Multiple obnoxious facilities location: A cooperative model

A given number of communities exist in an area. Several obnoxious facilities, such as polluting factories, garbage dumps, need to be located in the area. The nuisance emitted by the facilities is cumulative. The objective is to minimize the nuisance inflicted on the most affected community. This problem is useful for planners who frequently face the challenge of locating obnoxious facilities and have no easy way to determine a good set of locations for these facilities. No existing model considers the cumulative effect of nuisance generated by the facilities. A multi-start approach by the SNOPT and IPOPT solvers in Matlab, which are considered to be the best available general-purpose nonlinear solvers, gave poor results. However, an innovative, specially designed Voronoi-based heuristic produced much better results in a small fraction of the run time. In many cases, nuisance is cut by more than half, and run time is more than a hundred times faster. As detailed in the conclusions section, the applications of our methodology extend beyond the model presented in this article