# Space-Constrained Scheduling Optimization Method for Minimizing the Effects of Stacking of Trades
## 4 Method Verification
### Verifying the Outperformance of SSO for Handling a Large Network  
Another real-life plant construction project network with 134 activities, which is distributed with the P6 program by Primavera, Inc., was used to verify the capabilities of SSO in terms of validity in dealing with a large real-world network. The schedule information (i.e., \(i\), \(D_{i}\), \(r_{i}\), \(e_{i}\), \(m_{i}\), \(f_{i}\), and \(PS_{i}\), etc.) were entered into the system. The case study site was divided into 15 specific work areas. The occupation density functions for  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Activity ID** & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** & **I** & **J** & **K** & **L** & **M** \\ \hline \(i\) & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \hline Solution (\(k_{i}\), \(sd_{i}\)) & (3, 0) & (1, 0) & (2, 0) & (1, 0) & (1, 4) & (2, 8) & (1, 1) & (2, 0) & (1, 13) & (1, 0) & (1, 2) & (1, 0) &each specific work area and the alternatives of execution pattern for each activity were acquired from plant construction experts.  
When the case network was executed with EST and LST, the allowed occupation density of specific work areas was exceeded 12 and 8 times, respectively. Without space-constrained scheduling, project completion time and cost would inevitably increase. SSO identified the optimal set of pairs of execution patterns alternatives and deferred start times of activities that did not exceed the allowed occupation density of each specific work area. Therefore, the effect of stacking of trades on the work areas was minimized. Convergence time was only 325.8 s. The space interference level (\(f_{\text{SC}}\)) was reduced by 328% compared to the EST schedule. The schedule input data and output tables are not included due to a lack of space. However, there is no doubt that SSO finds near-global solutions even if the size of the network along with the number of activities and number of relationships is increased.  
Figure 8: Occupation density of work areas and level of space interference obtained original schedule and SSO method. (**A**) Original schedule (based EST). (**B**) Original schedule (based LST). (**C**) After optimizing schedule using SSO.  
It should be noted that the time for defining the occupation density function increases as the number of specific work areas increases. Furthermore, the occupation density function should be defined by construction experts in the relevant field. However, with the rapid development of image processing technology, the technical basis for automatically generating occupation density functions is being prepared. Many studies on image processing-based schedule progress management [24; 25; 26] were conducted, and these studies performed various analyses regarding object detection, location tracking, motion detection, volume estimation, etc., to calculate rates of progress. In addition, the accuracy of image processing is becoming more sophisticated. It is possible to develop a system that executes image-processing analysis, acquire historical data regarding activities, and input it into Equation (3) to generate occupancy density functions automatically. In future studies, it is recommended to develop an automated schedule system incorporating SSO and image processing-based progress management methods.