The Profitable Close Enough Arc Routing Problem

In this article, we deal with the Profitable Close-Enough Arc Routing Problem (PCEARP), which is an extension of the Close-Enough ARP (CEARP). The CEARP models the situation in which customers are not necessarily nodes of a network and the associated serviced can be performed from any traversed edge that is close enough to the customer. It consists of finding a minimum cost tour that services all the customers. In the PCEARP, a profit is associated with each customer and it is collected (only once) when the customer is serviced. The goal is to find a tour maximizing the difference between the total profit collected and the travel distance. A formulation for this new problem and some valid inequalities are presented, and a polyhedral study of its feasible solutions is conducted. We propose a heuristic and a branch-and-cut procedure for solving the PCEARP, and their performance has been tested on several sets of instances with different characteristics.