Technical Note—Location Theory, Dominance, and Convexity: Some Further Results

This note presents some generalizations of results on the single norm-one facility location problem due to Wendell and Hurter. It is first shown that a solution to the multifacility location problem with a single norm can be found in the convex hull of sources and destinations. In the particular case of the rectilinear norm, only intersection points belonging to this convex hull need be considered. When different 1_p-norms are envisaged, the octagonal hull contains one solution to the single facility location problem. This result is also extended to the multifacility case.