In recent years, the adoption of alternative fuels—most notably green methanol—has accelerated the low-carbon transition in the shipping industry. As critical hubs for the integration of transportation and energy, ports have to support simultaneous methanol bunkering and cargo operations. Faced with high volumes of vessel arrivals and limited resources, port operators need to optimize berth and bunkering facility schedules to improve operational efficiency. In this study, a simultaneous operation scheduling optimization model is developed, incorporating practical constraints such as berth size, bunkering speed, and interval time between operations. The objective is to minimize the total berthing time of vessels. The results show that bunkering operations significantly increase berthing time, particularly when relying solely on truck-to-ship bunkering. Vessels with high fuel demands or short cargo operation durations are most in need of high-efficiency bunkering facilities. The study recommends prioritizing ship-to-ship bunkering in busy ports to enhance operational efficiency. Additionally, increasing bunkering speed and reducing intervals between consecutive bunkering tasks are identified as effective strategies for further improving performance.