## 1 Introduction
[27; 28] focus on traffic management at hubs and stowage planning to improve transshipment efficiency; and furthermore, [PERSON] et al. [29] have integrated crane scheduling, yard management, and internal traffic planning to develop more comprehensive hub operation scheduling solutions. However, these studies primarily focus on optimizing the scheduling at an individual hub rather than across all hubs at the level of the entire multimodal transport network to improve overall operational efficiency. [PERSON] et al. [5] argued that the researchers need to pay attention to the impact of transshipment plans on congestion under the circumstances of road-rail multimodal transport, e.g., loading and unloading operations, traffic management at transshipment terminals coordinated with operation scheduling, and yard management problems. Some studies [8; 10; 30; 31; 32; 33] introduced queuing models to describe the process of transshipping operations. First, the first-come-first-served (FCFS) rule is used for transshipment sequencing. Then, the arrival of cargo at each hub is modeled as a Markovian queue, and based on Little's law to estimate the average waiting time. However, such methods have limitations in solving emergency multimodal transport problems. Since using average waiting time substitutes for actual waiting times, such methods cannot accurately estimate the impact of transshipment operations on the schedule of multimodal transport. More importantly, as only the FCFS rule was considered, these achievements do not fully demonstrate the role of transshipment sequence selection in congestion management. When considering time goals, the FCFS rule may not be the optimal sequencing rule for managing congestion in multimodal transport systems. For example, to shorten the waiting time for hazmat at the hub, [PERSON] et al. [32] introduced a hazmat priority rule (i.e., hazmat containers have priority over regular containers) besides the FCFS rule to optimize the transshipment sequence. This study enlightens that congestion can also be managed by transshipment sequence selection besides hub capacity and transport route, further optimizing the road-rail multimodal transport schedule. Given the significant value of shortening response times in emergencies, it is necessary to develop an [PERSON] method to explore the systematic effects of transshipment sequence selection on the road-rail multimodal transport schedule. This paper focuses on the dependency between transshipment sequence selection and waiting time, and proposes an integrated optimization problem of transport routes and transshipment sequences (after this referred to as ITRTSP, see Section 2.1) at the operational level, comprising two sub-problems: (1) Allocating hubs for all cargoes to determine transport routes; (2) Selecting transshipment sequences for cargoes at the same hub. Due to the further consideration of transshipment sequence selection based on hub allocation, ITRTSP is highly similar to the hybrid flow shop scheduling problem (HFSP) [34] in objectives, variables, and constraints. Usually, the road-rail multimodal transport process in emergencies (see Figure 1 for the meanings of symbols in Section 2.1) can be divided into five fixed sequential operations: 1 road transport from an origin to a hub responsible for loading onto trains (referred to as an upstream station); 2 transshipment at the upstream station, including queuing (operation 2-1) and loading (operation 2-2); 3 rail transport to a hub responsible for unloading from trains (referred to as a downstream station); 4 transshipment at the downstream station, including queuing (operation 4-1) and unloading (operation 4-2); 5 road transport to a destination. From Figure 1, it can be seen that if all cargoes are treated as jobs that need to be processed (transshipped), and the upstream and downstream stations are treated as multiple parallel machines with limited loading and unloading efficiency, then ITRTSP can be modeled as a two-stage HFSP with transport constraints [35].