model of consumer behavior, Management Sci 50 pp 15– (2004) · Zbl 1168.91427
[8] H.Topaloglu,S.Kunnumkal, Computing time-dependent bid-prices in network revenue management problems, Technical Report, Cornell University, School of Operations Research and Industrial Engineering, 2006, Available at http://legacy.orie.cornell.edu/huseyin/publications/publications.html.
[9] van Ryzin, On the choice-based linear programming model for network revenue management, M&SOM 10 pp 288– (2008) · doi:10.1287/msom.1070.0169
[10] van Ryzin, Computing virtual nesting controls for network revenue management under customer choice behavior, M&SOM (2007)
[11] Zhang, An approximate dynamic programming approach to network revenue management with customer choice, University of Chicago, Trans Sci (2006)
[12] Zhang, Revenue management for parallel flights with customer choice behavior, Oper Res 53 pp 415– (2005) · Zbl 1165.90342
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.