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Minisum location problem with farthest Euclidean distances

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  • Jian-lin Jiang
  • Ya Xu

Abstract

The paper formulates an extended model of Weber problem in which the customers are represented by convex demand regions. The objective is to generate a site in R 2 that minimizes the sum of weighted Euclidean distances between the new facility and the farthest points of demand regions. This location problem is decomposed into a polynomial number of subproblems: constrained Weber problems (CWPs). A projection contraction method is suggested to solve these CWPs. An algorithm and the complexity analysis are presented. Three techniques of bound test, greedy choice and choice of starting point are adopted to reduce the computational time. The restricted case of the facility is also considered. Preliminary computational results are reported, which shows that with the above three techniques adopted the algorithm is efficient. Copyright Springer-Verlag 2006

Suggested Citation

  • Jian-lin Jiang & Ya Xu, 2006. "Minisum location problem with farthest Euclidean distances," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 285-308, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:285-308
    DOI: 10.1007/s00186-006-0084-2
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    References listed on IDEAS

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    1. P. Hansen & D. Peeters & J.-F. Thisse, 1982. "An Algorithm for a Constrained Weber Problem," Management Science, INFORMS, vol. 28(11), pages 1285-1295, November.
    2. Stefan Nickel & Justo Puerto & Antonio M. Rodriguez-Chia, 2003. "An Approach to Location Models Involving Sets as Existing Facilities," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 693-715, November.
    3. Carrizosa, E. & Munoz-Marquez, M. & Puerto, J., 1998. "The Weber problem with regional demand," European Journal of Operational Research, Elsevier, vol. 104(2), pages 358-365, January.
    4. Arthur P. Hurter, Jr. & Margaret K. Schaefer & Richard E. Wendell, 1975. "Solutions of Constrained Location Problems," Management Science, INFORMS, vol. 22(1), pages 51-56, September.
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    Cited by:

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    2. 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.
    3. 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.

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