A note on the continuous p-defense-sum problem

The continuous p-defense-sum problem consists of locating p facilities in a convex polyhedron, such that the sum of the distances among all their pairs is maximized. We indicate that it is sufficient to search for optimal sites at the polyhedron's vertices only, and show that the optimal solution can be degenerate, i.e., more than one facility being located at the same point. An integer programming formulation is also given, taking the possible degeneracy into account.