A cutting plane algorithm for the capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) consists of finding a set of minimum cost routes that service all the positive-demand edges of a given graph, subject to capacity restrictions. In this paper, we introduce some new valid inequalities for the CARP. We have designed and implemented a cutting plane algorithm for this problem based on these new inequalities and some other which were already known. Several identification algorithms have been developed for all these valid inequalities. This cutting plane algorithm has been applied to three sets of instances taken from the literature as well as to a new set of instances with real data, and the resulting lower bound was optimal in 47 out of the 87 instances tested. Furthermore, for all the instances tested, our algorithm outperformed all the existing lower bounding procedures for the CARP.