Abstract
A well-known localization theorem in continuous single facility location of Wendell and Hurter states that any Weber problem in the plane in which all norms are identical admits an optimal solution within the convex hull of the destination points. In this paper it is shown that this result fails for general norms as soon as the dimension is at least three. A new localization theorem is then proposed that is valid under very general conditions. This makes it possible to consider most unconstrained single facility location problems as constrained problems. It is indicated how to construct an easily implemented form of such constraints.
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