## 4 Method Design
### Optimising Scheduling Scenarios  
First, the indicators of the scheduling scenarios are processed without dimension. Second, the weighted normalised matrix of the criteria layer is calculated. Third, the distances from each scheduling scenario to the optimal solution and worst solution are calculated, and the closeness degree from each scheduling scenario to the optimal solution is calculated. Table 8 shows the distances from each scenario to the optimal solution and worst solution without consideration of peak to valley and closeness degree. Table 9 shows the distances from each scenario to the optimal solution and the worst solution, avoiding the sharp period and closeness degree. Table 10 shows the distances from each scenario to the optimal solution and the worst solution, avoiding sharp and peak periods and closeness degrees.  
Therefore, the optimised scheduling scenario could be obtained, which corresponds to the minimum value of the closeness degree of all scheduling scenarios under each type of time window. In Table 8, the optimised scheduling scenario is the 49 th under the time windows without consideration of peak to valley. In Table 9, the optimised scheduling scenario is the 10 th under the time windows of avoiding a sharp period. In Table 10, the optimised scheduling scenario is the fourth under the time windows of avoiding the peak and sharp periods.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **NFVs** & **NEVs** & **TC** & **Rest Time** & **RCE** & **Purchase Strategy** \\ \hline
1 & 20 & 20 & 339,030 & 24.0 & 451.36 & 0, 1, 1, 0, 0, 1, 0, 0, 0, 1 \\
2 & 21 & 20 & 381,600 & 22.8 & 479.96 & 1, 1, 1, 0, 0, 0, 0, 0, 0, 1 \\
3 & 22 & 20 & 397,170 & 24.0 & 439.92 & 0, 1, 0, 0, 1, 0, 0, 1, 1 \\
4 & 23 & 20 & 395,620 & 24.0 & 447.72 & 0, 0, 1, 0, 1, 1, 0, 1, 0 \\
5 & 20 & 21 & 354,060 & 25.2 & 475.28 & 1, 1, 0, 0, 0, 1, 0, 1, 0 \\
6 & 21 & 21 & 354,960 & 25.2 & 460.72 & 1, 1, 0, 0, 0, 1, 0, 1, 0 \\
7 & 20 & 22 & 354,960 & 30.0 & 487.24 & 1, 1, 0, 0, 0, 1, 0, 1, 0, 1 \\
8 & 22 & 23 & 377,100 & 30.0 & 540.28 & 1, 1, 0, 0, 1, 1, 0, 0 \\
9 & 24 & 23 & 294,480 & 26.1 & 402.80 & 0, 1, 1, 0, 0, 1, 0, 0, 0, 1 \\
10 & 20 & 24 & 339,030 & 25.0 & 527.80 & 0, 1, 1, 0, 0, 1, 0, 1, 0, 0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Scheduling scenarios avoiding sharp periods.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **NFVs** & **NEVs** & **TC** & **Rest Time** & **RCE** & **Purchase Strategy** \\ \hline
1 & 20 & 20 & 345,780 & 25.0 & 423.28 & 0, 1, 1, 0, 1, 0, 0, 0, 0, 1 \\
2 & 21 & 20 & 389,970 & 30.0 & 665.60 & 0, 1, 1, 0, 0, 1, 0, 0, 0, 1 \\
3 & 20 & 21 & 345,600 & 22.9 & 430.56 & 0, 1, 1, 1, 0, 0, 1, 0, 1 \\
4 & 21 & 23 & 393,660 & 32.9 & 492.96 & 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Scheduling scenarios avoiding sharp and peak periods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \
\begin{tabular}{c} **Distance of** \\ **Optimal Solution** \\ \end{tabular} &
\begin{tabular}{c} **Distance of Worst** \\ **Solution** \\ \end{tabular} & **Closeness Degree** & **Order** \\ \hline
1 & 0.4802 & 0.1077 & 0.1832 & 46 \\
2 & 0.4563 & 0.1143 & 0.2003 & 43 \\
3 & 0.4591 & 0.1477 & 0.2434  
+++ ==WARNING: Truncated because of repetitions==
& 41 \\  
++