Considering the potential of time-of-use electricity pricing in reducing ship energy costs, the impact of shore power equipment connection and disconnection on berthing times, and the number of retrofitted ships equipped with onboard shore power receiving systems, this study aims to enhance terminal operational efficiency and reduce carbon emissions from auxiliary engine usage during ship berthing. Under the time-of-use electricity pricing mechanism, a joint shore power usage and berth allocation scheme is proposed. To this end, a bi-objective optimization model is developed to minimize both total operational costs and total carbon emission costs. An improved Non-Dominated Sorting Genetic Algorithm (NSGA-II) is designed to solve the model, incorporating heuristic methods, neighborhood crowding degree calculation, and a dynamic crowding degree update strategy. Case studies and sensitivity analyses based on the operational data of a container terminal show that the proposed improved NSGA-II algorithm outperforms the traditional NSGA-II algorithm in terms of both solution quality and computational performance in most test scenarios. When the proportion of retrofitted ships reaches 70%, the total carbon emission cost experiences the greatest reduction, while the total operating cost sees the smallest increase. Moreover, compared to the shortest off-peak period, the longest off-peak period in the time-of-use pricing scheme reduces total operational costs by 7.65%, total carbon emission costs by 2.47%, and increases the number of ships using shore power by 33%. These results indicate that lower electricity prices during off-peak periods significantly incentivize ships to use shore power. Time-of-use pricing helps reduce total operational costs. Among ship costs, waiting and deviation costs have a significant impact on total operational costs, while delay costs have a smaller effect.