On the Distance-Constrained Close Enough Arc Routing Problem

Abstract

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