## 6 Experiments and Results
### Further Analysis  
In Section 4, the prediction is based on the assumption that processing times satisfy certain constraints with a given probability. As the probability threshold increases, the system's ability to absorb uncertainty improves, but the scheduling performance may decrease. Therefore, selecting the probability threshold involves a trade-off between uncertainty absorption and scheduling performance. Following [47], a threshold of 0.85 is chosen, and the effectiveness of the proposed prediction strategy is verified through experiments. We compare the initialization scheduling schemes generated with and without the prediction strategy for all test cases. Each scheme is run 20 times, and the average completion time and number of rescheduling events are compared. The results are shown in Figure 11.  
As shown in Figure 11, the makespans of the prediction-based and non-prediction-based scheduling methods are nearly identical, while the number of reschedules is reduced in the prediction-based method. Therefore, the proposed prediction method significantly \begin{table}
\begin{tabular}{c c c c} \hline
**Method** & **Avg Makespan** & **Avg Tardiness** & **Avg Factory Load** \\ \hline FAR1 + MAR1 + SPT & 152.5570 \(\pm\) 10.3291 & 340.3910 \(\pm\) 40.8320 & 658.8920 \(\pm\) 0.3928 \\ FAR1 + MAR2 + SPT & 120.6490 \(\pm\) 8.3210 & 212.2750 \(\pm\) 41.7754 & 771.1400 \(\pm\) 16.2458 \\ FAR1 + MAR3 + SPT & 133.3275 \(\pm\) 14.4204 & 348.8570 \(\pm\) 82.0908 & 942.0190 \(\pm\) 42.2810 \\ FAR2 + MAR1 + SPT & 149.5805 \(\pm\) 10.5789 & 331.1560 \(\pm\) 63.8415 & 69.0110 \(\pm\) 0.4405 \\ FAR2 + MAR2 + SPT & 120.3770 \(\pm\) 12.0717 & 200.5355 \(\pm\) 50.2503 & 764.2850 \(\pm\) 25.3700 \\ FAR2 + MAR3 + SPT & 132.5515 \(\pm\) 10.5213 & 332.6000 \(\pm\) 63.9346 & 929.0045 \(\pm\) 22.8944 \\ FAR1 + MAR1 + EDD & 141.3315 \(\pm\) 7.4195 & 404.9715 \(\pm\) 52.0484 & 69.3950 \(\pm\) 0.6024 \\ FAR1 + MAR2 + EDD & 124.3380 \(\pm\) 12.2159 & 292.2310 \(\pm\) 46.5486 & 76.6565 \(\pm\) 15.2888 \\ FAR1 + MAR3 + EDD & 137.9690 \(\pm\) 13.8511 & 429.9040 \(\pm\) 78.6745 & 968.0980 \(\pm\) 38.5276 \\ FAR2 + MAR4 + EDD & 145.7560 \(\pm\) 9.9641 & 430.5280 \(\pm\) 48.5627 & 659.5075 \(\pm\) 0.6525 \\ FAR2 + MAR2 + EDD & 116.6630 \(\pm\) 9.3815 & 291.9735 \(\pm\) 57.8797 & 776.2800 \(\pm\) 21.3636 \\ FAR2 + MAR3 + EDD & 136.9060 \(\pm\) 13.6345 & 416.4960 \(\pm\) 69.3839 & 965.7185 \(\pm\) 43.6098 \\ FAR1 + MAR1 + LCR & 131.3435 \(\pm\) 8.4095 & 397.8990 \(\pm\) 38.0280 & 659.0970 \(\pm\) 0.6666 \\ FAR1 + MAR2 + LCR & 116.6145 \(\pm\) 7.3871 & 281.7150 \(\pm\) 58.0040 & 773.8695 \(\pm\) 25.7305 \\ FAR1 + MAR3 + LCR & 129.0545 \(\pm\) 10.2834 & 404.3545 \(\pm\) 65.9814 & 958.8905 \(\pm\) 32.4785 \\ FAR2 + MAR1 + LCR & 133.1555 \(\pm\) 9.4063 & 415.0705 \(\pm\) 77.6714 & **658.7055 \(\pm\) 0.6640** \\ FAR2 + MAR2 + LCR & 112.7030 \(\pm\) 8.2004 & 256.8007 \(\pm\) 37.8803 & 793.5140 \(\pm\) 20.7099 \\ FAR2 + MAR3 + LCR & 133.6625 \(\pm\) 10.9616 & 434.4575 \(\pm\) 64.0535 & 974.2605 \(\pm\) 35.5795 \\ FAR1 + MAR1 + RAND & 124.0835 \(\pm\) 7.5009 & 288.9380 \(\pm\) 49.3850 & 659.4990 \(\pm\) 1.0215 \\ FAR1 + MAR2 + RAND & 112.8370 \(\pm\) 11.7223 & 197.1655 \(\pm\) 42.9985 & 784.8950 \(\pm\) 19.6604 \\ FAR1 + MAR3 + RAND & 135.7470 \(\pm\) 11.9744 & 392.2830 \(\pm\) 73.1358 & 984.9085 \(\pm\) 39.3767 \\ FAR2 + MAR1 + RAND & 121.0806 \(\pm\) 6.6896 & 287.0665 \(\pm\) 54.8079 & 659.0645 \(\pm\) 0.6109 \\ FAR2 + MAR2 + RAND & 115.0515 \(\pm\) 10.4489 & 214.7640 \(\pm\) 43.8436 & 785.8260 \(\pm\) 18.6741 \\ FAR2 + MAR3 + RAND & 134.6400 \(\pm\) 14.9668 & 392.6080 \(\pm\) 104.4888 & 988.4450 \(\pm\) 48.9537 \\ Hybrid-shift strategy & 88.1500 \(\pm\) 9 & 50.7400 \(\pm\) 0 & 665.9400 \(\pm\) 0 \\ Proposed scheduling method & **83.6725 \(\pm\) 2.1910** & **39.5960 \(\pm\) 11.6871** & 695.2530 \(\pm\) 6.8797 \\ \hline \end{tabular}
\end{table} 
Table 7: Comparisons of different dynamic scheduling methods. Figure 11: Comparison of the dynamic scheduling method with and without predictions.