A hybrid heuristic procedure for the Windy Rural Postman Problem with Zigzag Time Windows

Abstract In arc routing applications, some streets may require service along both sides of the street. For a subset of these streets, the vehicle operator may choose to service both sides during a single traversal. We refer to this as zigzag service. In contrast to servicing each side separately, the vehicle stops more frequently and incurs a traversal cost, two service costs, and a penalty cost associated with the slowed travel time required to perform the zigzag service. The tradeoff is that the vehicle only needs to service the street once on its route. However, for other streets zigzag service is only possible during the early part of a day when there is very little traffic. This scenario is modeled by the Windy Rural Postman Problem with Zigzag Time Windows (WRPPZTW). We develop a hybrid heuristic for the WRPPZTW that combines standard insertion and local search techniques with integer programming. We compare the computational performance of our heuristic to an exact procedure from Nossack et al. (2017) on a set of small instances with 28 edges and test the scalability of our heuristic on a set of larger grid instances with as many as 1200 edges.