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Geometrical properties of the Fermat-Weber problem. (English) Zbl 0564.90013
This paper is devoted to the Fermat-Weber problem with mixed gauges in order to take into account nonsymmetric distances. A geometrical description of the set of solutions is obtained. Then the concept of metric hull is defined; general sufficient conditions are given such that the metric hull of existing facilities intersects the set of optimal locations. Particularly, it is shown that an optimal location can be found in the metric hull, in dimension two, whatever the gauges are and in dimension n with the rectilinear norm. The connection between metric hull, convex hull and octagonal hull is studied.

MSC:
90B05 Inventory, storage, reservoirs
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