## 6 Conclusions  
This paper proposes a mathematical model for ship scheduling in Yangtze River ports, taking into account berth preferences and inspections for seagoing ships. Initially, the background of the Yangtze River ports and their pressing issues were analyzed, leading to the development of a cooperative scheduling model for the waterway and berths. The model aims to minimize berth deviation costs and total scheduling time while maximizing berth utilization. An optimized NSGA-III algorithm was employed to solve the waterway-berth cooperative scheduling problem, resulting in the optimal cooperative scheduling scheme. The experimental results indicate that the optimized NSGA-III algorithm significantly outperforms the port's original scheduling scheme, achieving improvements of 30.81%, 13.73%, and 12.11% in the three objective values. Furthermore, berth deviation costs were cut by CNY 95 and CNY 362, and total scheduling time was reduced by 274.3 min and 1991.22 min, when compared to the NSGA-III and NSGA-II algorithms. Berth utilization rates saw a slight improvement over both algorithms. The innovative aspect of this model lies in its comprehensive consideration of berth preference costs and customs inspection factors over an extended planning period. By setting relevant constraints, the scheduling process is optimized to clearly reflect the actual costs and benefits of berth allocation. In waterway scheduling, the model's optimization objectives help avoid random and disorderly berth selection, optimize ship path planning, reduce congestion risk, and enhance the port's service level. Additionally, incorporating berth preference costs allows for a more balanced distribution of berth resources, preventing prolonged occupation of some berths while others remain idle, thereby improving the overall berth utilization rate at Yangtze River ports. Furthermore, the model's scheduling process adapts to customs inspection time constraints, enhancing the efficiency of the inspection departments. The limitation of this paper is that, despite the complex shipping operations at the target port involving both domestic and international trade, and the presence of some seagoing ships, there are still significant differences in scale, business processes, and trade volume compared to seaports. Due to the unique geographical location of the target port, the emphasis is solely on the \"seagoing ship inspection factors\" to highlight river-sea intermodal transportation. In the future, we plan to conduct more in-depth research on other seaports, examining additional influencing factors, such as integrating bonded warehouse scheduling, crane scheduling, and container truck scheduling, to develop a more comprehensive and effective model. We also plan to incorporate environmental concepts, enhancing the model's reliability from the perspective of ship energy saving and reducing fuel consumption, thereby promoting a green and low-carbon approach. S.Y. : Conceptualization, Methodology, Software, Data curation, Validation, Writing--original draft, Writing--review and editing. H.S. : Investigation, Project administration, Data curation, Methodology, Writing--review and editing. Z.Z. : Investigation, Project administration, Data curation, Supervision. X.Q. : Investigation, Project administration, Writing--original draft. Y.W. : Conceptualization, Methodology, Funding acquisition, Supervision, Writing--review and editing. All authors have read and agreed to the published version of the manuscript. This research was supported by the 2023 Dalian Science and Technology Talent Innovation Support Policy Project (No. 2023 RY005) of the Dalian Bureau of Science and Technology, the 2023 Dalian Science and Technology Talent Innovation Support Policy Project (No. 2023 RQ003) of the Dalian Bureau of Science and Technology, and the 2023 Liaoning Provincial Science and Technology Plan (Key) Project (No. 2023 JH1/10400047) of the Liaoning Provincial Department of Science and Technology. Not applicable.