Voyage cost optimization of battery-powered ships with a battery-swapping mode

A nonlinear programming model is established with ship speed and port berthing as main decision variables, to investigate the differences between pure battery-powered ships and traditional ones in voyage scheduling, and to explore the operation and management of inland ships with a power-swapping mode. The model comprehensively considers the closed-loop energy cost of a single voyage, ensuring the lowest total cost while meeting freight demand and hard time window constraints. Using the Gurobi solver to linearize nonlinear constraints, a heuristic algorithm is used to compare and analyze the effectiveness of the model in different case scenarios, obtain the corresponding minimum cost, and provide management suggestions for shipowners and shipping companies regarding battery package capacities.