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Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem

Author

Listed:
  • N Aras

    (Boğaziçi University)

  • M Orbay

    (Casual Male Retail Group Inc.)

  • I K Altinel

    (Boğaziçi University)

Abstract

In this paper, we consider the capacitated multi-facility Weber problem with rectilinear distance. 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 rectilinear distance separating them. We first give a new mixed integer linear programming formulation of the problem by making use of a well-known necessary condition for the optimal facility locations. We then propose new heuristic solution methods based on this formulation. Computational results on benchmark instances indicate that the new methods can provide very good solutions within a reasonable amount of computation time.

Suggested Citation

  • N Aras & M Orbay & I K Altinel, 2008. "Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 64-79, January.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:1:d:10.1057_palgrave.jors.2602262
    DOI: 10.1057/palgrave.jors.2602262
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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.
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    4. 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.
    5. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    6. 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.
    7. 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.
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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. Masashi Miyagawa, 2012. "Joint distribution of distances to the first and the second nearest facilities," Journal of Geographical Systems, Springer, vol. 14(2), pages 209-222, April.
    3. Miyagawa, Masashi, 2010. "Distributions of rectilinear deviation distance to visit a facility," European Journal of Operational Research, Elsevier, vol. 205(1), pages 106-112, August.
    4. 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.
    5. 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.
    6. 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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