A parametric 1-maximin location problem

A parametric 1-maximin location problem

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Article ID: iaor19911888
Country: United Kingdom
Volume: 42
Issue: 1
Start Page Number: 49
End Page Number: 55
Publication Date: Jan 1991
Journal: Journal of the Operational Research Society
Authors: ,
Abstract:

The authors 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. The authors 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 the authors construct the optimal trajectory as a function of the parameter, and demonstrate that the trajectory may be discontinuous.

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