The Weber problem with regional demand

This paper is devoted to the study of the Regional Weber Problem, an extension of the Weber problem which allows the demand not be concentrated onto a finite set of points. The most serious drawback of this formulation, from a resolution viewpoint, is the high computational cost involved in the evaluation of the objective function. A new approach is proposed, which requires a low amount of computation and where it is possible to control the error on the approximation. This approximation suggests a new methodology to solve the problem. This methodology is compared with the existing ones, showing its relevance from a practical point of view.