# Optimization of Multimodal Transport Paths Considering a Low-Carbon Economy Under Uncertain Demand
## 5 Calculation Analysis and Discussion
### Case Study  
To validate the effectiveness of the models developed and algorithms designed in this paper, taking a public rail-fly multimodal transportation system in the eastern region of China as the background, 17 cities are selected as the nodes of the transportation network. To facilitate the representation of the transportation scheme below, the actual network nodes \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{\(\mathbf{U_{s}}\)} & \multirow{2}{*}{\(\mathbf{R_{q}}\)} & **Total Transportation** & **Actual Carbon** & **Cost of Carbon** \\  & & & **Costs** & **Emissions** & **Emissions** \\ \hline
1 & 0.1t & 70 CNY/t & 115,374 & 3842 & 261.94 \\
2 & 1t & 70 CNY/t & 111,296 & 3899 & 202.93 \\
3 & 5t & 70 CNY/t & 119,182 & 3756 & 350 \\
4 & 8t & 70 CNY/t & 119,380 & 3756 & 560 \\
5 & 10t & 70 CNY/t & 119,520 & 3756 & 700 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Solution results under carbon offset policy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{R_{t}}\) & \(\mathbf{C^{{}^{\prime}}}\) & \multirow{2}{*}{\(\mathbf{E}\) **(kg)**} & **Cost of Carbon** & **Path** \\ (CNY/0) & (CNY) & & **Emissions** & **(Fractional Part I: Road, 2: Railroad, 3: Airplane)** \\ \hline
0 & 86,834 & 3669 & 0 & \(1\to 7.2\to 3.1\to 4.1\to 5.2\to 10.2\to 15.3\to 25\) \\
300 & 99,547 & 3894 & 1168.2 & \(1\to 7.2\to 3.1\to 4.1\to 5.2\to 10.2\to 15.3\to 25\) \\
400 & 118,775 & 3894 & 1557.6 & \(1\to 7.2\to 3.1\to 4.1\to 5.2\to 10.2\to 15.3\to 25\) \\
500 & 124,723 & 3871 & 1935.5 & \(1\to 7.2\to 3.1\to 4.1\to 5.2\to 10.3\to 25\) \\
1000 & 127,435 & 3756 & 3756 & \(1\to 7.2\to 3.1\to 4.1\to 5.2\to 10.3\to 25\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Impact of different carbon taxes on multimodal transport path optimization. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{\(\mathbf{U_{s}}\)} & \multirow{2}{*}{\(\mathbf{R_{s}}\)} & **Total** & **Actual Carbon** & **Costs/Benefits of** \\  & & & **Costs** & **Emissions** & **Carbon Emissions** \\ \hline
1 & 0.1t & 70 CNY/t & 114,256 & 3669 & 249.83 \\
2 & 1t & 70 CNY/t & 107,335 & 3734 & 191.38 \\
3 & 5t & 70 CNY/t & 107,064 & 3870 & \(-\)79.1 \\
4 & 8t & 70 CNY/t & 106,849 & 3799 & \(-\)294.07 \\
5 & 10t & 70 CNY/t & 106,706 & 3760 & \(-\)436.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Solution results under the carbon trading policy. are numbered, as shown in Table 10, from 1 to 17. The highway distance data in the figure are derived from the Gaode map; the railroad distance from the China Railway Network and the air transportation distance comes from the flight mileage of China Southern Airlines. The relevant data are shown in Table 11. Figure 8 shows the railroad transportation routes of the transportation network, and nodes 0 and 17 are the starting and ending points of the transportation tasks. Due to the excessive number of road and air transportation routes, they are not shown in the figure. A route selection scheme with the lowest total cost of transportation under the low-carbon policy is sought. As can be seen from Figure 9, among the four kinds of carbon emission policies, the mandatory carbon emission policy means are tough. The effect of energy saving and emission reduction is the most significant, and the cost is the lowest. The three kinds of policy means, namely, carbon tax, carbon trading and carbon compensation, are more moderate, and the effect of energy saving and emission reduction is the second-most effective. The optimal path scheme under mandatory carbon emissions is shown in Figure 10.