## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{
\begin{tabular}{c} **Battery** \\ **Cap.(kWh)** \\ \end{tabular} } & \multicolumn{5}{c}{**Complete Chargings**} & \multicolumn{5}{c}{**Partial Chargings**} \\ \cline{3-10}  & & & & **Operat. Costs** & **Total. Costs** & **\# Stations** & **Operat.** & **Total. Costs** \\ \hline \multirow{3}{*}{\(t8576\_s207\)} & 60 & 90 & 2 & 1.620 & 33.62 & 86 & 2 & 1.621 & 32.22 (-1.40) \\  & 120 & 76 & 1 & 1.392 & 29.38 & 75 & 1 & 1.397 & 29.02 (-0.36) \\  & 300 & 76 & 1 & 1.322 & 32.35 & 75 & 1 & 1.322 & 34.94 (-0.40) \\  & 500 & 76 & 1 & 1.307 & 35.75 & 75 & 1 & 1.307 & 35.31 (-0.45) \\ \hline \multirow{3}{*}{\(t1135\_s101\)} & 60 & 107 & 1 & 1.990 & 39.69 & 104 & 2 & 1.991 & 38.89 (-0.80) \\  & 120 & 94 & 2 & 1.644 & 36.45 & 92 & 3 & 1.644 & 35.97 (-0.48) \\  & 300 & 91 & 1 & 1.528 & 38.63 & 89 & 2 & 1.529 & 38.89 (-0.56) \\  & 500 & 80 & 1 & 1.493 & 37.74 & 79 & 1 & 1.501 & 37.30 (-0.44) \\ \hline \multirow{3}{*}{\(t1296\_s88\)} & 60 & 86 & 6 & 0.729 & 32.33 & 82 & 7 & 0.730 & 31.18 (-**.115**) \\  & 120 & 74 & 3 & 0.487 & 28.25 & 71 & 4 & 0.489 & 27.40 (-0.84) \\  & 300 & 64 & 1 & 0.408 & 26.58 & 62 & 1 & 0.412 & 25.77 (-0.81) \\  & 500 & 58 & 1 & 0.384 & 26.73 & 56 & 1 & 0.391 & 25.84 (-0.89) \\ \hline \multirow{3}{*}{\(t2633\_s67\)} & 60 & 148 & 18 & 3.818 & 60.11 & 151 & 16 & 3.709 & 60.56 (+0.44) \\  & 120 & 144 & 16 & 3.307 & 59.87 & 146 & 14 & 3.292 & 60.08 (+0.21) \\  & 300 & 139 & 12 & 2.978 & 62.27 & 141 & 11 & 2.787 & 62.64 (+0.37) \\  & 500 & 134 & 6 & 2.892 & 64.69 & 135 & 5 & 2.815 & 64.82 (+0.12) \\ \hline \multirow{3}{*}{\(t3067\_s209\)} & 60 & 182 & 50 & 3.618 & 79.81 & 180 & 46 & 3.621 & 78.12 (-1.70) \\  & 120 & 178 & 48 & 3.346 & 80.31 & 175 & 43 & 3.780 & 78.00 (-2.31) \\  & 300 & 174 & 36 & 3.114 & 82.58 & 171 & 33 & 3.164 & 80.67 (-1.91) \\  & 500 & 171 & 12 & 3.087 & 83.03 & 169 & 12 & 3.096 & 82.14 (-0.89) \\ \hline \multirow{3}{*}{\(t1580\_s209\)} & 60 & 108 & 5 & 1.966 & 41.01 & 109 & 2 & 1.721 & 40.37 (-0.65) \\  & 120 & 98 & 1 & 1.601 & 37.62 & 98 & 1 & 1.583 & 37.60 (-0.02) \\  & 300 & 91 & 1 & 1.474 & 38.58 & 91 & 1 & 1.462 & 38.57 (-0.01) \\  & 500 & 87 & 1 & 1.287 & 40.68 & 87 & 1 & 1.276 & 40.67 (-0.71) \\ \hline \multirow{3}{*}{\(t1487\_s209\)} & 60 & 124 & 4 & 2.464 & 46.86 & 118 & 4 & 2.464 & 44.76 (-2.10) \\  & 120 & 102 & 1 & 1.940 & 39.42 & 99 & 2 & 1.940 & 38.58 (-0.85) \\ \cline{1-1}  & 300 & 102 & 1 & 1.97 & 43.36 & 98 & 2 & 1.792 & 41.98 (-1.38) \\ \cline{1-1}  & 500 & 98 & 1 & 1.752 & 46.10 & 95 & 2 & 1.751 & 45.01 (-1.10) \\ \hline \multirow{3}{*}{\(t1060\_s209\)} & 60 & 82 & 2 & 1.490 & 30.69 & 78 & 3 & 1.493 & 29.54 (-1.15) \\ \cline{1-1}  & 120 & 66 & 2 & 1.218 & 25.81 & 64 & 3 & 1.219 & 25.53 (-0.48) \\ \cline{1-1}  & 300 & 63 & 1 & 1.132 & 26.89 & 61 & 2 & 1.134 & 26.34 (-0.56) \\ \cline{1-1}  & 500 & 60 & 1 & 1.112 & 28.36 & 57 & 2 & 1.121 & 27.27 (-1.09) \\ \hline \multirow{3}{*}{\(t1074\_s209\)} & 60 & 86 & 2 & 1.496 & 32.09 & 85 & 5 & 1.499 & 32.49 (+0.40) \\ \cline{1-1}  & 120 & 72 & 1 & 1.216 & 27.74 & 71 & 4 & 1.218 & 28.13 (+0.39) \\ \cline{1-1}  & 300 & 72 & 1 & 1.132 & 30.54 & 71 & 3 & 1.194 & 30.69 (+0.16) \\ \cline{1-1}  & 500 & 67 & 1 & 1.105 & 31.50 & 66 & 3 & 1.184 & 31.63 (+0.13) \\ \hline \multirow{3}{*}{\(t933\_s209\)} & 60 & 81 & 6 & 1.527 & 31.37 & 82 & 7 & 1.498 & 31.95 (+0.57) \\ \cline{1-1}  & 120 & 66 & 1 & 1.171 & 25.51 & 67 & 2 & 1.169 & 26.12 (+0.61) \\ \cline{1-1}  & 300 & 65 & 1 & 1.081 & 27.66 & 66 & 2 & 1.089 & 28.32 (+0.66) \\ \cline{1-1}  & 500 & 60 & 1 & 1.044 & 28.29 & 61 & 2 & 1.075 & 29.03 (+0.73) \\ \hline \hline \end{tabular} 

charging procedures are enabled. On average, total cost savings of about 1.2% are achieved. Only in three cases are the total costs higher when considering partial chargings. We now compare the initial solutions with the results obtained and described in Section 5.3.