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The multi-source Weber problem with constant opening cost

Author

Listed:
  • J Brimberg

    (Royal Military College of Canada
    GERAD)

  • N Mladenovic

    (GERAD
    Mathematical Institute)

  • S Salhi

    (The University of Birmingham)

Abstract

A constant fixed cost of establishing a facility is introduced within the framework of minisum facility location in the continuous space. The solution method developed uses a multi-phase heuristic that first solves a discrete version of the problem by existing methods to obtain an estimate of the optimal number of facilities. Some results are presented for test problems taken from the literature and compared with best-known solutions of the multi-source Weber problem with the addition of the appropriate fixed costs.

Suggested Citation

  • J Brimberg & N Mladenovic & S Salhi, 2004. "The multi-source Weber problem with constant opening cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 640-646, June.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:6:d:10.1057_palgrave.jors.2601754
    DOI: 10.1057/palgrave.jors.2601754
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    References listed on IDEAS

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    1. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    2. Margaret L. Brandeau & Samuel S. Chiu, 1989. "An Overview of Representative Problems in Location Research," Management Science, INFORMS, vol. 35(6), pages 645-674, June.
    3. Leon Cooper, 1963. "Location-Allocation Problems," Operations Research, INFORMS, vol. 11(3), pages 331-343, June.
    4. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 383-399, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Trampont, M. & Destré, C. & Faye, A., 2011. "Solving a continuous local access network design problem with a stabilized central column generation approach," European Journal of Operational Research, Elsevier, vol. 214(3), pages 546-558, November.
    2. Chandra Ade Irawan & Martino Luis & Said Salhi & Arif Imran, 2019. "The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem," Annals of Operations Research, Springer, vol. 275(2), pages 367-392, April.
    3. Chandra Ade Irawan & Said Salhi & Kusmaningrum Soemadi, 2020. "The continuous single-source capacitated multi-facility Weber problem with setup costs: formulation and solution methods," Journal of Global Optimization, Springer, vol. 78(2), pages 271-294, October.
    4. He, Shawei & Marc Kilgour, D. & Hipel, Keith W., 2017. "A general hierarchical graph model for conflict resolution with application to greenhouse gas emission disputes between USA and China," European Journal of Operational Research, Elsevier, vol. 257(3), pages 919-932.
    5. Venkateshan, Prahalad & Ballou, Ronald H. & Mathur, Kamlesh & Maruthasalam, Arulanantha P.P., 2017. "A Two-echelon joint continuous-discrete location model," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1028-1039.
    6. Jean-Paul Arnaout & John Khoury, 2022. "Adaptation of WO to the Euclidean location-allocation with unknown number of facilities," Annals of Operations Research, Springer, vol. 315(1), pages 57-72, August.
    7. Brimberg, Jack & Drezner, Zvi & Mladenović, Nenad & Salhi, Said, 2014. "A new local search for continuous location problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 256-265.
    8. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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