## 4 Numerical Experiments  
The numerical experiments presented in this work seek to compare the performance of the proposed heuristic with some of the best solutions from the literature provided by [PERSON] [6]. Tables 1 and 2 contain the results of the heuristic and total execution time in the 'Avg.' and 'T (seconds)' columns, respectively, along with the best-known solutions ('BKS') from the literature and their execution times. Additionally, the 'Gap' column presents the percentage variation between the heuristic solution and the 'BKS'. Finally, the 'nS' and 'nC' columns represent the number of satellites and customers, respectively.  
The analysis of the results reveals an average gap of 6.3% for the heuristic, with an average resolution time of 1.06 s. This effectiveness is consistent, showing variations in the average gap between sets of instances ranging from 4.3% to 9.5% and in the average time, fluctuating between 0.21 and 3.25 s. Despite some peak values reaching 19.6% with 12.22 s, these results are promising for implementation in the system, as they exhibit runtime close to instantaneous, significantly less than the maximum of 30 s.  
\begin{table}
\begin{tabular}{l r r r r r r} \hline \hline  & **nS** & **nC** & **BKS** & **T (s)** & **heur.* ** & **T (s)** & **\%dev2** \\ \hline
**Set 2a** & & & & & & \\ E-n22-k4-s6-17 & 2 & 21 & 417.07 & 27.00 & 443.16 & 0.05 & 6.3\% \\ E-n22-k4-s8-14 & 2 & 21 & 384.96 & 27.00 & 392.92 & 0.16 & 2.1\% \\ E-n22-k4-s9-19 & 2 & 21 & 470.60 & 35.00 & 499.13 & 0.09 & 6.1\% \\ E-n22-k4-s10-14 & 2 & 21 & 371.50 & 25.00 & 371.50 & 0.16 & 0.0\% \\ E-n22-k4-s11-12 & 2 & 21 & 427.22 & 31.00 & 446.05 & 0.02 & 4.4\% \\ E-n22-k4-s12-16 & 2 & 21 & 392.78 & 36.00 & 441.89 & 0.38 & 12.5\% \\ E-n33-k4-s19 & 2 & 32 & 730.16 & 60.00 & 749.59 & 0.13 & 2.7\% \\ E-n33-k4-s2-13 & 2 & 32 & 714.63 & 60.00 & 746.52 & 0.13 & 4.5\% \\ E-n33-k4-s3-17 & 2 & 32 & 707.48 & 58.00 & 831.24 & 0.11 & 17.5\% \\ E-n33-k4-s4-5 & 2 & 32 & 778.74 & 60.00 & 828.96 & 0.13 & 6.4\% \\ E-n33-k4-s7-25 & 2 & 32 & 756.85 & 53.00 & 800.33 & 0.39 & 5.7\% \\ E-n33-k4-s14-22 & 2 & 32 & 779.05 & 60.00 & 827.04 & 0.75 & 6.2\% \\  & & & **Avg.** & **44.33** & & **0.21** & **6\%** \\
**Set 2b** & & & & & & & \\ E-n51-k5-s2-17 & 2 & 50 & 597.49 & 60.00 & 595.08 & 0.43 & \(-\)0.4\% \\ E-n51-k5-s4-46 & 2 & 50 & 530.76 & 60.00 & 577.58 & 0.51 & 8.8\% \\ E-n51-k5-s6-12 & 2 & 50 & 554.81 & 60.00 & 567.68 & 1.04 & 2.3\% \\ E-n51-k5-s11-19 & 2 & 50 & 581.64 & 60.00 & 610.19 & 3.94 & 4.9\% \\ E-n51-k5-s2-47-47 & 2 & 50 & 538.22 & 60.00 & 583.27 & 0.43 & 8.4\% \\ E-n51-k5-s32-37 & 2 & 50 & 552.28 & 60.00 & 590.80 & 0.82 & 7.0\% \\ E-n51-k5-s2-4-17-46 & 4 & 50 & 530.76 & 60.00 & 555.18 & 12.22 & 4.6\% \\ E-n51-k5-s6-12-32-37 & 4 & 50 & 531.92 & 60.00 & 554.58 & 3.53 & 4.3\% \\ E-n51-k5-s11-19-27-47 & 4 & 50 & 527.63 & 60.00 & 565.77 & 6.30 & 7.2\% \\  & & & **Avg.** & **60.00** & & **3.25** & **5\%** \\
**Set 2c** & & & & & & & \\ E-n51-k5-s11-19 & 2 & 50 & 617.42 & 60.00 & 644.72 & 2.41 & 4.4\% \\ E-n51-k5-s11-19-27-47 & 4 & 50 & 530.76 & 60.00 & 617.93 & 1.27 & 16.4\% \\ E-n51-k5-s2-17 & 2 & 50 & 601.39 & 60.00 & 621.14 & 0.42 & 3.3\% \\ E-n51-k5-s2-4-17-46 & 4 & 50 & 601.39 & 60.00 & 676.94 & 0.18 & 12.6\% \\ E-n51-k5-s2-47-47 & 2 & 50 & 530.76 & 59.00 & 625.33 & 0.40 & 17.8\% \\ E-n51-k5-s32-37 & 2 & 50 & 752.59 & 60.00 & 840.39 & 0.14 & 11.7\% \\ E-n51-k5-s4-46 & 2 & 50 & 702.33 & 60.00 & 746.77 & 0.10 & 6.3\% \\ E-n51-k5-s6-12 & 2 & 50 & 567.42 & 60.00 & 598.83 & 0.54 & 5.5\% \\ E-n51-k5-s6-12-32-37 & 4 & 50 & 567.42 & 60.00 & 609.00 & 7.45 & 7.3\% \\  & & & & **Avg.** & **59.89** & & **1.43** & **9\%** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results from the first set of instances from the literature.