On the Distance-Constrained Close Enough Arc Routing Problem

Arc routing problems consist basically of finding one or several routes traversing a given set arcs and/or edges that must be serviced. The Close-Enough Routing Problem, Generalized Directed Rural Postman does not assume customers are located at specific arcs, but can serviced by any arc subset. Real-life applications include for meter reading, in which vehicle equipped with receiver travels street network. If the gets within certain distance meter, collects its data. Therefore, only few streets close enough to meters need traversed. In this paper we study generalization problem case fleet vehicles is available. This problem, Distance-Constrained Close Enough consists minimum total cost such their length exceed maximum distance. article, propose new formulation Problem and present some families valid inequalities use branch-and-cut algorithm solution. Extensive computational experiments have been performed on benchmark instances results compared those obtained other heuristic exact methods.