A Parametric 1-Maximin Location Problem
作者:
ErkutErhan,
ÖncüT. Sabri,
期刊:
Journal of the Operational Research Society
(Taylor Available online 1991)
卷期:
Volume 42,
issue 1
页码: 49-55
ISSN:0160-5682
年代: 1991
DOI:10.1057/jors.1991.6
出版商: Taylor&Francis
关键词: Facilities;Location;Maximin;Parametric;Undesirable
数据来源: Taylor
摘要:
AbstractWe introduce a version of the weighted 1-maximin problem in a convex polygon, where the weights are functions of a parameter. The 1-maximin problem is applicable in the location of undesirable facilities. Its objective is to find an optimal location such that the minimum weighted distance to a given set of points is maximized. We show that the parametric 1-maximin problem is equivalent to a 1-minimax problem, where the costs are non-linearly decreasing functions of distance. Using different values of the parameter in the 1-maximin problem, one can model different disutility functions for the users of the facility. Furthermore, the parameterization provides for a systematic way of reducing the effects of the weights, resulting in the unweighted 1-maximin problem in the limit. For two example problems we construct the optimal trajectory as a function of the parameter, and demonstrate that the trajectory may be discontinuous.
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