## 5 Computational Experiments and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **No. of Depot** & **No. of Customer** & **Depot Capacity** & **Vehicle Capacity** \\ \hline Perl 1 & 2 & 12 & 280 & 140 \\ Perl 2 & 15 & 55 & 550 & 120 \\ Perl 3 & 7 & 85 & 850 & 160 \\ Gaskell 1 & 5 & 21 & 15,000 & 6000 \\ Gaskell 2 & 5 & 22 & 15,000 & 4500 \\ Gaskell 3 & 5 & 29 & 15,000 & 4500 \\ Gaskell 4 & 5 & 32 & 35,000 & 8000 \\ Gaskell 5 & 5 & 36 & 15,000 & 250 \\ Christofides 1 & 5 & 50 & 10,000 & 160 \\ Christofides 2 & 10 & 75 & 10,000 & 140 \\ Christofides 3 & 10 & 100 & 10,000 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of Perl, Gaskell, and Christofides dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Gaskell 1**} & \multicolumn{3}{c}{**Gaskell 2**} & \multicolumn{3}{c}{**Gaskell 3**} & \multicolumn{3}{c}{**Gaskell 4**} & \multicolumn{3}{c}{**Gaskell 5**} \\ \cline{2-10}  & **Mean** & **Best** & **Mean** & **Best** & **Mean** & **Best** & **Mean** & **Best** \\ \hline SA-Z & – & 429.6 & – & 585.1 & – & 523.2 & – & 577.6 & – & 471.3 \\ PSO & – & 437.1 & – & 592.1 & – & 572.1 & – & 574.1 & – & 470.7 \\ PMG & – & 435.9 & – & 591.8 & – & 572.1 & – & 571.7 & – & 470.7 \\ PMGE & – & 435.9 & – & 591.7 & – & 572.1 & – & 571.7 & – & 470.7 \\ HLRP & – & 432.9 & – & 588.5 & – & 572.1 & – & 570.8 & – & 470.7 \\ HBMO & – & 431.9 & – & 587.2 & – & 572.1 & – & 569.8 & – & 470.7 \\ SHS & 449.1 & 443.7 & 602.9 & 598.0 & 550.6 & 541.2 & 578.7 & 576.2 & 528.5 & 520.7 \\ PHS & 437.9 & 431.7 & 584.3 & 577.9 & 522.7 & 511.8 & 562.6 & 559.9 & 475.5 & **464.1** \\ HS-SA & **429.3** & **424.9** & **577.3** & **575.2** & **502.5** & **493.1** & **559.5** & **552.4** & **473.5** & **464.1** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative results of Gaskell dataset for LRP. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Perl 1**} & \multicolumn{3}{c}{**Perl 2**} & \multicolumn{3}{c}{**Perl 3**} \\ \cline{2-7}  & **Mean** & **Best** & **Mean** & **Best** & **Mean** & **Best** \\ \hline HR & – & **204.0** & – & 1146.9 & – & 1657.6 \\ SA-W & – & **204.0** & – & 1119.8 & – & 1656.7 \\ SA-Z & – & **204.0** & – & 1115.4 & – & **1642.0** \\ TACO & – & **204.0** & – & 1139.9 & – & 1642.6 \\ PSO & – & **204.0** & – & 1135.9 & – & 1656.9 \\ PMG & – & **204.0** & – & 1136.2 & – & 1656.9 \\ PMGE & – & **204.0** & – & 1135.9 & – & 1656.9 \\ HLRP & – & **204.0** & – & 1135.9 & – & 1657.1 \\ HBMO & – & **204.0** & – & 1127.1 & – & 1655.2 \\ SHS & **204.0** & **204.0** & 1161.4 & 1158.8 & 1846.3 & 1832.1 \\ PHS & **204.0** & **204.0** & 1115.6 & **1113.2** & 1666.0 & 1653.0 \\ HS-SA & **204.0** & **204.0** & **1114.7** & **1113.2** & **1658.4** & 1645.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative results of Perl dataset for LRP. Figure 4: Best result of Gaskell dataset for LRP. Figure 5: Best result of Christofides dataset for LRP. Figure 3: Best result of Perl dataset for LRP. As compared to the SHS and PHS in [7], the hybrid HS-SA performed significantly better for all instances in Perl, Gaskell, and Christofides, except Perl 1. However, for Perl 3, results in SA-Z [10] and TACO [11] are slightly better than the hybrid HS-SA algorithm. All algorithms managed to find the optimal solution in Perl 1 since the number of customers and depots are small. The SHS did not perform well for medium and large size. This indicates that the SHS should be improved and modified to get better solutions [7]. From the numerical experiments in LRP, hybrid HS-SA has successfully solved the problem with comparable results. Therefore, the proposed algorithm will be used to solve the LIRP that utilizes the EPQ model for defect and non-defect items in reverse logistics. The computational results for all test instances in LIRP are shown in Tables 6-8. Since there is no benchmark for the EPQ model in LIRP, the comparison is assessed between the hybrid HS-SA algorithm with SHS and PHS only.