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On the Choice-Based Linear Programming Model for Network Revenue Management

  • Qian Liu

    ()

    (Industrial Engineering and Logistics Management Department, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Garrett van Ryzin

    ()

    (Graduate School of Business, Columbia University, New York, New York 10027)

Registered author(s):

    Gallego et al. [Gallego, G., G. Iyengar, R. Phillips, A. Dubey. 2004. Managing flexible products on a network. CORC Technical Report TR-2004-01, Department of Industrial Engineering and Operations Research, Columbia University, New York.] recently proposed a choice-based deterministic linear programming model (CDLP) for network revenue management (RM) that parallels the widely used deterministic linear programming (DLP) model. While they focused on analyzing "flexible products"--a situation in which the provider has the flexibility of using a collection of products (e.g., different flight times and/or itineraries) to serve the same market demand (e.g., an origin-destination connection)--their approach has broader implications for understanding choice-based RM on a network. In this paper, we explore the implications in detail. Specifically, we characterize optimal offer sets (sets of available network products) by extending to the network case a notion of "efficiency" developed by Talluri and van Ryzin [Talluri, K. T., G. J. van Ryzin. 2004. Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50 15-33.] for the single-leg, choice-based RM problem. We show that, asymptotically, as demand and capacity are scaled up, only these efficient sets are used in an optimal policy. This analysis suggests that efficiency is a potentially useful approach for identifying "good" offer sets on networks, as it is in the case of single-leg problems. Second, we propose a practical decomposition heuristic for converting the static CDLP solution into a dynamic control policy. The heuristic is quite similar to the familiar displacement-adjusted virtual nesting (DAVN) approximation used in traditional network RM, and it significantly improves on the performance of the static LP solution. We illustrate the heuristic on several numerical examples.

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    Article provided by INFORMS in its journal Manufacturing & Service Operations Management.

    Volume (Year): 10 (2008)
    Issue (Month): 2 (October)
    Pages: 288-310

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    Handle: RePEc:inm:ormsom:v:10:y:2008:i:2:p:288-310
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