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Minisum Location with Closest Euclidean Distances

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  • J. Brimberg
  • G.O. Wesolowsky

Abstract

This paper considers the problem of locating a facility not among demand points, as is usually the case, but among demand regions which could be market areas. The objective is to find the location that minimizes the sum of weighted Euclidean distances to the closest points of the demand regions. It is assumed that internal distribution within the areas is “someone else's concern”. A number of properties of the problem are derived and algorithms for solving the problem are suggested. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • J. Brimberg & G.O. Wesolowsky, 2002. "Minisum Location with Closest Euclidean Distances," Annals of Operations Research, Springer, vol. 111(1), pages 151-165, March.
    • Handle: RePEc:spr:annopr:v:111:y:2002:i:1:p:151-165:10.1023/a:1020901719463
    DOI: 10.1023/A:1020901719463
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    Cited by:

    1. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    2. Jack Brimberg & Henrik Juel & Mark-Christoph Körner & Anita Schöbel, 2014. "Locating an axis-parallel rectangle on a Manhattan plane," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 185-207, April.
    3. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
    4. Jianlin Jiang & Xiaoming Yuan, 2012. "A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand," Computational Optimization and Applications, Springer, vol. 51(3), pages 1275-1295, April.
    5. Nazlı Dolu & Umur Hastürk & Mustafa Kemal Tural, 2020. "Solution methods for a min–max facility location problem with regional customers considering closest Euclidean distances," Computational Optimization and Applications, Springer, vol. 75(2), pages 537-560, March.
    6. André Berger & Alexander Grigoriev & Andrej Winokurow, 2017. "An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions," Computational Optimization and Applications, Springer, vol. 68(3), pages 661-669, December.

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