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Nondifferentiability Detection and Dimensionality Reduction in Minisum Multifacility Location Problems

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  • J. Fliege

    (University of Dortmund)

Abstract

The minisum multifacility location problem is regarded as hard to solve, due to nondifferentiabilities whenever two or more facilities coincide. Recently, several authors have published conditions for the coincidence of facilities. In the present paper, these conditions are extended to more general location problems and improved with respect to new sufficient coincidence conditions for location problems with mixed asymmetric gauges. Some of these conditions are formulated only in terms of the given weights and certain values from a preprocessing step.

Suggested Citation

  • J. Fliege, 1997. "Nondifferentiability Detection and Dimensionality Reduction in Minisum Multifacility Location Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 365-380, August.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022635712721
    DOI: 10.1023/A:1022635712721
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    References listed on IDEAS

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    1. O. Lefebvre & C. Michelot & F. Plastria, 1991. "Sufficient Conditions for Coincidence in Minisum Multifacility Location Problems with a General Metric," Operations Research, INFORMS, vol. 39(3), pages 437-442, June.
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    4. Henrik Juel & Robert F. Love, 1980. "Sufficient Conditions for Optimal Facility Locations to Coincide," Transportation Science, INFORMS, vol. 14(2), pages 125-129, May.
    5. Plastria, Frank, 1987. "Solving general continuous single facility location problems by cutting planes," European Journal of Operational Research, Elsevier, vol. 29(1), pages 98-110, April.
    6. Durier, Roland & Michelot, Christian, 1985. "Geometrical properties of the Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 20(3), pages 332-343, June.
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    Cited by:

    1. 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.

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