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How bad can the centroid be?

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  • Plastria, Frank

Abstract

In this note we first show that the centroid (or centre of gravity) gives in value a (σ+1)-approximation to any continuous single facility minisum location problem for any gauge with asymmetry measure σ, and thus a 2-approximate solution for any norm.

Suggested Citation

  • Plastria, Frank, 2016. "How bad can the centroid be?," European Journal of Operational Research, Elsevier, vol. 252(1), pages 98-102.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:1:p:98-102
    DOI: 10.1016/j.ejor.2016.01.002
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    References listed on IDEAS

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    1. 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.
    2. Pelegrin, Blas & Michelot, Christian & Plastria, Frank, 1985. "On the uniqueness of optimal solutions in continuous location theory," European Journal of Operational Research, Elsevier, vol. 20(3), pages 327-331, June.
    3. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    4. Frank Plastria, 2011. "The Weiszfeld Algorithm: Proof, Amendments, and Extensions," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 357-389, Springer.
    5. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    6. Roger C. Vergin & Jack D. Rogers, 1967. "An Algorithm and Computational Procedure for Locating Economic Facilities," Management Science, INFORMS, vol. 13(6), pages 240-254, February.
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    Cited by:

    1. Murray, Alan T., 2021. "Contemporary optimization application through geographic information systems," Omega, Elsevier, vol. 99(C).
    2. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.

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