THE WEBER PROBLEM ON THE PLANE WITH SOME NEGATIVE WEIGHTS

This paper analyzes the properties of the Weber problem on the plane when some of the weights are negative. We provide exact solutions when distances are rectilinear or squared Euclidean. For the Euclidean case, we provide a theorem that limits the region of the plane where optimal points can be located. Heuristic algorithms based on this theorem are suggested and computational experience is described.