# Scheduling Optimization of Prefabricated Construction Projects by Genetic Algorithm
## 6 Case Study
### Simulation Results  
In this section, the project scheduling mathematical model established in Section 3 and the GA proposed in Section 4 are used to optimize the duration of the case. The relevant parameters of the algorithm are set as follows: population size = 40, maximum number of iterations = 100, crossover rate = 0.9, mutation rate = 0.03, and \(w\) = 0.5. Under normal circumstances, the prefabricated components required for project construction will be timely delivered to the site before the start of the activity to ensure the smooth progress of on-site assembly and construction. Generally, on-site construction arrangements are the leading factor, which governs the production and transportation arrangements of factory prefabricated components [89]. [PERSON] and [PERSON]'s research was based on the analysis on the assumption that the prefabricated components arrived on time [23]. However, delays in the delivery of prefabricated components are not rare in the construction process of prefabricated construction projects, which is also an important reason for the deviation of the project schedule [90]. Therefore, the case study in this section will be analyzed from the two situations of on-time supply and delayed supply of prefabricated components. Figure 7: Average operation time of the algorithm. In the case that the prefabricated components can supply on-site construction requirements on time, the optimal activity sequence of the project is obtained by using the algorithm as [1 2 14 3 4 15 17 6 5 16 7 18 8 9 19 10 11 12 13 20 21 22 23 24 25]. The Gantt chart and resource consumption distribution chart of project scheduling are shown in Figures 8 and 9, respectively. Figure 8 shows that under the condition of punctual supply of prefabricated components, subject to the constraints of three limited renewable resources, the maximum completion time of the project is 22 days. During the project construction, the resource allocation is well-distributed under this scheduling arrangement (Figure 9). On the other hand, considering the situation that prefabricated components cannot supply on-site construction requirements on time, the optimal sequence of activities is still [1 2 14 3 4 15 17 6 5 16 7 18 8 9 19 10 11 12 13 20 21 22 23 24 25]. We assume that the prefabricated components required for the construction of activity 9 are delayed by 2 days. Originally planned to start on the 12 th day, activity 9 needs to be adjusted to start on the 14 th day at the earliest. The delay of activity 9 will have a certain effect on the schedule of the subsequent activities, and the unexecuted activities need to be readjusted. The updated project scheduling Gantt chart and resource consumption distribution diagram are shown in Figures 10 and 11. Figure 10 demonstrates that in the event that the delivery of the prefabricated components required in activity 9 is delayed by 2 days, the maximum completion time of the project is delayed by 24 days. Activities 10, 11, 12, 13, 20, 21, 22, 23, and 24 all delayed the start time compared with the schedule in Figure 8. Especially for activity 20, even if all its predecessors have been executed on the 13 th day, due to the constraints of renewable resources, activity 20 has to wait until the 16 th day to start work. It is worth noting that due to the rescheduling of the delayed delivery of the prefabricated components, according to Figure 11, the resource consumption of 0 occurred on the 14 th day. The project manager needs to pay attention to this situation. It is necessary to focus on the losses caused by the delayed delivery of prefabricated components and make timely adjustments. In addition, according to the resource consumption distribution maps in Figures 9 and 11, project managers can predict the peak point of project resource usage and take the corresponding preventive measures to avoid project delays caused by resource allocation. Figure 9: Distribution of resource consumption under the on-time supply of prefabricated components.