In order to reduce the emission of polluting gases from auxiliary generators during ship berthing, and in response to the growing adoption of shore power infrastructure, this paper incorporates the distribution of shore power into the berth scheduling plan of container terminals. Building upon the traditional berth scheduling model, relevant constraints for shore power allocation and carbon emission reduction targets are introduced, establishing a mathematical model that integrates ship-in-port activities, shore power usage, and carbon emissions. To solve the model effectively, an Improved Bat Algorithm (IBA) incorporating a stagnation mutation strategy is proposed. The inertia weight method is employed to update individual optimization speeds, preventing the algorithm from converging to local optima. Case studies show that considering shore power distribution increases the complexity of the berth scheduling problem. When the number of ships does not exceed 25, the mathematical model can be solved accurately with optimal solution quality; however, when the number increases to 30, the model cannot be solved within a reasonable time frame. In comparison, the IBA achieves efficient solutions for all test cases with significantly shorter computation times. The maximum deviation between IBA results and the exact model solutions is only 2.37%. Furthermore, compared to traditional Genetic Algorithms and the basic Bat Algorithm, IBA demonstrates superior performance in terms of solution quality and computational efficiency, with an average increase in computation time of only about 10 seconds compared to the basic bat algorithm. A matching analysis between the shore power retrofit ratio of berths and ships revealed that under a fixed dock berth retrofit ratio, terminal costs decrease as the ship retrofit ratio increases. However, once the two ratios reach equilibrium, the rate of cost reduction levels off and remains largely stable. These results indicate that optimal cost savings are achieved when the shore power retrofit ratios of berths and ships are appropriately matched. Ensuring a balance between supply and demand can effectively prevent resource waste and enhance the efficiency of shore power utilization.