An Adaptive Metaheuristic for Vehicle Routing Problems with Time Windows and Multiple Service Workers

Distribution planning in urban areas faces a lack of available parking space at customer sites. One approach to mitigate the issue is to cluster nearby customers around known parking locations. Deliveries from each parking location to its assigned customers occur by a second mode of transport (for example by foot). These lead to long service times at each of the clusters. However, long service times in conjunction with time windows can lead to inefficient routes as nearby customer clusters with overlapping service times may not be connected. As a consequence, assigning additional service workers to each vehicle is a strategy to reduce service times. The additional workers can do the last mile deliveries in parallel to reduce the service time of a cluster and hence permit more efficient routing. The trade-off between paying additional workers to reduce costs for vehicles and driving creates a new decision problem called the vehicle routing problem with time windows and multiple service workers (VRPTWMS). The present work introduces a stochastic cluster first, route second algorithm. The clustering takes care of assigning and scheduling customers to parking locations. Its goal is to allow the routing algorithm to obtain high quality results. These two stages are linked together with a feedback loop based on the well established ant colony optimization metaheuristic. This allows learning from prior results and leads to vastly improved solution quality. For each of the used benchmark instances new best known solutions were generated. Furthermore, it is shown that applying the concept of bi-modal transportation potentially reduces both cost and environmental impact in regular vehicle routing problems with time windows.