## 6 Analysis of Results
### Large-sized Instances with Varying Profit Margins (Selling Prices)  
During the considered horizon, one could consider a reduction in product prices (and margins) due to the sales period. For running an experiment under these conditions, the parameters \(h_{s}\) and \(h_{e}\), which represent the beginning and end of the especial sales period, were set to \(h_{s}=11\) and \(h_{e}=12\). The remaining parameters were not changed. Table 6 provides the summarized results of the solutions generated by our methodologies. For each problem magnitude, the first instance was considered, and a comparison among the solving methods was provided in terms of percentage gap.  
From Table 6, one can notice that the BR versions of GRASP and ILS outperform the other solving methodologies. In this scenario with varying profit margin, the BR-GRASP is able to provide the BKS for the eight tested instances. For the remaining methodologies, their performance--in terms of gaps, SE, and CPU times--is similar to the one presented in Table 5.  
Figure 3: Convergence chart for the BR-GRASP in a particular instance.  
\begin{table}
\begin{tabular}{c|c|c c c|c c c c|c c c c|c c c c c|c c c c c} \hline \multicolumn{13}{c}{**Best Solution (attractiveness)**} & \multicolumn{13}{c}{**AVC Attractiveness (SE)**} & \multicolumn{1}{c}{**AGP (\%) wxL BKS**} & \multicolumn{1}{c}{**AVC Time (s)**} \\ \cline{2-13} \multicolumn{1}{c|}{**Instance**} & **G** & **BR-GR** & **GR** & **ILS** & **BR-ILS** & **G** & **BR-CR** & **GR** & **ILS** & **BR-ILS** & **G** & **BR-GR** & **CR** & **ILS** & **BR-ILS** & **G** & **BR-GR** & **CR** & **ILS** & **BR-ILS** \\ \hline
**a500m51** & 100,167 104,906 104,748 103,961 104,422 & 100,167 (0) & 104,497 (73) & 104,440 (51) & 103,482 (82) & 104,104 (66) & 4.52 & 0.00 & 0.15 & 0.88 & 0.46 & 0 & 8 & 8 & 8 & 10 \\
**a500m01** & 181,871 196,375 29,1584 & 194,961 19,5518 & 188,711 (0) & 196,021 (78) & 195,541 & 193,967 (108) & 193,570 (708) & 39.00 & 0.00 & 0.29 & 0.98 & 0.28 & 0.15 & 17 & 15 & 20 \\
**a500m05m1** & 110,916 137,875 113,097 13,123 13,1515 & 1196,096 (10) & 113,830 (53) & 112,408 (48) & 112,744 (79) & 131,329 (524) & 62.00 & 0.08 & 0.68 & 0.57 & 0.32 & 0.15 & 14 & 17 & 21 \\
**a1000m1** & 2112,437 219,874 215,415 216,246 217,287 & 212,437 (0) & 217,540 (111) & 214,911 (0) & 215,857 (09) & 217,058 (60) & 25.00 & 1.18 & 0.80 & 0.32 & 0 & 30 & 30 & 36 & 40 \\
**a1500m51** & 1439,137 127,689 159,158 116,160 17,147 143,139 (0) & 117,1289 (61) & 115,750 (7) & 116,112 (72) & 117,057 (82) & 17,273 (0) & 0.00 & 1.38 & 0.05 & 0.15 & 0 & 23 & 23 & 41 & 36 \\
**a1500m1** & 2232,228 26,275 22,4375 226,296 217,294 220 (20) & 222,727 29,230 (20) & 22,027 27,59 (22) & 22,035 (75) & 22,265 (71) & 22,274 (86) & 22,39 & 0.20 & 2.27 & 0.77 & 0.39 & 0 & 48 & 44 & 69 & 69 \\
**a2000m51** & 117,377 120,696 118,292 119,967 120,628 & 117,377 (0) & 120,545 (41) & 118,147 (43) & 119,599 (59) & 120,442 (42) & 2.75 & 0.00 & 1.99 & 0.60 & 0.06 & 0 & 33 & 32 & 40 & 30 \\
**a2000m1** & 231,988 236,010 229,241 234,086 235,096 & 231,988 (0) & 235,431 (111) & 229,029 (60) & 233,674 (89) & 234,831 (64) & 1.70 & 0.00 & 2.87 & 0.82 & 0.39 & 0 & 60 & 57 & 65 & 63 \\ \hline _AVC_ & - & - & - & - & - & - & - & **2.89** & **0.00** & **1.35** & **0.79** & **0.29** & **0.29** & **28** & **37** & **36** \\ \hline \end{tabular}
\end{table}
Table 6: Comparison of the results obtained by the proposed methodologies.