## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Instance** & **Battery Capacity (kWh)** & **\# Vehicles** & **\# Stations** & **Operat. Costs (Mio)** & **Total Costs (Mio)** \\ \hline \multirow{4}{*}{t876\_s207} & 60 & 80 (+10) & 47 & 1.019 & 40.77 \\  & 120 & 75 (+6) & 44 & 1.060 & 39.72 \\  & 300 & 72 (+3) & 33 & 1.098 & 38.51 \\  & 500 & 69 (+0) & 7 & 1.157 & 33.96 \\ \hline \multirow{4}{*}{t1135\_s101} & 60 & 87 (+12) & 33 & 1.187 & 39.89 \\  & 120 & 82 (+7) & 27 & 1.219 & 37.90 \\  & 300 & 76 (+1) & 15 & 1.265 & 35.79 \\  & 500 & 75 (+0) & 2 & 1.379 & 35.62 \\ \hline \multirow{4}{*}{t1296\_s88} & 60 & 61 (+14) & 43 & 0.082 & 32.18 \\  & 120 & 49 (+3) & 32 & 0.112 & 28.16 \\  & 300 & 49 (+3) & 25 & 0.108 & 25.79 \\  & 500 & 47 (+0) & 6 & 0.116 & 22.77 \\ \hline \multirow{4}{*}{t2633\_s67} & 60 & 144 (+19) & 29 & 2.193 & 59.84 \\  & 120 & 137 (+12) & 21 & 2.438 & 57.69 \\  & 300 & 131 (+6) & 17 & 2.514 & 59.82 \\  & 500 & 126 (+1) & 8 & 2.621 & 61.32 \\ \hline \multirow{4}{*}{t3067\_s209} & 60 & 179 (+14) & 90 & 2.681 & 87.83 \\  & 120 & 171 (+6) & 69 & 2.820 & 82.49 \\  & 300 & 169 (+4) & 39 & 2.871 & 81.07 \\  & 500 & 166 (+1) & 14 & 2.994 & 81.19 \\ \hline \multirow{4}{*}{t1580\_s209} & 60 & 87 (+12) & 55 & 1.133 & 45.33 \\  & 120 & 81 (+6) & 45 & 1.289 & 42.10 \\  & 300 & 75 (+0) & 20 & 1.367 & 36.74 \\  & 500 & 75 (+0) & 7 & 1.323 & 36.83 \\ \hline \multirow{4}{*}{t1487\_s209} & 60 & 101 (+12) & 53 & 1.421 & 50.02 \\  & 120 & 92 (+3) & 37 & 1.573 & 44.40 \\  & 300 & 90 (+1) & 24 & 1.682 & 44.13 \\  & 500 & 89 (+0) & 7 & 1.753 & 43.53 \\ \hline \multirow{4}{*}{t1060\_s209} & 60 & 59 (+5) & 43 & 0.952 & 32.35 \\  & 120 & 55 (+1) & 30 & 0.991 & 28.56 \\  & 300 & 54 (+0) & 13 & 0.989 & 26.11 \\  & 500 & 54 (+0) & 3 & 0.986 & 26.04 \\ \hline \multirow{4}{*}{t1074\_s20} & 60 & 64 (+8) & 39 & 0.897 & 33.05 \\  & 120 & 59 (+3) & 33 & 0.971 & 30.76 \\  & 300 & 57 (+1) & 16 & 0.988 & 28.07 \\  & 500 & 56 (+0) & 6 & 0.994 & 27.69 \\ \hline \multirow{4}{*}{t933\_s209} & 60 & 64 (+10) & 35 & 0.956 & 32.06 \\  & 120 & 58 (+4) & 25 & 0.961 & 28.38 \\ \cline{1-1}  & 300 & 55 (+1) & 15 & 0.970 & 26.99 \\ \cline{1-1}  & 500 & 54 (+0) & 4 & 0.969 & 26.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of solving an E-VSP given locations of charging stations by reduced Algorithm 1 incorporating partial charging procedures. are specified when enabling partial charging procedures, and the best solutions found are in bold. We first compare the results to the first experiment conducted and described in Section 5.2. We observe that in two of the 17 cases, when the first experiment lead to feasible vehicle rotations, the total costs obtained by the application of the savings algorithm were already lower by comparison to solving a location planning problem for charging stations. In the other cases, higher total costs are obtained. In general, the higher total costs arise from higher demands for vehicles needed within the savings algorithm. Regarding each instance, the numbers of vehicles used has increased, which is reasonable due to the heuristic solution procedure of the savings algorithm. The solving of instance \(t1296\_s88\) leads to the highest increase of 23.4%. By contrast, the number of charging stations used decreases in every case. In some cases, such as instance \(t1060\_s209\), the number of charging stations needed is enormously reduced (30 to two). However, since the costs for additional vehicles prevail over the cost savings arising from the lower number of charging stations used, the total costs increase. This holds true both for complete and partial charging procedures. Regarding these two charging procedures, the total costs obtained are lower in seven of the ten instances for all battery capacities when partial charging procedures are applied. \begin{table}