# A Two-Echelon Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations
## 5 Numerical Experiments
### Computational Results and Analysis
#### 5.2.3 Comparison of Carbon Emission between ICVs and EVs in the Second-Echelon  
One of the important advantages of EVs is the reduction in carbon emissions. To illustrate the effects of emission reduction, we compare the emissions of our solution with that of fossil fuel-based internal combustion vehicles (ICVs) for the second echelon. The unit emissions of EVs are calculated based on the formulation of [PERSON] et al. (2018) [20], and the unit emissions of ICVs are calculated based on the formulation of [PERSON] et al. (2017) [38]. The parameters of an EV are adopted from [PERSON] et al. (2019) [51], and the parameters of an ICV are adopted from [PERSON] et al. (2017) [38]. We assume that the road grade angle is 0, the vehicle acceleration is 0, and the EV and the ICV have the same travel speed.  
The results are shown in Table 6, where \"EV\" means the emissions when only EVs are adopted and \"ICV\" means the emissions when only ICVs are adopted.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Inst**} & \multicolumn{3}{c}{**Instance Size**} & \multicolumn{3}{c}{**[PERSON] (2017)**} & \multicolumn{3}{c}{**VNS**} & \multirow{2}{*}{**Gap (VNS/Wang** (2017))**} \\ \cline{2-2} \cline{5-10}  & **m** & **n** & **1** & **Best** & **Avg** & **Time (s)** & **Best** & **Avg** & **Time (s)** & **(2017)** \\ \hline
2-1 & 2 & 20 & 4 & 857.05 & 857.05 & 64.77 & 857.05 & 857.05 & 73.45 & 0.00\% \\
2-2 & 2 & 20 & 4 & 986.73 & 986.73 & 78.05 & 986.73 & 986.73 & 80.19 & 0.00\% \\
2-3 & 2 & 20 & 4 & 853.67 & 853.67 & 100.40 & 853.67 & 853.67 & 123.35 & 0.00\% \\
2-4 & 2 & 30 & 6 & 1310.07 & 987.17 & 1310.07 & 1310.07 & 1310.07 & 1056.69 & 0.00\% \\
2-5 & 2 & 30 & 6 & 1415.36 & 1415.36 & 1209.68 & 1415.36 & 1415.36 & 1233.37 & 0.00\% \\
2-6 & 2 & 30 & 6 & 1440.31 & 1440.31 & 1444.67 & 1440.31 & 1440.31 & 1425.45 & 0.00\% \\
2-7 & 2 & 40 & 8 & 1915.31 & 1915.31 & 1433.08 & 1915.31 & 1915.31 & 1433.29 & 0.00\% \\
2-8 & 2 & 40 & 8 & 1915.59 & 1915.59 & 2004.07 & 1919.59 & 1915.59 & 1904.75 & 0.21\% \\
2-9 & 2 & 40 & 8 & 1918.16 & 1918.16 & 2012.39 & 1918.16 & 1918.16 & 1983.08 & 0.00\% \\
2-10 & 2 & 50 & 10 & 2309.42 & 2309.42 & 2100.89 & 2307.70 & 2307.70 & 2142.66 & \(-0.07\%\) \\
2-11 & 2 & 50 & 10 & 2376.50 & 2376.50 & 2387.79 & 2377.84 & 2322.84 & 2223.04 & 0.06\% \\
2-12 & 2 & 50 & 10 & 67,586.62 & 67,586.62 & 2366.45 & 60,314.84 & 60,314.84 & 2245.89 & \(-10.76\%\) \\
2-13 & 3 & 60 & 12 & 81,753.85 & 81,753.85 & 3104.56 & 77,195.14 & 77,195.14 & 3004.35 & \(-5.58\%\) \\
2-14 & 3 & 60 & 12 & 2818.74 & 2818.74 & 3399.97 & 2802.56 & 2802.56 & 3179.97 & \(-0.57\%\) \\
2-15 & 3 & 60 & 12 & 2783.41 & 2783.41 & 3374.67 & 2761.43 & 2761.43 & 3113.37 & \(-0.79\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results for the middle-sized instances.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Inst**} & \multicolumn{3}{c}{**Instance Size**} & \multicolumn{3}{c}{**[PERSON] (2017)**} & \multicolumn{3}{c}{**VNS**} & \multirow{2}{*}{**Gap (VNS/Wang** (2017))**} \\ \cline{2-2} \cline{5-10}  & **m** & **n** & **1** & **Best** & **Avg** & **Best** & **Avg** & **(2017))** \\ \hline
3-1 & 5 & 100 & 20 & 4816.65 & 4816.65 & 4788.05 & 4788.05 & \(-0.60\%\) \\
3-2 & 5 & 100 & 20 & 4529.14 & 4529.14 & 4522.59 & 4522.59 & \(-0.14\%\) \\
3-3 & 5 & 100 & 20 & 4592.02 & 4592.02 & 4457.66 & 4457.66 & \(-3.01\%\) \\
3-4 & 10 & 100 & 20 & 4640  
From last column in Table 6, it can be concluded that using EVs in transportation systems rather than ICVs is more environmental. The emissions of EVs can be reduced by about 20%. Thus, compared to ICVs, applying EVs is more environmentally friendly.