On path-bridge inequalities for the orienteering arc routing problems

One of the recent variants of arc routing problems is the orienteering arc routing problem. In Archetti et al. [A branch and-cut algorithm for the orienteering arc routing problem, Computers and Operations Research. 2016;66:95-104] an integer programming formulation is proposed for the problem and some families of valid inequalities introduced and proven to be valid for the associated polyhedron. Here, the class of path-bridge inequalities is introduced for the problem and is proven to be facet inducing. Since the large class of path-bridge inequalities contain those classes introduced in Archetti et al. [A branch and-cut algorithm for the orienteering arc routing problem, Computers and Operations Research. 2016;66:95-104] this paper can be considered as a generalization of the results of that paper.