## 6 Conclusions  
To explore the role of transshipment scheduling at hubs in managing congestion in road-rail multimodal transport, this paper proposes a nonlinear 0-1 programming model. Through a joint decision on transport route and transshipment sequence, the waiting time can be adjusted in the model, thereby optimizing the emergency multimodal transport makespan. A key distinction from the existing literature on multimodal transport lies in that it sets specific variables and constraints to describe the impact of the transshipment sequence on waiting time. A recursive method for calculating waiting times is proposed. A memetic algorithm framework is designed with route selection as the outer layer and transshipment sequence selection as the inner layer for solving the model. Finally, using China's inland road-rail multimodal transport network as an application context, the performance of the solution methods is validated.  
From the numerical experiments, the following conclusions can be drawn. First, transshipment scheduling at hubs in managing congestion should be fully recognized in emergency road-rail multimodal transport activities. For example, congestion can be controlled by transshipment sequence selection, thereby shortening the makespan. Second, production scheduling models and methods may be reasonable and effective choices to accurately quantify the dependency between transshipment scheduling and waiting time in multimodal transport problems. Third, when solving two-stage HFSPs for real-scale examples (such as ITRTSP proposed in this paper), setting machine allocation (hub allocation) as the outer layer and job sequencing (transshipment sequencing) as the inner layer may yield better results.  
The contributions of this paper to multimodal transport research are mainly summarized in three aspects. First, it proposes and demonstrates that congestion can be controlled by adjusting transshipment sequences at hubs to enhance emergency transport efficiency in multimodal transport systems. Second, it constructs a two-stage HFSP model with transport constraints to quantitatively describe the dependency between transshipment sequence selection and waiting time in road-rail multimodal transport. Third, it proposes a recursive method (WTC) for calculating minimum waiting times and designs a memetic algorithm framework for solving ITRTSP.  
This study aims to explore the impact of transshipment sequencing as one aspect of the operation scheduling at hubs on emergency transport efficiency in multimodal transport network settings. However, the study has certain limitations. First, it focuses solely on the dependency between transshipment sequencing and waiting time. Second, it only uses common search algorithms in HFSP, due to its early stage in applying HFSP modeling concepts to manage congestion in road-rail multimodal transport systems. Future research should build on this work by fully considering other aspects of operation scheduling at hubs, such as more complex transshipment planning operations [23; 24], yard storage strategies [25], and traffic management [27]. Meanwhile, exploring more advanced optimization algorithms or the application of simulation models is also set to be a major area of interest.  
Conceptualization, S.T.; methodology, S.T.; software, S.T., S.L. and C.L.; validation, S.T. and S.L.; investigation, S.L. and Z.L.; data curation, S.L. and C.L.; writing--original draft preparation, S.T.; writing--review and editing, S.T. and S.L.; visualization, S.L. and Z.L.; supervision, Z.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.