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An Extended Multifacility Minimax Location Problem Revisited

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  • C. Michelot
  • F. Plastria

Abstract

We consider the following model of Drezner (1991) for the location of several facilities. The weighted sum of distances to all facilities plus a set-up cost is calculated for each separate demand point. The maximal value among these sums is to be minimized. In this note we show that if the weights used in the model decompose into a product of two factors, one depending only on the demand point, the other only on the new facilities, there exists at least one optimal solution such that all new facilities coincide. We also investigate when a unique optimal solution of coincidence type exists, and obtain a full description of the set of optimal solutions when the weights have this multiplicative structure and the norm is round. An example shows that this kind of coincidence does not necessarily happen when the weights may have any value. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • C. Michelot & F. Plastria, 2002. "An Extended Multifacility Minimax Location Problem Revisited," Annals of Operations Research, Springer, vol. 111(1), pages 167-179, March.
    • Handle: RePEc:spr:annopr:v:111:y:2002:i:1:p:167-179:10.1023/a:1020953703533
    DOI: 10.1023/A:1020953703533
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    Cited by:

    1. Fusheng Wang, 2013. "A hybrid algorithm for linearly constrained minimax problems," Annals of Operations Research, Springer, vol. 206(1), pages 501-525, July.
    2. Gert Wanka & Oleg Wilfer, 2017. "Duality results for nonlinear single minimax location problems via multi-composed optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 401-439, October.

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