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Technical Note—Location Theory, Dominance, and Convexity: Some Further Results

Author

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  • P. Hansen

    (Institut d'Economie Scientifique et de Gestion, Lille, France, and Faculté Universitaire Càtholique de Mons, Mons, Belgium)

  • J. Perreur

    (Université de Dijon, Dijon, France)

  • J.-F. Thisse

    (Université Càtholique de Louvain, Louvain-La-Neuve, Belgium)

Abstract

This note presents some generalizations of results on the single norm-one facility location problem due to Wendell and Hurter. It is first shown that a solution to the multifacility location problem with a single norm can be found in the convex hull of sources and destinations. In the particular case of the rectilinear norm, only intersection points belonging to this convex hull need be considered. When different 1 p -norms are envisaged, the octagonal hull contains one solution to the single facility location problem. This result is also extended to the multifacility case.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:5:p:1241-1250
    DOI: 10.1287/opre.28.5.1241
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    Cited by:

    1. 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.
    2. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2021. "Directional approach to gradual cover: the continuous case," Computational Management Science, Springer, vol. 18(1), pages 25-47, January.
    3. Roland Rathelot & Patrick Sillard, 2008. "The Importance of Local Corporate Taxes in Business Location Decisions: Evidence From French Micro Data," Economic Journal, Royal Economic Society, vol. 118(527), pages 499-514, March.
    4. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
    5. 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.
    6. E. Carrizosa & J. B. G. Frenk, 1998. "Dominating Sets for Convex Functions with Some Applications," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 281-295, February.
    7. Blanco, Víctor & Puerto, Justo, 2021. "Covering problems with polyellipsoids: A location analysis perspective," European Journal of Operational Research, Elsevier, vol. 289(1), pages 44-58.
    8. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    9. G. Wanka, 2000. "Multiobjective Control Approximation Problems: Duality and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 457-475, May.
    10. 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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