The Weber obnoxious facility location model: A Big Arc Small Arc approach

In this paper we propose the Weber obnoxious facility location problem. As in the classic Weber location problem, the objective is to minimize the weighted sum of distances between the facility and demand points. However, the facility location is required to be at least a given distance from demand points because it is “obnoxious” to them. A practical example is locating an airport. Since in most applications the nuisance generated by the facility “travels by air”, we concentrate on the case where the required minimum distance between the facility and demand points is Euclidean. The Weber objective distance can be measured by a different norm. We develop very efficient algorithms to optimally solve the single facility problem based on geometric branch and bound and on a finite candidate set. We tested it on problems with up to 10,000 demand points using Euclidean, Manhattan, and ℓp for p=1.78 norms for the Weber objective. The largest problems were optimally solved in a few seconds of computer time. Many extensions to the basic Weber obnoxious facility location problem are proposed for future research.