Models on ship scheduling in transshipment hubs with considering bunker cost

This paper studies a decision problem for scheduling ships׳ starting operation time in a transshipment hub with considering the bunker cost and the transshipment cost of containers. Based on the information about the handing capacity of the container port in each period, the port operator makes a proper decision and informs the shipping companies about the start operation days of each liner route. The optimized decision may help shipping companies significantly reduce the cost. This study proposes a mixed integer programming model. The NP-hardness of the problem is proved. A local branching based solution method is also developed for solving the model. Extensive numerical experiments demonstrate the optimality of the solution by the proposed method is less than 3% for large-scale problem instances.