Obnoxious Facility Location Problem with Forbidden Regions

In this paper, we consider an optimal location problem for an obnoxious facility such as disposal center. We formulate this problem as a single facility minimax location problem on the plane under the presence of forbidden regions where the facility is not permitted. The solution for a minimax location problem without forbidden regions is known to be a center of minimum covering circle, but we must consider the case where the solution is not feasible. First we seek the optimal feasible solution with Euclidean distance, secondary we consider it with rectilinear distance. In order to solve these problems, we derive some useful properties and fully utilizing them, we propose efficient algorithms to find the optimal location.