On general routing problems

Abstract

Abstract In two recent papers by C. S. Orloff (Networks, 4(1974)35–64, 147–162) general routing problems for one or more vehicles on a graph G = (N,A) are introduced and discussed. The single vehicle problem is to find an optimal tour on G, containing required subsets Q ⊆ N and R ⊆ A. We show that a proposed conversion of required nodes to required arcs is not allowed and that the problem remains polynomial complete if Q = θ. Furthermore, the proposed transformations from M vehicle to single vehicle problems are shown to be incorrect; correct transformations are presented as well.