Integer programming formulation and polyhedral results for windy collaborative arc routing problem

This paper is concerned with the collaborative uncapacitated arc routing problem on windy graphs. An integer programming formulation is presented for the problem. A new technique is presented for constructing affinely independent feasible tours and is used to examine the associated polyhedron. Moreover, some well-known valid inequalities such as path-bridge inequalities are adjusted for the problem and are proven to be facet inducing. Finally, a branch-and-cut algorithm is developed for the problem and some tables of numerical results are presented to compare and evaluate the efficiency of the presented algorithm.