## 4 Example Experiments
### Comparison with the FCFS Rule  
As mentioned, existing studies mainly adopt the FCFS rule for transshipment sequencing. To demonstrate the differences between the method proposed in this paper and the FCFS rule, the examples in Section 3.1 were refined according to the actual conditions of transshipment hubs. The transshipment efficiencies of the upstream and downstream stations (see Tables 14 and 15) were determined based on the \"Railway Station Classification Rating Method\" issued by the Ministry of Transport of the People's Republic of China. The quantity of equipment at each origin was regenerated (see Table 16, with a total of 7000 units). Keeping the outer layer algorithm described in Section 3.2 unchanged, the inner layer algorithm (Step 4) was modified to use the FCFS rule for solving (abbreviated as GA_FCFS). The data in Tables 14 and 16 were input into GA_GA and GA_FCFS for calculation, and the resulting multimodal transport schemes are shown in columns 2 to 5 of Table 17. To show the differences, columns 6 and 7 of Table 17 present a multimodal transport scheme [M], where hub allocation is the same as GA_GA, but transshipment sequence is determined by the FCFS rule. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & **GA** & **SA** & **TS** & **SA\_GA** & **TS\_GA** & **GA\_SA** & **GA\_TS** \\ \hline test13 & 3.08 & 3.33 & 3.19 & 0.78 & 0.51 & 0.96 & 0.87 \\ test14 & 3.67 & 3.85 & 3.77 & 0.99 & 0.68 & 1.24 & 1.14 \\ test15 & 4.06 & 4.24 & 4.16 & 1.23 & 1.06 & 1.61 & 1.49 \\ test16 & 4.85 & 5.01 & 4.93 & 1.59 & 1.35 & 2.01 & 1.85 \\ test17 & 6.62 & 6.78 & 6.71 & 1.97 & 1.72 & 2.49 & 2.28 \\ test18 & 6.45 & 6.62 & 6.56 & 1.88 & 1.60 & 2.27 & 2.11 \\ test19 & 8.42 & 8.64 & 8.56 & 2.56 & 2.38 & 3.19 & 2.82 \\ test20 & 8.20 & 8.41 & 8.36 & 2.79 & 2.45 & 3.26 & 3.13 \\ test21 & 8.80 & 8.97 & 8.89 & 3.22 & 2.82 & 3.44 & 3.30 \\ test22 & 9.03 & 9.25 & 9.11 & 3.31 & 3.04 & 3.65 & 3.42 \\ \hline \end{tabular}
\end{table} 
Table 13: The Gaps (%) between other algorithms and GA_GA. Furthermore, the sensitivity analysis of equipment quantity and transshipment efficiency at hubs was conducted. Initially, four examples were considered with varying equipment quantities (7000, 9000, 11,000, and 13,000 units). GA_GA, IG+ECTT, and GA_FCFS were used to calculate these examples, with the results shown in Figure 8. Taking the scale of 11,000 units as an example, the average time consumed in each operation by GA_GA and GA_FCFS is presented in Figure 9. In Figure 9, \(\overline{\sum_{i}^{k}}\) denotes the average time by all equipment in operation \(k\) (\(k\in\{1,\,2,\,\ldots,\,7\}\)). Subsequently, with a fixed equipment quantity of 11,000 units, six examples (see columns 2 and 3 of Table 18) were designed based on Tables 14 and 15 by enhancing transshipment efficiencies at upstream stations ([C1]) and downstream stations ([C2]). Upstream stations FY, KM, and TL were selected, along with downstream stations KS, AKS, and LS, with enhancing transshipment efficiencies \begin{table}
\begin{tabular}{c c c} \hline \hline
**Origin Number** & **Quantity** & **Origin Number** & **Quantity** \\ \hline
1 & 380 & 11 & 397 \\
2 & 400 & 12 & 151 \\
3 & 220 & 13 & 240 \\
4 & 530 & 14 & 365 \\
5 & 360 & 15 & 550 \\
6 & 535 & 16 & 135 \\
7 & 455 & 17 & 445 \\
8 & 170 & 18 & 520 \\
9 & 118 & 19 & 265 \\
10 & 339 & 20 & 425 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: The regenerated equipment quantities (unit).