A metaheuristic algorithm and structured analysis for the Line-haul Feeder Vehicle Routing Problem with Time Windows

Synchronisation in vehicle routing is a rather new field of research and naturally new problems arise. One of these problems is the Line-haul Feeder Vehicle Routing Problem (LFVRP). It uses a fleet of small and large vehicles to serve two types of customers. The first type provides additional parking space and can be visited by both vehicle classes. The second type can only be visited by the small vehicle class as these customers provide only limited parking space. The main characteristic of the small vehicle class is the limited capacity. To overcome this particular disadvantage, the small vehicles can use the large vehicles as virtual depots. In other words, a small and large vehicle can meet at a parking lot or at a customer with enough space (type-1 customer) and perform a transfer of goods. For a successful reloading operation, both vehicles must be present at the same place at the same time. Thus, both vehicle tours must be synchronized. After using the large vehicle as virtual depot, the small vehicle can proceed immediately afterwards because it does not need to go back to the physical depot. Consequently, less time and distance is required which results in a reduction of the overall costs. The advantage of the LFVRP over classical variants of the Vehicle Routing Problem has been shown in previous papers. Yet, customer time windows have been neglected so far and as time windows play an important role in vehicle routing research, they need to be addressed properly. Therefore, we aim to close this gap by introducing the Line-haul Feeder Vehicle Routing Problem with Time Windows (LFVRPTW). We discuss the complexity of customer time windows for the LFVRPTW and adopt the previously introduced algorithm for the LFVRP. Furthermore, we provide a thorough computational analysis on the impact of different time window characteristics and show the advantage of the LFVRPTW over other variants of the Vehicle Routing Problem with Time Windows.