Scheduling of Mixed Fleet Passing Through River Bottleneck in Multiple Ways

This paper addresses the scheduling problem of a mixed fleet passing through a river bottleneck in multiple ways, considering the impact of streamflow velocity, the fuel cost with different sailing speeds, and the potential opportunity cost of various types and sizes of vessels. From the perspective of centralized management by river bottleneck authorities, a unified scheduling approach is proposed, and a nonlinear model is constructed, where the total fuel cost and potential opportunity cost of the fleet are minimized. To handle the nonlinear terms in the model, an outer approximation technique is applied to linearize the model while ensuring the approximation error remains controlled. The optimal value range of the nonlinear variables is also proven to ensure solution speed. Furthermore, the applicability and effectiveness of the model and solution method are validated through a real-world case study on the Yangtze River. The results show the following: (1) Unified collaborative scheduling by bottleneck authorities can ensure the optimal total cost of the fleet is effectively met and that the vessels passing through the river bottleneck are arranged under rational ways. (2) When fuel consumption is the same as that of traditional oil-fuelled vessels, giving priority to liquefied natural gas (LNG)-fuelled vessels to pass through the river bottleneck can reduce the potential opportunity cost and the total cost of the fleet reasonably. (3) In accordance with changes in the fuel price, streamflow velocity, and proportion of LNG-fuelled vessels, timely adjusting the opportunity cost expectations, vessel arrival time, and service times of bottleneck passing ways is crucial for shipowners and authorities to reduce fleet waiting times at the bottleneck, delay time, and the total cost.