## 3 Solution Method
### Recursive Method for Waiting Time Calculation
The bipartite network diagrams for these two schemes are shown in Figures 2a and 2b, respectively. Taking A in the two figures as an example, the solid arrows and the labels above them (A1, A2, A3, A4, and A5) represent the operations \(\mid\)1, \(\mid\)2-2, \(\mid\)3, \(\mid\)4-2, and \(\mid\)5 for A, respectively; the numbers below represent the time required to complete the operations, respectively. The symbols for B and C have similar meanings. The dashed arrows in the two figures represent transshipment sequences at hubs. From Figure 2a, A2 is the immediate predecessor activity of B2. Since A arrives at 2 before B, and C arrives at 4 before B, Figure 2a can be considered adopting the FCFS rule to determine the transshipment sequence. Unlike Figure 2a, in Figure 2b, B2 is adjusted to be the immediate predecessor activity of A2, resulting in B arriving at 4 before C; consequently, B4 is adjusted to be the immediate predecessor activity of C4. Set \(SM_{i}\) = 0, and use WTC to calculate \(t_{i}^{2}\), \(t_{i}^{5}\), and \(EM_{i}\) for Figure 2a,b, with the results shown in columns 3, 4, and 5 of Table 4. Then, replace \(t_{i}^{2}\) and \(t_{i}^{5}\) with the average waiting time \(\overline{t_{i}^{2}}\) and \(\overline{t_{i}^{5}}\), respectively, then calculate the average end moment (\(\overline{EM_{i}}\)) with the results shown in columns 6, 7, and 8 of Table 4.  
From Table 4, it can be seen that when using \(EM_{i}\), the makespans of Figures 2a and 2b are 50 h and 44 h, respectively, so Figure 2b is superior to Figure 2a. However, when using \(\overline{EM_{i}}\), the makespans of Figures 2a and 2b are 45.5 h and 47.5 h, respectively, so Figure 2a is superior to Figure 2b. That is, different waiting time estimate methods can lead to an opposite decision here. If the average waiting time is used for makespan calculation, the FCFS rule is the best sequencing rule, no specialized decision is needed for the transshipment sequence selection. However, if WTC is used for makespan calculation, the makespan of Figure 2b reduces by 6 h compared to Figure 2a, necessitating a special transshipment sequence selection decision. This suggests that introducing WTC for minimum waiting time calculation and transshipment sequence selection can result in a higher-quality multimodal transport scheme, thereby confirming the effectiveness of the simulation approach. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & \(i\) & \(t_{i}^{2}\) **(h)** & \(t_{i}^{5}\) **(h)** & \(EM_{i}\) **(h)** & \(t_{i}^{2}\) **(h)** & \(t_{i}^{5}\) **(h)** & \(EM_{i}\) **(h)** \\ \hline \multirow{3}{*}{Figure 2a} & A & 0 & 0 & 31 & 3.5 & 0 & 34.5 \\  & B & 7 & 2 & 50 & 3.5 & 1 & 45.5 \\  & C & 0 & 0 & 41 & 0 & 1 & 42 \\ \hline \multirow{3}{*}{Figure 2b} & A & 10 & 0 & 41 & 5 & 0 & 36 \\  & B & 0 & 0 & 41 & 5 & 1.5 & 47.5 \\ \cline{1-1}  & C & 0 & 3 & 44 & 0 & 1.5 & 42.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of the two schemes. Figure 2: The bipartite network diagrams of the two transshipment sequencing schemes: (**a**) A\(\rightarrow\)B; (**b**) B\(\rightarrow\)A.