# Proactive Production Scheduling Approach for Off-Site Construction with Due Date Uncertainty
## 4 Experimental Study
### Results and Discussion
It can be applied not only to PC production but also to other prefabricated products, such as MEP (mechanical, electrical, and plumbing) systems or facade elements. The flexibility and adaptability of this model make it a valuable tool in industries where the production schedules need to account for uncertainties in the delivery timelines. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multirow{2}{*}{**Solver**} & \multicolumn{2}{c}{**Production**} & \multicolumn{4}{c}{**Tardiness Based on a Confidence Level (h)**} \\ \cline{3-10}  & \multicolumn{2}{c}{**Sequence**} & \multicolumn{1}{c}{**50\%**} & \multicolumn{1}{c}{**60\%**} & \multicolumn{1}{c}{**70\%**} & \multicolumn{1}{c}{**80\%**} & \multicolumn{1}{c}{**90\%**} & \multicolumn{1}{c}{**100\%**} \\ \hline EDD & [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] & 155.6 & 169.4 & 183.9 & 202.1 & 228.7 & 324.7 \\ NEHedd & [6, 1, 3, 8, 5, 4, 7, 9, 2, 10, 12, 11] & 165.4 & 179.6 & 195.8 & 216.0 & 249.0 & 335.8 \\ basic GA & [6, 4, 2, 8, 5, 7, 3, 9, 1, 10, 12, 11] & 159.0 & 170.5 & 184.1 & 204.9 & 227.9 & 328.5 \\ Proposed model with 50\% & [7, 1, 2, 4, 8, 6, 3, 9, 5, 10, 12, 11] & **138.8** & 155.2 & 171.8 & 185.9 & 213.5 & 343.1 \\ \({}^{\prime\prime}\) & with 60\% & [7, 1, 2, 4, 8, 6, 3, 5, 9, 10, 12, 11] & 139.2 & **155.0** & 171.6 & 185.8 & **213.0** & 343.3 \\ \({}^{\prime\prime}\) & with 70\% & [6, 1, 2, 4, 8, 3, 7, 5, 9, 10, 12, 11] & 142.0 & 156.1 & **169.8** & 190.4 & 216.4 & 316.5 \\ \({}^{\prime\prime}\) & with 80\% & [7, 1, 2, 4, 6, 8, 3, 5, 9, 10, 12, 11] & 139.6 & 155.3 & 171.3 & **185.4** & 213.5 & 342.5 \\ \({}^{\prime\prime}\) & with 90\% & [7, 1, 2, 4, 8, 6, 3, 5, 9, 10, 12, 11] & 139.2 & **155.0** & 171.6 & 185.8 & **213.0** & 343.3 \\ \({}^{\prime\prime}\) & with 100\% & [6, 1, 2, 4, 7, 3, 9, 8, 5, 10, 12, 11] & 149.3 & 161.5 & 177.9 & 194.5 & 224.7 & **303.8** \\ \hline \hline \end{tabular} Bold and italics indicate the lowest tardiness value within the same confidence level.  
\end{table} 
Table 4: Experimental results based on a confidence level. Figure 6: Test results on different solvers: (**a**) distribution of tardiness; (**b**) cumulative distribution of tardiness. However, the model operates under the assumption that suppliers have access to reliable data on the probabilistic distribution of due date changes for each order. This requirement poses a limitation as not all suppliers may have sufficient historical data to accurately predict how delivery dates may fluctuate. In cases where such data are unavailable, the suppliers will need to begin collecting and analyzing both the original and revised due dates for each project. These data are crucial for refining the model and accurately estimating the mean and variance of the due date uncertainty. Despite this limitation, the proposed model offers considerable potential for improving supply chain reliability and reducing disruptions caused by unexpected schedule changes. By proactively managing uncertainties, suppliers can enhance their ability to meet delivery targets, minimize delays, and optimize resource utilization. Furthermore, as suppliers gather more data and improve their ability to estimate due date changes, the model will become even more effective at handling uncertainties, thereby offering long-term benefits in terms of cost efficiency and operational stability. In conclusion, the proposed model contributes to the development of intelligent scheduling systems that can significantly improve the robustness and flexibility of production schedules in the prefabrication industry. It also highlights the importance of data collection and analysis in refining predictive models, thereby offering a practical solution to the challenges faced by suppliers in dynamic and uncertain production environments.