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New heuristic methods for the capacitated multi‐facility Weber problem

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  • Necati Aras
  • İ. Kuban Altınel
  • Metin Orbay

Abstract

In this paper we consider the capacitated multi‐facility Weber problem with the Euclidean, squared Euclidean, and ℓp‐distances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006

Suggested Citation

  • Necati Aras & İ. Kuban Altınel & Metin Orbay, 2007. "New heuristic methods for the capacitated multi‐facility Weber problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 21-32, February.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:1:p:21-32
    DOI: 10.1002/nav.20176
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    References listed on IDEAS

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    1. P. Hansen & J. Perreur & J.-F. Thisse, 1980. "Technical Note—Location Theory, Dominance, and Convexity: Some Further Results," Operations Research, INFORMS, vol. 28(5), pages 1241-1250, October.
    2. Leon Cooper, 1972. "The Transportation-Location Problem," Operations Research, INFORMS, vol. 20(1), pages 94-108, February.
    3. Hanif D. Sherali & Intesar Al-Loughani & Shivaram Subramanian, 2002. "Global Optimization Procedures for the Capacitated Euclidean and l p Distance Multifacility Location-Allocation Problems," Operations Research, INFORMS, vol. 50(3), pages 433-448, June.
    4. Hanif D. Sherali & Frederick L. Nordai, 1988. "NP-Hard, Capacitated, Balanced p -Median Problems on a Chain Graph with a Continuum of Link Demands," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 32-49, February.
    5. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    6. Hanif D. Sherali & Cihan H. Tuncbilek, 1992. "A squared‐euclidean distance location‐allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 447-469, June.
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    Cited by:

    1. 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.
    2. Cristiana L. Lara & Francisco Trespalacios & Ignacio E. Grossmann, 2018. "Global optimization algorithm for capacitated multi-facility continuous location-allocation problems," Journal of Global Optimization, Springer, vol. 71(4), pages 871-889, August.
    3. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.

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