Locating an obnoxious facility on a network subject to damage area restriction

Abstract

This thesis considers the problem of locating an obnoxious facility that will inflict damage within a neighborhood λ(λ≥0) of its location point on a given Euclidean network. The objective of the problem is to find a location point that minimizes the sum of weights within a circle of radius λ centered at the location point. In the problem, each weight represents a numerical scale which typically signifies the extent of the undesirability (or the damage cost) due to the facility located near the weighted point. The weights are assumed discretely distributed over all the nodes are continuously uniformly distributed on links of the network. For the problem, the optimal solution properties are analyzed, and ended up with a conclusion that there is at least one optimal location point in a finite set of points in the network. Furthermore, it is shown that such a set can be easily generated. An extension problem of finding such a location point with additional consideration of the customer service costs is also considered. The objective function of this problem is analyzed, and both exact heuristic procedures to find an optimal location point are suggested.