## 3 Modeling the Temporary Facility Layout Problem
### ANP-Based Modeling for Layout Planning
#### 3.1.3 Step 3: Consistency Check  
Through the derived comparison matrices, the eigenvectors of the matrices are obtained, which represent the weights of the elements. The local priority vector is computed as Equation (2):  
\[\text{Aw}=\lambda_{\text{max}} \tag{2}\]  
where A is defined as the matrix of pairwise comparison values; w is the priority vector, which is called the principal eigenvector; and \(\lambda_{\text{max}}\) is the maximum or principal eigenvalue of matrix A.  
In order to obtain the pairwise comparison matrices, the local priority vectors are derived, which are illustrated in Tables 5 and 6.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{2}{c}{**Minimize the Total Number of**} & \multirow{2}{*}{**PEO**} & \multirow{2}{*}{**CHZ**} & \multirow{2}{*}{**CHM**} & \multirow{2}{*}{**STE**} & \multirow{2}{*}{**Priorities**} & \multirow{2}{*}{**CR**} \\ \cline{1-1} \cline{5-7} Proper equipment operation (PEO) & 1 & 1 & 2 & 2 & 0.3257 \\ \hline Control of hazardous zones (CHZ) & 1 & 1 & 3 & 2 & 0.3564 & 0.0172 \\ \hline Control of hazardous material (CHM) & 1/2 & 1/3 & 1 & 1/2 & 0.1243 \\ \hline Safety of task execution (STE) & 1/2 & 1/2 & 2 & 1 & 0.1936 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pairwise comparisons of safety with respect to resource travelling cost.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Objective** & **Safety** & **Productivity** & **Cost** & **Priorities** & **CR** \\ \hline Safety & 1 & 2 & 2 & 0.4934 & & \\ Productivity & 1/2 & 1 & 1/2 & 0.1958 & 0.0516 \\ Cost & 1/2 & 2 & 1 & 0.3108 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pairwise comparisons of objectives with respect to the objective criterion.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Control of Hazard Zones** & **ESU** & **LPE** & **SCD** & **ACT** & **FCR** & **WSC** & **Priorities** & **CR** \\ \hline Effective space utilization (ESU) & 1 & 3 & 2 & 2 & 3 & 2 & 0.3075 & \\ \hline Labor productivity and ergonomics (LPE) & 1/3 & 1 & 1/2 & 1/2 & 1 & 1/2 & 0.0918 & \\ \hline Short construction duration (SCD) & 1/2 & 2 & 1 & 2 & 1/2 & 1/2 & 0.1352 & 0.0663 \\ \hline The ability to dynamically change the TFs (ACT) & 1/2 & 2 & 1/2 & 1 & 1/2 & 1/2 & 0.1078 & \\ \hline Facilities closeness relationships (FCRs) & 1/3 & 1 & 2 & 2 & 1 & 2 & 0.1882 & \\ \hline Workspace conflicts (WSC) & 1/2 & 2 & 2 & 2 & 1/2 & 1 & 0.1694 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Pairwise comparisons of productivity with respect to control of hazard zones.  
After the local priority vectors are derived, the consistency is verified through a consistency index (CI) and a consistency ratio (CR). Lack of consistency in the pairwise comparisons indicates lack of understanding of the problem by the layout planners, which is caused by wrong decisions [65; 66]. The consistency ratio is acceptable if it is less than 0.1 [64]. The CI and CR are defined as Equation (3):  
\[\text{CR }=\text{CI}/\text{RI with CI }=(\lambda_{\text{max}}-\text{n})/(\text{n}-1) \tag{3}\]  
where CR represents the consistency ratio; CI represents the consistency index; RI represents the random index; and n is the size of matrix A.