## 5 Experimental Results

Table 2: The cycle times of experimental results for small problems (\(b\) = 10% of length of the conveyor). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No.** & \multicolumn{6}{c}{**Number of Workstations**} \\ \cline{2-10}  & **LINGO** & **SA** & **Improvement** & **LINGO** & **SA** & **Improvement** & **LINGO** & **SA** & **Improvement** \\ \hline
1 & 13.1430 & 13.1430 & 0.00\% & 10.000 & 10.000 & 0.00\% & 7.5000 & 7.5000 & 0.00\% \\
2 & 20.2993 & 20.2993 & 0.00\% & 14.2993 & 14.2993 & 0.00\% & 12.4792 & 12.1336 & 0.00\% \\
3 & 2.2856 & 2.2856 & 0.00\% & 1.74724 & 1.7875 & \(-\)1.43\% & 1.3354 & 1.3354 & 0.00\% \\
4 & 43.4900 & 43.4900 & 0.00\% & 31.2930 & 31.1691 & 0.00\% & 26.6361 & 26.6361 & 0.00\% \\
5 & 1.7707 & 1.7707 & 0.00\% & 1.2385 & 1.2375 & 0.00\% & 1.0275 & 1.0275 & 0.00\% \\
6 & 1.2802 & 1.2802 & 0.00\% & 0.9250 & 0.9250 & 0.00\% & 0.7250 & 0.7250 & 0.00\% \\
7 & 2.2163 & 2.2269 & \(-\)0.48\% & 1.5394 & 1.5394 & 1.5394 & 0.00\% & 1.3195 & 1.3195 & 0.00\% \\
8 & 20.7750 & 20.7750 & 0.00\% & 15.0000 & 15.0000 & 0.00\% & 11.9647 & 11.9647 & 0.00\% \\
9 & 32.1847 & 32.1847 & 0.00\% & 22.5000 & 22.5000 & 0.00\% & 18.2445 & 18.2445 & 0.00\% \\
10 & 23.1543 & 23.1543 & 0.00\% & 16.5375 & 16.5375 & 0.00\% & 13.1543 & 13.1543 & 0.00\% \\ \hline  & Average & \multicolumn{3}{c}{\(-\)0.05\%} & \multicolumn{3}{c}{0.00\% *} & \multicolumn{3}{c}{0.00\% \\ \hline \end{tabular}
\end{table} 
Table 3: The cycle times of experimental results for small problems (\(b\) = 15% of length of the conveyor). According to the experimental results, the main effect of all factor levels are illustrated in Figure 12. The smaller the cycle time the better. Therefore, \(F\), \(H\), \(\alpha\) and \(\beta\) are set as \(W_{max}\times 10\), \(I\times 1500\), 0.1 and 0.005, respectively. Moreover, the \(\gamma\) used for generating initial solutions is set as 0.1. Based on the setting of parameters, the results of the proposed SA are shown in column 3, 6 and 9 in Tables 2 and 3. It is found that the proposed SA results in a higher cycle time in 6 cases out of 60. This research then checked the six results generated by LINGO 17 in detail, and interference was found in Problem 3 with three workstations for both \(b=10\%\) and \(b=15\%\). Interference always affects the performance of operators, and it can be avoided by the proposed SA. The detail of this operation is introduced in Section 4.3. Therefore, the performance difference between LINGO 17 and the proposed SA is almost the same if Problem 3 with three workstations for both \(b=10\%\) and \(b=15\%\) are excluded. Moreover, the computation time of the proposed SA is strongly related to the number of iterations which is based on the number of tasks (\(F=I\times 1500\)). Using a computer with Intel Core i7-9700 3.00 GHz for Problems 1 to 3, the average computation time is 214 s. For Problems 4 to 7, the average computation time is 249 s. For Problems 8 and 9, the average computation time is 264 s. Additionally, for Problem 10, the computation time is 301 s. As regards LINGO 17, the computation times for 60 cases are shown in Figure 13.  
In Figure 13, the computation times required by LINGO 17 are case by case. In general, it is found that more computing time is required when there are more tasks or workstations. When there are 10 tasks (Problem 10), the computation times for all cases are 21,600 s (6 h). This means that more computation time would be required if a maximum computation time was not set. Six larger problems were also collected from the literature. The original objectives of these problems are not the same as in the present study. The collected problems are modified for testing the performance of the proposed SA. The corresponding information is summarized in Table 5.