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A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems

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  • Ralph W. Swain

    (The Ohio State University)

Abstract

This paper presents a new approach to determining the optimal facility locations for uncapacitated location problems in two stages. First, it is shown that a subset of all solutions to the uncapacitated public facility location problem can be obtained by considering a closely related private location problem. The exact nature of the problem is established using the Generalized Lagrange Multiplier results given by Everett. In the second section of the paper a particularly efficient parametric decomposition algorithm, which is based on the results of the first section, is presented. Computational results are given which summarize the current level of experience with the algorithm.

Suggested Citation

  • Ralph W. Swain, 1974. "A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems," Management Science, INFORMS, vol. 21(2), pages 189-198, October.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:2:p:189-198
    DOI: 10.1287/mnsc.21.2.189
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    Cited by:

    1. C. Arbib & F. Marinelli, 2009. "Exact and Asymptotically Exact Solutions for a Class of Assortment Problems," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 13-25, February.
    2. Diego Ruiz-Hernández & Javier Elizalde & David Delgado-Gómez, 2017. "Cournot–Stackelberg games in competitive delocation," Annals of Operations Research, Springer, vol. 256(1), pages 149-170, September.
    3. Daniel Serra & Charles Revelle & Ken Rosing, 1999. "Surviving in a competitive spatial market: The threshold capture model," Economics Working Papers 359, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Marianov, Vladimir & Serra, Daniel, 2001. "Hierarchical location-allocation models for congested systems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 195-208, November.
    5. Monabbati, Ehsan & Kakhki, Hossein Taghizadeh, 2015. "On a class of subadditive duals for the uncapacitated facility location problem," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 118-131.
    6. Galvao, Roberto D. & Acosta Espejo, Luis Gonzalo & Boffey, Brian & Yates, Derek, 2006. "Load balancing and capacity constraints in a hierarchical location model," European Journal of Operational Research, Elsevier, vol. 172(2), pages 631-646, July.
    7. Sorensen, Paul & Church, Richard, 2010. "Integrating expected coverage and local reliability for emergency medical services location problems," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 8-18, March.
    8. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Rosing, K. E. & ReVelle, C. S. & Schilling, D. A., 1999. "A gamma heuristic for the p-median problem," European Journal of Operational Research, Elsevier, vol. 117(3), pages 522-532, September.
    10. Rafael Bernardo Carmona-Benítez, 2020. "Dimensionality-reduction Procedure for the Capacitated p-Median Transportation Inventory Problem," Mathematics, MDPI, vol. 8(4), pages 1-16, March.
    11. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.

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