Location Dominance on Spherical Surfaces

This paper investigates the nature of optimal solutions for a location problem on a spherical surface with the great circle distance as measure. The results are based upon Wendell and Hurter's generalization of Kuhn's characterization of a convex hull by dominance. It is shown that the search for an optimal solution for the “minisum” single facility location problem on the sphere, where demand points are not located entirely on a great circle arc, can be restricted to the spherically convex hull of the demand points.