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: | Erkut E., Sabri Oncu T. |
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.