Container shipping route and schedule design with port time windows and coordinated arrivals

This paper deals with the liner shipping routing and scheduling problem by proposing a model that incorporates port time windows and split deliveries in cases where port demand exceeds ship capacity. Additionally, it introduces the concept of limited berth availability at ports, that results in vessel arrival coordination requirements. Moreover, it tests the cost-efficiency of an extra constraint for further restricting the arrival times of ships serving the same port. It develops a novel mathematical formulation for the vehicle routing problem and solves it using tabu search algorithm. Numerical experiments in a hub-and-spoke network demonstrate the function and effectiveness of the model, as well as the fluctuations of the cost by altering various decision variables.