## 5 Case Studies for Construction Site Layout Planning and Managerial Implication
### Case Study 2  
Multi-storey building construction sites have limited space. Therefore, 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 to reduce the material transportation times and to enhance the general construction efficiency. A real case study obtained from [PERSON] et al. (2018) was used to validate the proposed method. The objective was 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 study, several assumptions related to the problem are listed as follows. * The building has 30 floors and floors one to eight can be used as materials storage. * There are 10 types of materials and each floor has five storage cells that can only be used by 1 type of material. * There are three types of transportation costs: horizontal movement, vertical movement from the ground floor to the storage floor, and vertical movement from the storage floor to the demanding floor. * There are fixed and predetermined physical and demand quantities. * Only one lift used as the materials hoist. * All storage cell areas are large enough to meet storage requirements. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Metaheuristic** & \multicolumn{3}{c}{**Results**} & \multicolumn{3}{c}{**Best Layout**} & \multicolumn{3}{c}{**Parameters**} \\ \hline \hline
**Algorithms** & **Best** & **Average** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **F1–F11** & _pop\_size_ & _maxIter_ & _maxFE_ \\ \hline GA ([PERSON] et al., 2018) & 15,090 & N/A & N/A & \(11\,5\,8\,7\,2\,9\,3\,1\,6\,4\,10\) & 100 & 90 & 9,000 \\ Multi-searching TS ([PERSON] et al., 2018) & 12,880 & N/A & N/A & \(8\,11\,5\,7\,9\,3\,6\,1\,2\,4\,10\) & N/A & N/A & N/A \\ CBO ([PERSON] et al., 2018) & 12,546 & 12,558 & 45.51 & \(9\,11\,5\,6\,7\,4\,3\,1\,2\,8\,10\) & 50 & 200 & 10,000 \\ ECBO ([PERSON] et al., 2018) & 12,546 & 12,555 & 32.11 & \(9\,11\,5\,6\,7\,4\,3\,1\,2\,8\,10\) & 50 & 200 & 10,000 \\ SOS\({}^{*}\) & 12,546 & 12,560.56 & 42.52 & \(9\,11\,5\,6\,7\,4\,3\,1\,2\,8\,10\) & 50 & 30 & 3000 \\ HSOS-LO \({}^{*}\) & 12,546 & 12,553.86 & 19.37 & \(9\,11\,5\,6\,7\,4\,3\,1\,2\,8\,10\) & 50 & 20 & 3000 \\ \hline \hline \end{tabular} \({}^{*}\) Present study.  
\end{table} 
Table 4: Result comparison with previous research. Figure 4: Convergence graphic of metaheuristic algorithms for Case 1. The objective function is calculated using Equation (9):  
\[\text{Min}\left(\sum_{j=1}^{J}\sum_{l=1}^{L}\sum_{k=1}^{K}Q_{j,m}\left(C_{j,l}^{v}+ D_{l,k}C_{j}^{h}\right)x_{j,l,k}+\sum_{m=1}^{M}\sum_{j=1}^{J}Q_{j,m}\left(C_{j,m}^{v}-C_{ j,l}^{v}\right)\delta_{j,l,k,m}\right) \tag{9}\]  
where:  
* \(j=\) Index of Material types. * \(l=\) Index of a building's floor used for material storage as supply sources. * \(k=\) Index of storage cells on building floors. * \(m=\) Index of a building floor requesting the materials. * \(J=\) The total number of material. * \(L=\) The total number of floors for storage. * \(K=\) The total number of cells on the building level's. * \(M=\) The total number of levels. * \(Q_{j,m}=\) Floor \(m\)'s demand in a building for material type \(j\). * \(C_{j}^{h}=\) Cost of horizontal unit transportation of material type \(j\). * \(C_{j,l}^{v}=\) Cost of vertical unit transportation of material type \(j\) to a building's floor \(l\) from the ground. * \(C_{j,m}^{v}=\) Cost of vertical unit transportation of material type \(j\) to a building's floor \(m\) from the ground. * \(D_{l,k}=\) Distance from the material hoist on level \(l\) to cell \(k\). * \(x_{j,l,k}=\) Binary decision variable for storing material \(j\) on level \(l\) inside cell \(k\).