Technical Note—On Location Dominance on Spherical Surfaces

In a recent paper Aly et al. (Aly, A. A., D. C. Kay, D. W. Litwhiler, Jr. 1979. Location dominance on spherical surfaces. Opns. Res.27 972–981.) proved that an optimal solution to a “minisum” problem on a sphere must lie in the convex hull of the demand points if the demand points are not located entirely on a great circle arc. The case when all demand points are on a great circle arc remains an open question. In this note we prove that if demand points are located on a great circle arc, so is the optimal solution point.