Location of a facility minimizing nuisance to or from a planar network

In this paper we investigate the location of a facility anywhere inside a planar network. Two equivalent problems are analyzed. In one problem it is assumed that the links of the network create a nuisance or hazard and the objective is to locate a facility where the total nuisance is minimized. An equivalent problem is locating an obnoxious facility where the total nuisance generated by the facility and inflicted on the links of the network is minimized. Exact and approximate solution methods for its solution are proposed and tested on a set of planar networks with up to 40,000 links yielding good results.