The general unweighted problem of locating obnoxious facilities on the plane

In this paper the following generalization of the spatial structure of the efficient location of obnoxious facilities is considered. We have a closed polygonal frontier line surrounding a number of regions, characterized either protected or restricted, all of which possess polygonal perimeters. By the term protected we mean a region for which care should be taken to locate the facility as far as possible from its perimeter. By restricted, on the other hand, we mean a region inside which it is forbidden to build the obnoxious facility. The area outside the frontier line is considered restricted and may also contain protected regions. Given this geometrical structure, we ask for a point in a free area (an area characterized neither protected nor restricted) which maximizes the minimum distance between that point and the union of perimeters of all protected regions. In this paper an algorithm is proposed locating the optimal solution of the above problem.