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An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

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  • Stefano Benati

Abstract

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method. Copyright Kluwer Academic Publishers 2003

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  • Stefano Benati, 2003. "An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 43-58, September.
    • Handle: RePEc:spr:annopr:v:122:y:2003:i:1:p:43-58:10.1023/a:1026182020346
    DOI: 10.1023/A:1026182020346
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    Cited by:

    1. Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    2. Dong-Guen Kim & Yeong-Dae Kim, 2013. "A Lagrangian heuristic algorithm for a public healthcare facility location problem," Annals of Operations Research, Springer, vol. 206(1), pages 221-240, July.
    3. Goldengorin, Boris & Ghosh, Diptesh, 2004. "A Multilevel Search Algorithm for the Maximization of Submodular Functions," Research Report 04A20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    4. repec:dgr:rugsom:04a20 is not listed on IDEAS

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