# Research on an Assembly Building Buffer Zone Based on Gray Critical Chain
## 4 Case Study
### Monte Carlo Simulation  
In order to verify that the buffer size and assembly building project duration derived from the improved grey critical chain method proposed in this paper have an optimization effect, the method of this paper is compared with the traditional project management methods (C&PM and RSEM), and Monte Carlo simulation is carried out using MATLAB 2020, and the number of trials is set to 1000 times. Assuming that the project activity duration obeys the lognormal distribution [44]. \(\mathrm{x}\)-N(\(\mu_{\mathrm{x}}\),\(\sigma_{\mathrm{x}}\)\({}^{2}\)), then \(\mathrm{T}=\mathrm{I}\mathrm{n}\mathrm{x}\), obeys the lognormal distribution, i.e., \(\mathrm{T}\)-\(\mathrm{I}\mathrm{n}\)(\(\mu_{\  
Analysis of the above results reveals that the buffer size obtained by the method described in this article is lower than that obtained by the C&PM method and higher than that obtained by the RSEM method. Upon analyzing the reasons behind this, it is found that C&PM did not take into account the difficulty level of the process and the impact of uncertain factors. All buffers were set at 50% of the process, resulting in excessive protection of project duration and unnecessary slack in the work of project personnel. The RSEM method sets the buffer zone based on the central limit theorem, assuming that the project processes are independent of each other. However, in actual projects, there are uncertain factors such as human, technical, and management aspects that affect the project duration, thus limiting the applicability of this method. This article's method considers five factors that influence the project duration in prefabricated construction processes: personnel experience, degree of prefabricated component production, technical complexity, construction scheme rationality, and construction space satisfaction. It also refers to other uncertain coefficients and use the OPA-entropy weighting method to quantify the influencing factors, which can effectively absorb the extension of the project duration caused by uncertain factors and shorten the project duration in line with the actual situation of prefabricated projects.  
Based on the simulation results, it can be found that the buffer size obtained by the proposed method is smaller than that of the C&PM method. The overall project duration obtained by the proposed method is 9.66 days less than that of the C&PM method, representing a time save of 14.3%. Compared to the RSEM method, the proposed method results in a time save of 7.68 days, representing a time reduction of 11.7%. Upon analyzing the reasons behind this, it is found that this method considers the impact of student syndrome, avoids unnecessary project duration caused by staff procrastination, and results  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Simulation Value**} & \multicolumn{3}{c}{**Difference in Value**} \\ \cline{2-7}  & **C\&PM** & **RSEM** & \begin{tabular}{c} **Improvement of the Gray** \\ **Critical Chain Method** \\ \end{tabular} & \
\begin{tabular}{c} **Compare to C\&PM** \\ **d** \\ \end{tabular} &
\begin{tabular}{c} **Compare to RSEM** \\ **\%** \\ \end{tabular} \\ \hline Buffer/d & 9.875 & 2.678 & 4.572 & \(-\)5.303 & - & 1.707 & - \\ \hline Durations/d & 67.62 & 65.64 & 57.96 & \(-\)9.66 & \(-\)14.3\% & \(-\)7.68 & \(-\)11.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of simulation results.  
Figure 6: Comparison of simulation duration between this method and traditional methods.  
in a project duration lower than that of the RSEM method. The method proposed in this paper is more reasonable and able to optimize the duration of assembly building projects, which provides a reference for the project management method of the critical chain of assembly buildings.