## 4 Computational Experiments and Statistical Analysis
The axes of the main effect plots are the levels of each factor. It can be seen that for different weight vectors, the objectives E[E/T] and SD[E/T] imply that the AHP is capable of selecting a different solution of the Pareto frontier according to the preferences given by the decision-maker in the AHP method. In the case of the probability distributions (the PDST and PDPT factors), the lognormal distribution presents a slightly greater E [E/T] and SD[E/T] in comparison with the uniform distribution, which gives the idea that despite using the same expected values of the processing and setup times under the same coefficient of variation, the solutions vary with the change of the distribution used. Additionally, as expected, as the coefficient of variation of the setup and the processing times increase (the CVST and CVPT factors) the objectives E[E/T] and SD[E/T] also increment, indicating a higher variability in the obtained solutions of the Pareto frontier. These aspects led us to highlight the importance of including uncertainty in the optimization problem when it is really present, and the value of making an accurate distribution fitting to make adequate decisions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Factor** & **Levels** \\ \hline PD of processing times (PDPT) & lognormal [lgn] and uniform [unf] \\ CV of processing times (CVPT) & 0.3, 0.4 and 0.5 \\ PD of setup times (PDST) & lognormal [lgn] and uniform [unf] \\ CV of setup times (CVST) & 0.3, 0.4, and 0.5 \\ vectors of criteria weights of AHP (WV) & 1, 2, 3, 4, 5, 6, 7, and 8 \\ number of jobs & 20, 50, and 100 \\ number of machines & 5, 10, and 20 \\ generation size of SDST & SSD50, and SSD125 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Factors of the experimental design and their corresponding levels. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Source** & **E[E/T]** & **SD(E/T)** & **E[CI]** & **E[PI]** \\ \hline
**WV** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**PDST** & 0.0000 & 0.0000 & 0.0000 & 0.1750 \\
**PDPT** & 0.0000 & 0.0000 & 0.0530 & 0.1920 \\
**SizeSDST** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**CVST** & 0.0000 & 0.0000 & 0.0160 & 0.1620 \\
**CVPT** & 0.0000 & 0.0000 & 0.0030 & 0.0460 \\
**Jobs** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**Machines** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**WV*PDST** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**WV*PDPT** & 0.0030 & 0.9150 & 0.0210 & 0.9510 \\
**WV*SizeSDST** & 0.0040 & 0.0000 & 0.0000 & 0.0000 \\
**WV*CVST** & 0.0580 & 0.0040 & 0.0000 & 0.9440 \\
**WV*CVPT** & 0.0000 & 0.0000 & 0.0000 & 0.6190 \\
**WV*Jobs** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**WV*Machines** & 0.0000 & 0.0010 & 0.0060 & 0.0010 \\
**PDST*PDPT** & 0.5290 & 0.0470 & 0.4400 & 0.8040 \\
**PDST*SizeSDST** & 0.0000 & 0.0000 & 0.0000 & 0.9560 \\
**PDST*CVST** & 0.0310 & 0.0000 & 0.0010 & 0.3280 \\
**PDST*CVPT** & 0.1570 & 0.0000 & 0.0050 & 0.0070 \\
**PDST*Jobs** & 0.0000 & 0.0000 & 0.0000 & 0.6420 \\
**PDST*Machines** & 0.9610 & 0.0000 & 0.0600 & 0.3650 \\
**PDPT*SizeSDST** & 0.4970 & 0.0000 & 0.2970 & 0.9380 \\
**PDPT*CVST** & 0.0100 & 0.3370 & 0.0000 & 0.0000 \\
**PDPT*CVPT** & 0.0070 & 0.0000 & 0.0150 & 0.3610 \\
**PDPT*Jobs** & 0.0000 & 0.0000 & 0.0390 & 0.2530 \\
**PDPT*Machines** & 0.1500 & 0.0000 & 0.5470 & 0.0000 \\
**SizeSDST*CVST** & 0.0000 & 0.0000 & 0.0000 & 0.0110 \\
**SizeSDST*CVPT** & 0.0000 & 0.0000 & 0.0010 & 0.0000 \\
**SizeSDST*Jobs** & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\
**SizeSDST*Machines** & 0.0000 & 0.0090 & 0.0000 & 0.0000 \\
**CVST*CVPT** & 0.0340 & 0.0000 & 0.0470 & 0.0000 \\
**CVST*Jobs** & 0.0000 & 0.0000 & 0.0040 & 0.0000 \\
**CVST*Machines** & 0.0000 & 0.1730 & 0.2650 & 0.7880 \\
**CVPT*Jobs** & 0.0000 & 0.0000 & 0.0000 & 0.0780 \\
**CVPT*Machines** & 0.0000 & 0.2110 & 0.0000 & 0.0230 \\ \hline \(R^{2}_{aj}\) & 99.82\% & 77.30\% & 89.76\% & 92.01\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(p\)-values and \(R^{2}_{adj}\) of the ANOVAs for each objective function.