# Electric-Vehicle Routing Planning Based on the Law of Electric Energy Consumption
## 6 Case Study
### Results and Analysis
#### 6.2.2 L-EVRPTW Path under Nonlinear Energy Consumption (L-EVRPTW-NL)  
To further compare the results, we implemented the optimal routes of L-EVRPTW but with the driving-cycle-based energy consumption functions, and the results are listed in Table 15. We found that additional visits to recharging stations and more energy are required to complete the routes, which is because the linear energy consumption function in L-EVRPTW is less realistic when simulating the energy consumption in operation. Moreover, the order of visits to recharging stations may also be adjusted during the implementation. It is notable that, the solution of L-EVRPTW-NL would be a feasible solution to EVRPTW-DC. As a result of these adjustments, the cost of L-EVRPTW-NL is largely increased when compared to that of EVRPTW-DC and L-EVRPTW. It is shown that the additional costs mainly come from recharging and time window violation. We then present the cost compositions of EVRPTW-DC, L-EVRPTW, and L-EVRPTW-NL in Table 16. It is shown that recharging cost contributes the largest proportion of total cost in almost every experiment, and can be up to 54%. When considering the nonlinear energy consumption function, as in EVRPTW-DC and L-EVRPTW-NL, the recharging cost is larger than that of L-EVRPTW with the linear energy consumption function. This indicates that the pattern of energy consumption has a significant impact on the total costs, and a larger recharging cost would be expected with a more realistic assumption. Moreover, EVs need to be recharged a few more times when implementing the nonlinear energy consumption function, and the average path length is usually longer for EVRPTW-DC. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **1** & **2** & **3** \\ \hline
**Total Cost (Yuan)** & 693.85 & 1022.25 & 1114.72 \\ \hline
**Total Distance (km)** & 504.80 & 690.70 & 719.20 \\ \hline
**Cost of Distance (Yuan)** & 201.92 & 276.28 & 287.68 \\ \hline
**Recharged Energy (kW-h)** & 298.53 & 405.01 & 545.35 \\ \hline
**Recharging Cost (Yuan)** & 358.23 & 486.01 & 654.42 \\ \hline
**Cost of Time Window Violation (Yuan)** & 133.70 & 259.96 & 172.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Results of L-EVRPTW-NL. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Scenario 1**} & \multicolumn{2}{c}{**Scenario 2**} & \multicolumn{2}{c}{**Scenario 3**} \\ \cline{2-7}  & **EVRPTW-** & **L-EVRPTW** & **EVRPTW-** & **L-EVRPTW** & **EVRPTW-** & **L-EVRPTW** \\  & **DC** & **LC** & **LC** & **LC** & **LC** & **LC** \\ \hline
**Total Cost (Yuan)** & 440.53 & 482.08 & 946.67 & 783.01 & 1032.09 & 721.74 \\ \hline
**Total Distance (km)** & 438.48 & 494.60 & 703.31 & 686.35 & 730.40 & 695.80 \\ \hline
**Cost of Distance (Yuan)** & 175.39 & 197.84 & 281.32 & 274.54 & 292.16 & 278.32 \\ \hline
**Recharged Energy (kW-h)** & 159.30 & 149.72 & 424.02 & 293.34 & 414.79 & 272.98 \\ \hline
**Recharging Cost (Yuan)** & 191.16 & 179.66 & 508.82 & 352.01 & 497.75 & 327.57 \\ \hline
**Cost of Time Window Violation** & 73.98 & 104.58 & 156.53 & 156.46 & 242.18 & 115.85 \\ \hline
**Number of EVs** & 6 & 6 & 8 & 8 & 9 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Results of EVRPTW-DC and L-EVRPTW models. As can be seen from the above analysis, in general, the delivery paths under L-EVRPTW cannot be completely carried out under the nonlinear energy consumption function, and the costs of recharging and time window violation may be increased due to the actual recharging needs or due to the recharging operation, which makes the total cost higher than the theoretical value. In addition, L-EVRPTW and L-EVRPTW-NL have similar distance costs while the gap is due to recharging and time window violation costs.