## 5 Numerical Example
### Result Analysis
#### 5.2.2 Model Solution Results
For caps between baseline and minimum emission levels, adaptive multimodal strategies emerge through dynamic allowance-price optimization, demonstrating cost reduction and  
Figure 14: Total cost, carbon emissions, and carbon emission cost under different carbon tax values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Carbon Tax** & & **Total Cost** & **Carbon** & **Proportion of** \\
**Rate** & **Transportation Scheme** & **(CNY)** & **Emissions** & **Carbon** \\
**(CNY/kg)** & & **(kg)** & **Emission Cost** \\ \hline
0.1 & 1-H-2-R-7-R-9-R-13-H-14 & 169,206.5 & 83,494 & 4.93\% \\
0.5 & 1-R-2-R-7-R-9-R-13-H-14 & 201,693.5 & 77,352 & 19.17\% \\
1 & 1-R-2-R-7-R-9-W-11-H-14 & 239,666.3 & 68,349 & 28.52\% \\
2 & 1-R-2-W-6-W-9-W-11-W-14 & 289,033.9 & 38,909 & 26.92\% \\
3 & 1-R-2-W-6-W-9-W-11-W-14 & 327,943.3 & 38,909 & 35.59\% \\
4 & 1-W-4-W-6-W-9-W-11-W-14 & 377,825.9 & 30,500 & 32.29\% \\
5 & 1-W-4-W-6-W-9-W-11-W-14 & 398,246.3 & 30,500 & 38.29\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Changes of optimal transportation scheme under different carbon tax values. stabilization with expanding allowances. These findings necessitate comprehensive consideration of allowance-price dynamics, multimodal configuration interactions, and cargo-specific attributes when formulating transportation strategies under emission-constrained operational frameworks. Under the mandatory carbon emission policy with allowance caps parameterized between 30,000 and 90,000 kg (increment: 10,000 kg), the evolution of optimal transportation strategies is systematically documented in Table 10. When the emission cap is set at 30,000 kg, no feasible solution exists, indicating all potential routes exceed this constraint. Progressive cap increases from 30,000 kg to 90,000 kg induce strategic shifts from the initial \"1-W-4-R-5-W-9-W-11-W-14\" configuration to the optimized \"1-H-2-R-7-R-9-R-13-H-14\" scheme, achieving 33% cost reduction and 71% transit time improvement while incurring significant carbon emission increases. Strategic stabilization occurs beyond 90,000 kg caps. This policy demonstrates dual regulatory effects as a rigid constraint mechanism: (1) loosened caps incentivize economically favorable but environmentally detrimental modal combinations with reduced transit durations; (2) cargo-type differential responses emerge--for time-insensitive shipments dominated by maritime transport in baseline scenarios, carbon cap adjustments exert limited impacts on modal selection and cost structures. Practical implementation requires comprehensive integration of transportation demand patterns and market dynamics with environmental constraints. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Carbon Quota (kg)** & **Transportation Scheme** & **Total Cost (CNY)** & **Total Time (h)** \\ \hline
30,000 & — & — & — \\
40,000 & 1-W-4-R-5-W-9-W-11-W-14 & 240,374.51 & 132.72 \\
50,000 & 1-H-2-W-6-W-9-W-11-W-14 & 201,564.58 & 102.72 \\
60,000 & 1-H-2-R-7-R-9-W-11-W-14 & 190,081.62 & 80.72 \\
70,000 & 1-R-2-R-7-R-9-R-11-R-14 & 171,317.29 & 59.58 \\
80,000 & 1-R-2-R-7-R-9-R-13-R-14 & 163,017.26 & 48.41 \\
90,000 & 1-H-2-R-7-R-9-R-13-H-14 & 160,857.12 & 38.41 \\ \hline \hline \end{tabular} note—indicates that it does not exist.  
\end{table} 
Table 10: Changes of optimal transportation scheme under mandatory carbon emission policy. Figure 15: Comparative analysis of cost responsiveness to carbon trading and carbon offset policy scenarios. (**a**) Variation of total cost as a function of carbon price and allowance allocation under carbon trading policy. (**b**) Variation of total cost as a function of carbon price and allowance allocation under carbon offset policy.