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An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

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  • John Penuel
  • J. Cole Smith
  • Yang Yuan

Abstract

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • John Penuel & J. Cole Smith & Yang Yuan, 2010. "An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 391-402, August.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:5:p:391-402
    DOI: 10.1002/nav.20401
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    References listed on IDEAS

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    1. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    2. Gilbert Laporte & François V. Louveaux & Luc van Hamme, 1994. "Exact Solution to a Location Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 28(2), pages 95-103, May.
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