Deploying, scheduling, and sequencing heterogeneous vessels in a liner container shipping route

Previous studies on liner container shipping operations usually assume identical container ships deployed in the same shipping route. However, in real operations, this assumption does not always hold considering the distinct capacities, ages, fuel efficiencies, cost structures, etc. of these ships. These distinctions significantly influence the number of containers transported, the bunker fuel consumption, and the operating cost of a shipping route. In this regard, this paper considers the joint ship deployment, sequencing, and scheduling problem for a fleet of heterogeneous vessels in a shipping route. A mixed integer programming model is developed to select the optimal ships from a set of candidate ships together with their sequences, schedules, and sailing speeds in the shipping route to minimize the total cost. A tailored solution algorithm is subsequently developed to calculate the global optimal solution. Numerical experiments demonstrate that this algorithm significantly outperforms the classical branch-and-cut algorithm in solving the model. In addition, by applying our model in a real-case shipping route, we find that the model is able to reduce the total cost by 5% compared with that considering homogeneous vessels. Finally, several managerial insights are obtained to guide the operations of a liner shipping route.