## 5 Numerical Example
### Result Analysis
#### 5.2.2 Model Solution Results  
Experimental results demonstrate that under carbon emission-excluded scenarios, optimal transportation strategies for different cargo types exhibit distinct characteristics, as detailed in Table 8. Time-sensitive cargo demonstrates a \"time-priority\" pattern characterized by shorter transportation cycles accompanied by elevated carbon emissions and economic costs, whereas low time-sensitivity cargo adopts a \"cost-priority\" approach, predominantly utilizing waterway transportation to minimize transportation expenses. This study conducts a comparative differential analysis of high-value, timeliness-strong cargo transportation strategies under distinct carbon emission policies. Under carbon taxation regimes, the optimal transportation strategy exhibits phased evolution with progressive tax increments. The solution results are shown in Table 9 and as illustrated in Figure 14. When the tax rate reaches 0.1 CNY/kg, the optimal solution remains identical to the baseline scenario; at 1 CNY/kg, the optimal strategy shifts from road-rail intermodal to road-rail-water intermodal transportation, reducing carbon emissions by 11.63%; at 2 CNY/kg, emissions decrease by 43% with a 1.6 percentage point reduction in emission cost proportion within total expenditures. Strategic stability emerges between 2 and 3 CNY/kg, where tax adjustments fail to alter routing decisions. However, when the tax rate escalates to 4 CNY/kg, the optimal strategy transitions to exclusive waterway transportation, achieving minimal emissions of 30,500 kg (63.47% reduction versus baseline) while incurring 134% cost inflation. The findings demonstrate that moderate carbon tax escalation effectively promotes modal shift toward sustainable transportation structures, whereas excessive taxation achieves significant emission reductions at prohibitive economic  
Figure 13: Single iteration comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of** & **Transportation** & **Mode of** & **Total Cost** & **Total** & **Carbon** \\
**Cargo** & **Route** & **Transport** & **(CNY)** & **Time (h)** & **Emissions (kg)** \\ \hline \(n=1\) & 1-2-7-9-13-14 & H-R-R-R-H & 160,857.12 & 38.41 & 83,494 \\ \(n=2\) & 1-2-6-9-11-14 & R-W-W-W-W & 87,732.70 & 114.72 & 38,909 \\ \(n=3\) & 1-2-7-9-12-14 & R-R-R-R-R-R & 132,215.62 & 58.68 & 72,593 \\ \(n=4\) & 1-2-6-9-11-14 & R-W-W-W-W & 70,844.38 & 114.72 & 38,909 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Optimal transportation scheme for different types of cargo. costs, necessitating scientifically calibrated carbon taxation standards and implementation frameworks to guide multimodal transportation systems toward low-carbon development. Under carbon trading and mandatory emission policies, analytical results demonstrate that total operational costs exhibit an upward trajectory with decreasing emission allowances and increasing carbon prices. When carbon prices reach zero, optimal costs under both policies align with baseline scenario outcomes. As emission caps descend below the minimum emissions threshold of feasible solutions, total costs surge exponentially with carbon price escalation, converging with carbon taxation model results at zero emission allowance. Three distinct operational regimes emerge: (1) Below 30,000 kg emission caps, costs escalate rapidly with carbon price increases; (2) between 30,000 and 40,000 kg caps, cost growth moderates as multimodal combinations partially offset carbon pricing impacts despite suboptimal time-value costs; and (3) above 40,000 kg caps, transportation cost stability enables progressive total cost reduction with carbon price rises. The results are shown in Figure 15.  
Under carbon offset mechanisms, transportation schemes remain carbon price-insensitive when caps exceed baseline emissions due to non-tradable surplus allowances.