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Bid-Price Controls for Network Revenue Management: Martingale Characterization of Optimal Bid Prices

Mustafa Akan, Barí Ata

Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213
Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208
akan{at}cmu.edu, http://public.tepper.cmu.edu/facultydirectory/facultydirectoryprofile.aspx?id=286
b-ata{at}kellogg.northwestern.edu, http://www.kellogg.northwestern.edu/faculty/ata/personal

We consider a continuous-time, rate-based model of network revenue management. Under mild assumptions, we construct a simple -optimal bid-price control, which can be viewed as a perturbation of a bid-price control in the classical sense [Williamson, E. L. 1992. Airline network seat control. Ph.D. thesis, MIT, Cambridge, MA]. We show that the associated bid-price process forms a martingale and the corresponding booking controls converge in an appropriate sense to an optimal control as tends to 0. Moreover, we show that there exists an optimal generalized bid-price control, where the bid-price process forms a martingale and is used in conjunction with a capacity usage limit process. We also discuss its connection to the bid-price controls in the classical sense and sufficient conditions for the (near) optimality of the latter.

Key Words: bid-price controls; network revenue management; martingales
History: Received: January 20, 2007; revision received: January 14, 2009;