ON THE SET OF OPTIMAL POINTS TO THE WEBER PROBLEM

It is known that the planar Weber location problem with lp distances has all its solutions in the convex hull of the demand points. For l1 and l∞ distances, additional conditions are known which reduce the set of possible optimal points to the intersection of that convex hull, the efficient set, and the points defined by a certain grid. In this paper, we determine the smallest set which includes at least one optimal point for every Weber problem, based on a given set of demand points. It is shown that for 1 < p < ∞ a certain part of the convex hull is the smallest possible set, but for p = 1 or p = ∞ the known conditions do not necessarily yield the correct set. Finally, we find the smallest possible set for p = 1 or p = ∞.