# Proactive Production Scheduling Approach for Off-Site Construction with Due Date Uncertainty
## 4 Experimental Study  
### Overview  
An experimental study was conducted to validate the proposed model by assessing tardiness values at a specified confidence level under due date uncertainty, comparing it against two traditional dispatching rules, such as EDD and NEHedd [25], and a basic GA. EDD is a scheduling rule that prioritizes tasks by selecting the next job in the queue based on the earliest due date. This approach ensures that tasks with the earliest deadlines are completed first, helping to minimize tardiness and meet due date requirements effectively. NEHedd arranges tasks in a non-decreasing order of due dates, adding each new task sequentially while inserting it in the optimal position to construct the final solution. The basic GA identifies a scheduling solution that minimizes tardiness, assuming no due date uncertainty. The experimental data in Table 1, showing the processing time for each process and PC product type, were obtained from [PERSON] et al. [15].  
Contractors' order information such as product type, due date, and quantity for contractors used in this experimental study are described in Table 2. The model assumes a total of 12 products, with 2 products assigned to each of the 6 contractors. Given the unique characteristics of construction sites, delays in due dates are more frequent than early completions [2]. Accordingly, the due date distribution was designed to reflect this tendency. The daily schedule assumes 10 h for work, 14 h for non-work activities, and 4 h for overtime. All experimental methods assume that, once the initial schedule is established, it cannot be adjusted, even if due dates change during production.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Product Type**} & \multicolumn{6}{c}{**Processing Time (h)**} \\ \cline{2-7}  & **p1** & **p2** & **p3** & **p4** & **p5** & **p6** \\ \hline P1 & 2.0 & 3.6 & 2.5 & 10 & 1.0 & 1.1 \\ P2 & 3.1 & 3.2 & 1.0 & 10 & 1.5 & 2.1 \\ P3 & 2.2 & 2.8 & 1.7 & 10 & 1.0 & 0.8 \\ P4 & 0.8 & 1.9 & 1.2 & 10 & 1.0 & 1.2 \\ P5 & 1.2 & 2.0 & 2.6 & 10 & 0.8 & 0.9 \\ P6 & 3.0 & 4.0 & 1.1 & 10 & 1.6 & 2.5 \\ P7 & 1.1 & 2.2 & 1.6 & 10 & 1.0 & 2.1 \\ \hline \end{tabular}
\end{table}
Table 1: Processing time for each PC product type.  
\begin{table}
\begin{tabular}{l l l} \hline \multirow{2}{*}{**Contractor**} & \multirow{2}{*}{**Product Type**} & \multicolumn{2}{c}{**Due Date**} \\  & & **(Most Pessimistic, Most Likely, Most Optimistic Value)** \\ \hline C1 & P1 & (24, 24, 24) \\  & P2 & (24, 24, 24) \\ \hline C2 & P2 & (0, 24, 72) \\  & P3 & (0, 24, 72) \\ \hline C3 & P3 & (0, 48, 120) \\  & P4 & (0, 48, 120) \\ \hline C4 & P4 & (0, 48, 132) \\  & P5 & (0, 48, 132) \\ \hline C5 & P5 & (0, 72, 168) \\  & P6 & (0, 72, 168) \\ \hline C6 & P6 & (12, 96, 204) \\  & P7 & (12, 96, 204) \\ \hline \end{tabular}
\end{table}
Table 2: Order information.  
The parameters for the PC production simulation module were set to \(n\) of 100% and \(S\) of 1000. The GA parameters for the GA-based PC production schedule optimization module were set to a population size of 10, a crossover rate of 0.9, a mutation rate of 0.5, an elite number of 3, and stopping criteria of 1000 iterations based on references such as [PERSON] et al. [24] and validated through testing to achieve both computational efficiency and solution quality. The proposed model and the other algorithms were written in Python 3.9, and the tests were conducted on a system with the following specifications: Windows 11, Intel i7-1260P CPU, and 16.0 GB RAM.