IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/608.html
   My bibliography  Save this paper

Equivalence of Piecewise-Linear Approximation and Lagrangian Relaxation for Network Revenue Management

Author

Listed:
  • Sumit Kunnumkal
  • Kalyan Talluri

Abstract

The network revenue management (RM) problem arises in airline, hotel, media, and other industries where the sale products use multiple resources. It can be formulated as a stochastic dynamic program but the dynamic program is computationally intractable because of an exponentially large state space, and a number of heuristics have been proposed to approximate it. Notable amongst these (both for their revenue performance, as well as their theoretically sound basis) are approximate dynamic programming methods that approximate the value function by basis functions (both affine functions as well as piecewise-linear functions have been proposed for network RM) and decomposition methods that relax the constraints of the dynamic program to solve simpler dynamic programs (such as the Lagrangian relaxation methods). In this paper we show that these two seemingly distinct approaches coincide for the network RM dynamic program, i.e., the piecewise-linear approximation method and the Lagrangian relaxation method are one and the same.

Suggested Citation

  • Sumit Kunnumkal & Kalyan Talluri, 2011. "Equivalence of Piecewise-Linear Approximation and Lagrangian Relaxation for Network Revenue Management," Working Papers 608, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:608
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/608.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the Tractability of the Piecewiselinear Approximation for General Discrete-Choice Network Revenue Management," Working Papers 749, Barcelona Graduate School of Economics.
    2. Galí, Jordi & Monacelli, Tommaso, 2014. "Understanding the Gains from Wage Flexibility: The Exchange Rate Connection," CEPR Discussion Papers 9806, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    network revenue management; linear programming; approximate dynamic programming; Lagrangian relaxation methods;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bge:wpaper:608. 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: (Bruno Guallar). General contact details of provider: http://edirc.repec.org/data/bargses.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.