Arc routing in a node routing environment

We describe a special variant of the vehicle routing problem (VRP), where there are many customers per road segment. This class of VRPs arises in, e.g. mail delivery, and is a borderline case where both arc routing and node routing techniques may be applied for modeling and solving. In a real-world setting, the problem should be modeled so as to incorporate all important constraining factors. We use a simplified node routing model and aggregate customers into supernodes to reduce problem size. A tabu search metaheuristic for the standard node routing-based VRP is then applied to the aggregated version of the problem. Our method is tested both on test instances from the literature as well as on a portfolio of new test instances especially made to fit the problem at hand. Experimental results are reported, showing that aggregation of customers can lead to substantial improvements both in solution time and solution quality in this setting, especially for larger instances.