A metaheuristic for a time-dependent vehicle routing problem with time windows, two vehicle fleets and synchronization on a road network

In this work, we extend the time-dependent vehicle routing problem with time windows on a road network by considering two types of vehicles, large and small, to serve customers. Motivated from city logistics applications, large vehicles are forbidden from the downtown area. Accordingly, goods must be transferred from large to small vehicles to serve downtown customers. This leads to synchronization issues at transfer points, which are special locations without storage capacity. The problem is not a pure two-echelon vehicle routing problem, since customers outside of the downtown area can be served directly by large vehicles. The problem is further compounded by the presence of time-dependent travel times that are defined on the arcs of the road network and are used to model congestion periods. To solve this difficult problem, we propose an adaptation of the Slack Induction by String Removals metaheuristic, which is state-of-the-art for the classical capacitated vehicle routing problem. Computational results on a set of test instances with different characteristics empirically demonstrate the optimization capabilities of this new metaheuristic on a problem which is much more complicated than the capacitated vehicle routing problem.