## 5 Computational Experiments
### Cost Performance Differences with Partial and Full Charging
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Partial Charging (PC)**} & \multicolumn{4}{c}{**Full Charging (FC)**} \\ \hline
**Instance** & _CC\_PC_ & _TC\_PC_ & _CC\_FC_ & _TC\_FC_ & _CC\_PC/CC\_FC_ & **GAP11** \\ \hline C15\_1 & 35.53 & 1937.86 & 69.68 & 1972.01 & 0.51 & 1.76\% \\ C15\_2 & 32.65 & 1690.96 & 75.05 & 1733.36 & 0.43 & 2.51\% \\ C15\_3 & 24.89 & 1696.14 & 74.51 & 1745.76 & 0.33 & 2.93\% \\ C15\_4 & 19.65 & 1786.65 & 48.69 & 1815.68 & 0.40 & 1.63\% \\ C15\_5 & 21.62 & 1520.87 & 75.13 & 1574.37 & 0.29 & 3.52\% \\ C15\_6 & 22.98 & 1523.66 & 74.65 & 1575.33 & 0.31 & 3.39\% \\ C15\_7 & 25.97 & 1540.93 & 78.63 & 1593.58 & 0.33 & 3.42\% \\ C15\_8 & 21.25 & 1516.35 & 80.67 & 1575.78 & 0.26 & 3.92\% \\ C15\_9 & 23.31 & 1525.59 & 46.40 & 1548.68 & 0.50 & 1.51\% \\ C15\_10 & 17.93 & 1640.44 & 46.40 & 1668.91 & 0.39 & 1.74\% \\ Average & 24.58 & 1637.94 & 66.98 & 1680.35 & 0.38 & 2.63\% \\ \hline C25\_1 & 21.92 & 2151.14 & 75.06 & 2204.27 & 0.29 & 2.47\% \\ C25\_2 & 42.50 & 2332.27 & 153.06 & 2442.82 & 0.28 & 4.74\% \\ C25\_3 & 52.93 & 2378.67 & 173.13 & 2498.87 & 0.31 & 5.05\% \\ C25\_4 & 42.88 & 2333.95 & 148.01 & 2439.08 & 0.29 & 4.50\% \\ C25\_5 & 24.74 & 2150.58 & 77.25 & 2203.09 & 0.32 & 2.44\% \\ C25\_6 & 36.38 & 1947.82 & 102.69 & 2114.14 & 0.35 & 8.54\% \\ C25\_7 & 20.75 & 2151.87 & 51.46 & 2182.58 & 0.40 & 1.43\% \\ C25\_8 & 20.46 & 2151.12 & 77.29 & 2207.96 & 0.26 & 2.64\% \\ C25\_9 & 42.90 & 2334.02 & 146.01 & 2437.13 & 0.29 & 4.42\% \\ C25\_10 & 50.71 & 2368.77 & 167.42 & 2485.48 & 0.30 & 4.93\% \\ Average & 35.62 & 2230.02 & 117.14 & 2321.54 & 0.31 & 4.12\% \\ \hline C50\_1 & 76.31 & 4534.81 & 240.00 & 4698.50 & 0.32 & 3.61\% \\ C50\_2 & 83.67 & 4301.41 & 296.19 & 4513.93 & 0.28 & 4.94\% \\ C50\_3 & 90.45 & 4331.55 & 279.82 & 4520.92 & 0.32 & 4.37\% \\ C50\_4 & 57.87 & 4096.90 & 210.27 & 4249.31 & 0.28 & 3.72\% \\ C50\_5 & 84.25 & 4303.96 & 295.43 & 4515.14 & 0.29 & 4.91\% \\ C50\_6 & 84.79 & 4306.36 & 271.05 & 4492.63 & 0.31 & 4.33\% \\ C50\_7 & 86.42 & 4313.64 & 299.54 & 4526.76 & 0.29 & 4.94\% \\ C50\_8 & 90.19 & 4330.37 & 296.88 & 4537.07 & 0.30 & 4.77\% \\ C50\_9 & 81.98 & 4293.86 & 263.78 & 4475.66 & 0.31 & 4.23\% \\ C50\_10 & 45.85 & 4313.53 & 149.30 & 4416.98 & 0.31 & 2.40\% \\ Average & 78.18 & 4312.64 & 260.23 & 494.69 & 0.30 & 4.22\% \\ \hline C100\_1 & 129.97 & 8861.79 & 411.33 & 9143.15 & 0.32 & 3.18\% \\ C100\_2 & 134.65 & 8634.59 & 451.19 & 8951.12 & 0.30 & 3.67\% \\ C100\_3 & 152.49 & 8939.39 & 494.60 & 9281.49 & 0.31 & 3.83\% \\ C100\_4 & 142.35 & 8396.43 & 499.18 & 8753.27 & 0.29 & 4.25\% \\ C100\_5 & 125.44 & 8740.05 & 416.34 & 9030.94 & 0.30 & 3.33\% \\ C100\_6 & 129.44 & 8608.48 & 448.09 & 8927.13 & 0.29 & 3.70\% \\ C100\_7 & 127.93 & 8741.57 & 422.30 & 9035.94 & 0.30 & 3.37\% \\ C100\_8 & 126.43 & 8709.71 & 417.76 & 9001.05 & 0.30 & 3.34\% \\ C100\_9 & 122.43 & 8850.17 & 410.56 & 9138.30 & 0.30 & 3.26\% \\ C100\_10 & 141.26 & 8509.47 & 488.61 & 8856.83 & 0.29 & 4.08\% \\ Average & 133.24 & 8699.16 & 446.00 & 9011.92 & 0.30 & 3.60\% \\ \hline \hline \end{tabular} Note: The notation _CC\_PC_PC_) and _CC\_FC_(TC\_FC) represents charging (total) costs under partial and full charging strategies. GAP11 = 100% \(*\) (\(TC\_FC-TC\_PC\))/_TC\_PC_.  
\end{table} 
Table 7: Cost distribution patterns under partial and full charging strategies. size increases, the average percentage savings in the total cost under the partial charging strategy, compared to full charging, rises from less than 3% to approximately 4%. This trend is explained by the \(CC\_PC/CC\_FC\) metrics. For smaller instances, partial charging costs constitute a higher proportion of full charging costs, reaching up to 0.51. As the instance size grows, this proportion decreases and stabilizes around 0.3, indicating that full charging costs grow faster than partial charging costs. Thus, the cost-saving advantage of partial charging becomes more pronounced with larger problem sizes.