The windy rural postman problem with a time-dependent zigzag option

Abstract

In this research, we focus on the windy rural postman problem with the additional option to zigzag street segments during certain times of the day. If a street is narrow or traffic is light, it is possible (and often desirable) to service both sides of the street in a single pass by zigzagging. However, if a street is wide or traffic is heavy, we must service the street by two single traversals. For some streets, we further impose the restriction that they may only be zigzagged at specific times of the day, e.g., in the early morning when there is virtually no traffic. Real-life applications arise, among others, in trash collection and newspaper delivery. This specific arc routing problem combines two classes of problems known from the literature, arc routing problems with zigzag options and arc routing problems with time dependencies. We present and discuss two (mixed) integer programming formulations for the problem at hand and suggest exact solution approaches. Furthermore, we analyze the effects of zigzag and time window options on the objective function value and test our solution approaches on real-world instances.