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With the rapid advancement of battery technology, new energy hybrid tugboats have been progressively adopted. In order to align with the trend of electrifying tugboat fleets, a mixed-integer linear programming (MILP) model for the joint scheduling of new energy hybrid tugboats and berths has been established. The model incorporates the constraint imposed by the limited number of tugboat charging connectors. The objective is to minimize the total cost over the scheduling horizon, including ship waiting, delayed-departure costs, and the operating costs of both conventional diesel and hybrid tugboats. In light of the characteristics inherent to the problem, a hybrid solution approach combining CPLEX with a heuristic-enhanced whale optimization algorithm (WOA) is employed to solve the model. A case study was conducted using data on the energy consumption of tugboats at Xiamen Port. The effectiveness of the model and algorithm was then verified through a series of small-scale instance experiments. Finally, a comprehensive sensitivity analysis of key parameters is finally conducted, including the number of tugboat charging connectors, battery capacity, and charging rate. This analysis provides valuable guidance for port tugboat operations.
Chu et al. (Mon,) studied this question.