# Proactive Production Scheduling Approach for Off-Site Construction with Due Date Uncertainty
## 4 Experimental Study
### Results and Discussion  
The fitness value of the GA converged over 1000 iterations, as shown in Figure 5. The fitness value of 303.8 represented the minimum tardiness at a 100% confidence level, achieved after 975 iterations. Table 3 compares the performance of the proposed model against that of EDD, NEHedd, and basic GA, displaying the production sequences they generated and the corresponding tardiness results under two conditions: with and without due date uncertainty. When due date uncertainty was introduced, the proposed model achieved the lowest tardiness of 303.8 h at a 100% confidence level, followed by NEHedd with 324.7 h, basic GA with 328.5 h, and EDD with 335.8 h. Without due date uncertainty, the basic GA achieved the lowest tardiness of 114.5 h, followed by NEHedd with 115.5 h, the proposed model with 134.4 h, and EDD with 148.6 h. When comparing these results to the scenario where the due dates change, the corresponding tardiness values show confidence levels of 15%, 16%, 31%, and 39%. For example, the basic GA schedule demonstrated a tardiness of 114.5 h when there was no due date uncertainty (i.e., when the due date remained unchanged), which corresponds to a confidence level of 15% when the due date changes. In contrast, the proposed model exhibited a tardiness of 134.4 h without due date uncertainty, but this performance could be guaranteed at a higher confidence level of 31% when the due date changes. This result indicates that, without accounting for due date uncertainty, the reliability of the initially expected tardiness values is significantly lower. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Solver**} & \multirow{2}{*}{**Production Sequence**} & \multicolumn{2}{c}{_w/Due Date Uncertainty_} & \multicolumn{2}{c}{_w/o Due Date Uncertainty_} \\ \cline{3-5}  & & \multirow{2}{*}{**Tardiness (h)**} & **Confidence** & \multirow{2}{*}{**Tardiness (h)**} & **Confidence Level (\%)** \\  & & & & **Level (\%)** & \\ \hline EDD & [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] & 335.8 & 100 & 148.6 & 39 \\ NEHedd & [6, 1, 3, 8, 5, 4, 7, 9, 2, 10, 12, 11] & 324.7 & 100 & 115.5 & 16 \\ basic GA & [6, 4, 2, 8, 5, 7, 3, 9, 1, 10, 12, 11] & 328.5 & 100 & 114.5 & 15 \\ Proposed model & [6, 1, 2, 4, 7, 3, 9, 8, 5, 10, 12, 11] & 303.8 & 100 & 134.4 & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results based on different solvers. Figure 5: Evolutionary curve of GA. Figure 6a shows that the distribution of tardiness in the proposed model is skewed towards smaller values compared to the other solvers. The cumulative distribution in Figure 6b further demonstrates that the proposed model identifies schedules with smaller tardiness values at the same confidence level compared to the other solvers. Table 4 presents the optimal schedules obtained by varying the confidence level of the proposed model from 50% to 100%, alongside the schedules from the other three solvers for each confidence level. The proposed model shows that the tardiness value at the target confidence level is consistently lower than that of the other solvers. The results suggest that the proposed model can effectively find a schedule that minimizes tardiness at the user's desired confidence level under due date uncertainty. The proposed model presents a significant opportunity for enhancing production scheduling in the construction industry, particularly for small-sized prefabrication suppliers. One of the primary challenges faced by small-scale suppliers is the inability to quickly adjust production schedules in response to contractor-driven changes in due dates. The traditional scheduling methods lack the flexibility to respond to these fluctuations, which can lead to costly delays and inefficiencies. By integrating a robust, proactive scheduling approach, the proposed model addresses this issue, allowing suppliers to better manage their resource allocation and production timelines in a dynamic environment.