# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 3 Methodology
### Estimate the CQW of the Alternative Based on Its Capacity
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**No** & **Q1** & **Q2** & **Q3** & **Q4** & **Q5** & **Q6** & **Q7** & **Q8** & **Q9** \\ \hline
**Exp. 1** & 4 & 3 & 5 & 5 & 5 & 5 & 5 & 5 & 4 \\ \hline
**Exp. 2** & 4 & 4 & 1 & 3 & 4 & 3 & 3 & 1 & 4 \\ \hline
**Exp. 3** & 0 & 0 & 2 & 0 & 5 & 0 & 0 & 5 & 3 \\ \hline
**Exp. 4** & \(-1\) & \(-2\) & \(-4\) & \(-4\) & \(-5\) & \(-4\) & \(-4\) & \(-4\) & \(-4\) & \(-4\) \\ \hline
**Exp. 5** & 0 & 0 & 0 & \(-5\) & \(-5\) & 0 & 0 & \(-5\) & 0 \\ \hline
**Exp. 6** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
**Exp. 7** & \(-1\) & \(-2\) & \(-3\) & \(-2\) & \(-2\) & \(-4\) & 0 & 0 & 5 \\ \hline
**Exp. 8** & 5 & 5 & 0 & 5 & 5 & 4 & 3 & 5 & 5 \\ \hline
**Exp. 9** & 4 & 4 & 4 & 4 & 5 & 4 & 4 & 4 & 4 \\ \hline
**Exp. 10** & 3 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 5 \\ \hline
**Exp. 11** & 3 & 4 & 0 & 0 & 5 & \(-3\) & \(-2\) & 3 & 4 \\ \hline
**Exp. 12** & 5 & 4 & 4 & 4 & \(-2\) & 4 & \(-2\) & \(-3\) & 5 \\ \hline
**Exp. 13** & 3 & 4 & 0 & 4 & 4 & 0 & 1 & 2 & 3 \\ \hline
**Exp. 14** & 0 & 0 & 3 & 2 & 5 & 5 & 5 & 5 & 1 \\ \hline
**Exp. 15** & 3 & 0 & 5 & 0 & 0 & 0 & 4 & 5 & 5 \\ \hline
**Exp. 16** & 0 & 3 & 0 & 0 & 3 & 0 & 4 & 5 & 4 \\ \hline
**Exp. 17** & 5 & 5 & 3 & 2 & 5 & 5 & 5 & 3 & 5 \\ \hline
**Exp. 18** & \(-5\) & 3 & 1 & \(-1\) & 1 & 1 & \(-5\) & \(-4\) & \(-5\) \\ \hline
**Exp. 19** & 4 & 4 & 4 & 5 & 3 & 2 & 3 & 4 & 5 \\ \hline
**Exp. 20** & 1 & 2 & 3 & 2 & 5 & 3 & 2 & 4 & 4 \\ \hline \end{tabular}
\end{table} 
Table 6: Survey data on the influence of the nine criteria. The analysis extracted several components with eigenvalues greater than one; however, only the first principal component (PC1) was used to derive the quality coefficients. This decision was based on two key rationales. First, PC1 accounted for 63.18% of the total variance (Table 8), making it the dominant component that captured the most significant shared variance across all nine quality criteria. It can thus be interpreted as the primary underlying factor representing the \"overall capacity-quality relationship.\" Second, the goal of this step was to derive a single set of weights to link capacity to quality in a clear and applicable manner. Using only the loadings from PC1 provides a direct, interpretable, and parsimonious way to achieve this. The loadings of each criterion on PC1, presented in the rotated component matrix (Table 9), were then normalized using Equation (6) to compute the final coefficients (C), which quantify the proportional impact of production capacity on each specific quality criterion. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Kaiser-Meyer-Olkin Measure of Sampling Adequacy** & **0.708** \\ \hline \multirow{3}{*}{**Bartlett’s Test of Sphericity**} & Approx. Chi-Square & 142.271 \\ \cline{2-3}  & df & 36 \\ \cline{2-3}  & Sig. & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: KMO and Bartlett’s test. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{3}{*}{**Component**} & \multicolumn{3}{c}{**Initial Eigenvalues**} \\ \cline{2-4}  & & **Total** & **\% of Variance** & **Cumulative \%** \\ \hline \multirow{6}{*}{**Raw**} & 1 & 49.117 & 63.179 & 63.179 \\ \cline{2-4}  & 2 & 9.345 & 12.020 & 75.199 \\ \cline{2-4}  & 3 & 7.474 & 9.613 & 84.813 \\ \cline{2-4}  & 4 & 5.823 & 7.490 & 92.302 \\ \cline{2-4}  & 5 & 2.405 & 3.094 & 95.396 \\ \cline{2-4}  & 6 & 1.479 & 1.903 & 97.299 \\ \cline{2-4}  & 7 & 1.059 & 1.362 & 98.660 \\ \cline{2-4}  & 8 & 0.732 & 0.941 & 99.602 \\ \cline{2-4}  & 9 & 0.310 & 0.398 & 100.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Eigenvalue with variance explained. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Component** & \\ \cline{2-4}  & **1** & **2** \\ \hline C1 & 1.865 & 1.010 \\ \hline C2 & 1.827 & 0.436 \\ \hline C3 & 1.760 & 0.893 \\ \hline C4 & 2.383 & 1.350 \\ \hline C5 & 1.371 & 2.611 \\ \hline C6 & 2.484 & 0.717 \\ \hline C7 & 1.130 & 2.330 \\ \hline C8 & 0.568 & 3.355 \\ \hline C9 & 1.170 & 2.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Rotated component matrix.