## 5 Case Studies for Construction Site Layout Planning and Managerial Implication
### Case Study 3  
Given that multi-storey building construction sites have limited space for materials storage, planning for the construction site is critical for construction management. Developing sufficient structural strength in the lower floors to temporarily store materials needed for construction is required for reducing the material transportation times and enhancing the general construction efficacy. A real case study obtained from [PERSON] et al. (2018) was used to validate the proposed method. The objective was \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Optimized Storage Location (Floor, Cell)**} \\ \multirow{2}{*}{**Material Type**} & **GA** & **MIP** \\  & [(35)] & [(38)] & **HOS-LO \({}^{*}\)** \\ \hline
1 & (5,1) & (3,1) & (1,1) \\
2 & (6,1) & (4,5) & (2,1) \\
3 & (2,1) & (1,5) & (1,3) \\
4 & (7,1) & (3,5) & (2,2) \\
5 & (1,1) & (1,1) & (1,2) \\
6 & (7,5) & (2,5) & (1,4) \\
7 & (6,5) & (2,1) & (1,5) \\
8 & (1,5) & (4,1) & (2,3) \\
9 & (4,1) & (5,1) & (2,4) \\
10 & (5,5) & (5,5) & (2,5) \\ \hline Total cost (\$) & 4,562,620 & 4,293,020 & 4,287,996 \\ \hline \hline \end{tabular} \({}^{*}\) Present study.  
\end{table} 
Table 6: The comparative results between HSOS-LO and previous research. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithms** & **Best** & **Average** & **Worst** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Best–Average** & **Best–Worst** &
\begin{tabular}{c} **Average** \\ **Time** \\ \end{tabular} \\ \hline PSO & 4,288,196 & 4,288,533.60 & 4,290,468 & 423.14 & 0.008\% & 0.053\% & 0.562 \\ DE & 4,287,996 & 4,288,302.56 & 4,288,988 & 211.98 & 0.007\% & 0.023\% & 0.385 \\ SOS & 4,288,196 & 4,288,196 & 4,288,196 & 0.00 & 0.000\% & 0.000\% & 0.294 \\ HSOS-LO & 4,287,996 & 4,288,083.12 & 4,288,196 & 61.30 & 0.002\% & 0.005\% & 0.492 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative results of DE, PSO, SOS, and HSOS-LO for Case 2. Figure 7: Convergence graphic of metaheuristic algorithms for Case 2.  
to design a storage layout plan in the completed floors of a multi-storey building. It considered the horizontal movements between different storage cells and the hoist system. Also, it considered the vertical transportation of construction materials on different floors. In this case study, the primary objective is to design the temporary construction facilities layout aimed at minimizing the total travelling distance of site workers between different facilities. The site layout has 10 facilities and 10 locations, as can be seen in Figure 8. Entrance gate and guard post are placed permanently at location 4 and 5, respectively, while others are not. The objective is to design the temporary facilities layout to get the minimum travel distance, which is calculated by multiplying the frequency and distance between each facility. The daily frequency of trips and the distance between locations are shown in Tables 7 and 8. The objective function is defined using Equations (1)-(4). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Facility**} & \multicolumn{8}{c}{**Facility**} \\ \cline{2-10}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
1 & 0 & 10 & 8 & 9 & 3 & 9 & 0 & 0 & 0 & 0 \\
2 & 10 & 0 & 8 & 12 & 8 & 9 & 11 & 5 & 0 & 1 \\
3 & 8 & 8 & 0 & 4 & 3 & 8 & 0 & 0 & 0 & 0 \\
4 & 9 & 12 & 4 & 0 & 6 & 15 & 10 & 10 & 8 & 5 \\
5 & 3 & 8 & 3 & 6 & 0 & 9 & 5 & 3 & 2 & 1 \\
6 & 9 & 9 & 8 & 15 & 9 & 0 & 0 & 0 & 0 & 0 \\
7 & 0 & 11 & 0 & 10 & 5 & 0 & 0 & 7 & 7 & 10 \\
8 & 0 & 5 & 0 & 10 & 3 & 0 & 7 & 0 & 25 & 27 \\
9 & 0 & 0 & 0 & 8 & 2 & 0 & 7 & 25 & 0 & 16 \\
10 & 0 & 1 & 0 & 5 & 1 & 0 & 10 & 27 & 16 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Frequencies of trips between facilities. Figure 8: Site Layout for Case 3. The proposed HSOS-LO was applied in the case study and were compared to the outcome of previous research studies. HSOS-LO was run for 100 simulations and the mean of the best value was recorded.