## 5 Numerical Example
### Result Analysis
#### 5.2.2 Model Solution Results
Under hybrid uncertainty conditions with temporal confidence level parameterized at 0.8 and regret coefficient set to 0.25, the robust optimization analysis yields critical findings as documented in Table 11. The robust optimal transportation scheme \"1-Rail-2-Rail-7-Rail-9-Rail-13-Road-14\" demonstrates an expected total cost of CNY 154,297, accompanied by an average regret value of 0.06 and maximum regret value of 0.21 across all pricing scenarios. This solution maintains comprehensive transportation cost deviations within the predefined 0.25 regret coefficient threshold relative to robust objective function values across all operational scenarios, thereby satisfying robust feasibility criteria. Comparative analysis reveals strategic divergence between baseline and robust optimal solutions in both nodal sequences and modal combinations, highlighting the methodology's capacity to systematically address multimodal uncertainties. The identified scheme achieves cost-efficient robustness through balanced integration of railway dominance and strategic road transportation terminal legs, effectively mitigating pricing volatility impacts while maintaining temporal reliability under constrained confidence parameters. Based on the analytical results, critical parameters for the four low-carbon policy models were systematically configured: carbon tax rate at CNY 0.4/kg, mandatory emission cap at 70,000 kg, carbon trading/offset caps at 75,000 kg, and carbon price at CNY 0.3/kg. The comparative results (Figure 16) reveal differentiated policy impacts on environmental performance, economic costs, and decision stability under uncertainty. Regarding emission reductions, the baseline model exhibits the highest carbon output due to absent policy constraints. All low-carbon policies demonstrate emission mitigation efficacy with varying intensities: the mandatory policy achieves 11.63% reduction through rigid constraints, while tax, trading, and offset policies yield equivalent 6.15% reductions via market mechanisms. Economic analysis demonstrates tradeoff patterns: carbon taxation incurs 23.7% cost inflation alongside emission reductions; trading/offset policies maintain balanced cost-emission ratios; and the mandatory policy shows intermediate cost escalation, reflecting cost-environment equilibrium under regulatory constraints. Decision stability metrics reveal maximum regret values of 18.2% for baseline and 21.5% for tax policy, contrasted with elevated values under trading and offset mechanisms due to market complexity. The  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**Optimal Transportation Scheme**} & **Scenario- Optimal Total Cost (CNY)** & **Robust- Optimal Total Cost (CNY)** & **Regret Value (\%)** \\ \hline
1 & 1-H-2-R-7-R-9-R-13-H-14 & 117,104 & 120,958 & 3.29 \\
2 & 1-H-2-R-7-R-9-R-13-H-14 & 121,719 & 12,798 & 5.15 \\
3 & 1-H-2-  
mandatory policy enhances stability through deterministic constraints. The comparative conditions of total costs, carbon emissions, and stability under different policies are shown in Table 12. These findings highlight policy-specific optimization frontiers: mandatory constraints prioritize environmental rigor with moderate economic impacts; market-based mechanisms balance flexibility and sustainability; and taxation emphasizes emission control at higher costs. Strategic selection should integrate emission reduction targets, budgetary constraints, and operational risk tolerance to formulate context-specific decarbonization roadmaps for multimodal transportation systems.