New results on the Windy Postman Problem

In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which contains the Mixed Chinese Postman Problem as a special case. We present here a full description of the polyhedron associated to the Windy Postman Problem over graphs with up to 4 vertices and 10 edges. We introduce two new families of facet-inducing inequalities and we prove that these inequalities and the already known Odd Zigzag inequalities are mod-2 cut inequalities. Moreover, a Branch & Cut (B&C) algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of the B&C algorithm over several sets of large WPP and MCPP instances, with up to 3000 nodes and 9000 links, shows that up to our knowledge this is the best algorithm for the exact resolution of the WPP and the MCPP.