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On solving the planar k-centrum problem with Euclidean distances

Author

Listed:
  • Rodríguez-Chía, Antonio M.
  • Espejo, Inmaculada
  • Drezner, Zvi

Abstract

This paper presents a solution procedure based on a gradient descent method for the k-centrum problem in the plane. The particular framework of this problem for the Euclidean norm leads to bisector lines whose analytical expressions are easy to handle. This allows us to develop different solution procedures which are tested on different problems and compared with existing procedures in the literature of Location Analysis. The computational analysis reports that our procedures provide better results than the existing ones for the k-centrum problem.

Suggested Citation

  • Rodríguez-Chía, Antonio M. & Espejo, Inmaculada & Drezner, Zvi, 2010. "On solving the planar k-centrum problem with Euclidean distances," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1169-1186, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1169-1186
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    References listed on IDEAS

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    1. Drezner, Zvi & Nickel, Stefan, 2009. "Solving the ordered one-median problem in the plane," European Journal of Operational Research, Elsevier, vol. 195(1), pages 46-61, May.
    2. Zvi Drezner, 2009. "On the convergence of the generalized Weiszfeld algorithm," Annals of Operations Research, Springer, vol. 167(1), pages 327-336, March.
    3. E. Weiszfeld & Frank Plastria, 2009. "On the point for which the sum of the distances to n given points is minimum," Annals of Operations Research, Springer, vol. 167(1), pages 7-41, March.
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    6. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
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    8. S. Nickel & J. Puerto & A. M. Rodríguez-Chía & A. Weissler, 2005. "Multicriteria Planar Ordered Median Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 657-683, September.
    9. Ogryczak, Wlodzimierz & Sliwinski, Tomasz, 2003. "On solving linear programs with the ordered weighted averaging objective," European Journal of Operational Research, Elsevier, vol. 148(1), pages 80-91, July.
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    11. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
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