# Beyond Kanban: POLCA-Constrained Scheduling for Job Shops
## 3 POLCA and the Enhanced Contraint Programming: A Basic Case
### Computational Experiments
#### 3.4.3 Computational Results
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline
**Opt. Mode** & **Machines** & **POLCA** & **Mean (opt)** & **Std (opt)** & **Mean (sim)** & **Std (sim)** & **t-stat** & **\(p\)-Value** & **Levene p** & **Equal var** \\ \hline early & 6 & 1 & & & & & & & & \\  & & 2 & 654.701 & 126.251 & 931.521 & 179.359 & \(-3.991\) & 0.001 & 0.117 & True \\  & & 3 & 641.394 & 160.338 & 905.196 & 156.665 & \(-3.721\) & 0.002 & 0.999 & True \\ \hline
9 & 1 & & & & & & & & \\  & & 2 & 806.920 & 170.408 & 1013.899 & 141.613 & \(-2.954\) & 0.008 & 0.495 & True \\  & & 3 & 840.894 & 193.575 & 999.687 & 160.194 & \(-1.998\) & 0.061 & 0.326 & True \\ \hline
12 & 1 & 1753.359 & 808.434 & 1280.766 & 499.874 & 1.186 & 0.257 & 0.267 & True \\  & & 2 & 1316.496 & 612.008 & 1210.892 & 384.202 & 0.462 & 0.650 & 0.163 & True \\  & & 3 & 1322.166 & 646.300 & 1234.764 & 379.812 & 0.369 & 0.717 & 0.330 & True \\ \hline late & 6 & 1 & & & & & & & \\  & & 2 & 678.525 & 172.576 & 931.521 & 179.359 & \(-3.214\) & 0.005 & 0.607 & True \\  & & 3 & 658.054 & 148.399 & 905.196 & 156.665 & \(-3.622\) & 0.002 & 0.818 & True \\ \hline
9 & 1 & & & & & & & & \\  & & 2 & 800.254 & 194.122 & 1013.899 & 141.613 & \(-2.812\) & 0.012 & 0.242 & True \\  & & 3 & 775.861 & 175.774 & 999.687 & 160.194 & \(-2.976\) & 0.008 & 0.612 & True \\ \hline
12 & 1 & 1590.305 & 749.887 & 1322.260 & 475.042 & 0.723 & 0.483 & 0.447 & True \\  & & 2 & 1250.678 & 558.007 & 1210.892 & 384.202 & 0.186 & 0.855 & 0.423 & True \\  & & 3 & 1302.504 & 802.221 & 1234.764 & 379.812 & 0.241 & 0.812 & 0.250 & True \\ \hline \end{tabular}
\end{table} 
Table 4: Independent two-sample \(t\)-test results for the comparison of “opt” and “sim” modes across all experimental configurations, metric: avg_tardiness. Figure 2: Boxplots comparing Avg Tardiness distributions for each simulation mode under the same configuration. Only in a limited number of configurations--typically for avg_tardiness in the most complex settings with twelve workcenters--the difference between the two approaches was not statistically significant (\(p>0.05\)). In these cases, as confirmed by the boxplots, the distributions tend to overlap more, indicating greater heterogeneity of the instances and a lower statistical robustness of the advantage, although the median and the interquartile range for \"opt\" remain generally lower than for \"sim\". \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Opt. Mode** & **Machines** & **POLCA** & **Mean (opt)** & **Std (opt)** & **Mean (sim)** & **Std (sim)** & **t+stat** & _p-Value_ & **Levene p** & **Equal var** \\ \hline early & 6 & 1 & & & & & & & \\  & & 2 & 473.576 & 35.815 & 849.652 & 96.355 & \(-\)11.569 & 0.000 & 0.002 & False \\  & & 3 & 477.471 & 34.543 & 829.087 & 84.533 & \(-\)12.176 & 0.000 & 0.011 & False \\ \cline{2-10}  & 9 & 1 & & & & & & & \\  & & 2 & 731.893 & 44.079 & 1161.942 & 94.263 & \(-\)13.069 & 0.000 & 0.030 & False \\  & & 3 & 721.186 & 42.034 & 1133.333 & 92.866 & \(-\)12.786 & 0.000 & 0.055 & True \\ \cline{2-10}  & 12 & 1 & 1004.566 & 126.821 & 1608.930 & 407.973 & \(-\)3.235 & 0.028 & 0.038 & False \\  & & 2 & 1029.989 & 130.862 & 1505.763 & 283.209 & \(-\)4.823 & 0.000 & 0.108 & True \\  & & 3 & 1035.781 & 118.854 & 1519.316 & 279.517 & \(-\)5.034 & 0.000 & 0.049 & False \\ \hline late & 6 & 1 & & & & & & & \\  & & 2 & 479.033 & 40.507 & 849.652 & 96.355 & \(-\)11.213 & 0.000 & 0.004 & False \\  & & 3 & 473.396 & 36.795 & 829.087 & 84.533 & \(-\)12.200 & 0.000 & 0.019 & False \\ \cline{2-10}  & 9 & 1 & & & & & & & \\  & & 2 & 715.541 & 39.251 & 1161.942 & 94.263 & \(-\)13.825 & 0.000 & 0.011 & False \\  & & 3 & 704.814 & 38.552 & 1133.333 & 92.866 & \(-\)13.477 & 0.000 & 0.036 & False \\ \cline{2-10}  & 12 & 1 & 1038.370 & 105.014 & 1644.480 & 383.543 & \(-\)3.469 & 0.023 & 0.028 & False \\  & & 2 & 992.641 & 108.622 & 1505.763 & 283.209 & \(-\)5.349 & 0.000 & 0.056 & True \\  & & 3 & 1019.169 & 132.581 & 1519.316 & 279.517 & \(-\)5.112 & 0.000 & 0.070 & True \\ \hline \hline \end{tabular}
\end{table}