# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 3 Methodology
### Estimate the CQW of the Alternative Based on Its Capacity
The model's core novelty lies in linking factory capacity to the CQW via PCA coefficients (as established in the section \"Determining the CQW by PCA\"), thereby inherently recognizing that larger, more resourceful suppliers may be better positioned to excel across various quality attributes due to potential economies of scale, more efficient resource allocation, and greater flexibility [32; 34]. Consequently, the higher ranking of suppliers with larger normalized capacities reflects the model's underlying logic, which suggests that robust production capability translates to enhanced performance across multiple evaluation criteria. While the framework integrates production capacity as a key performance indicator, it is important to note that specific granular operational details, such as a supplier's direct access to batching plants or proximity to raw material sources, were not explicitly factored into the current model. Such logistical elements can significantly influence a supplier's cost-effectiveness, delivery reliability, and responsiveness [36]. While deemed outside the immediate scope of this initial framework's primary capacity-to-quality linkage, future refinements could incorporate a broader range of supply chain and operational logistics to provide an even more granular and comprehensive supplier capability assessment, further enhancing the model's predictive power and practical utility in real-world scenarios. The criteria quality weight (\(CQW_{ij}\)) of the \(i\)th criterion and \(j\)th alternative supplier can be determined based on the value of \(\overline{C}_{i}\) and \(NCS_{j}\), as shown in Equation (8). \[CQW_{ij}=\overline{C}_{i}\times NCS_{j} \tag{8}\]  
For more clarification on the computation of the CQW, the following example was elaborated: the \(CQW_{15}\) can be calculated based on the \(\overline{C}\)'s first criterion (\(\overline{C}_{1}\)) and the \(NCS\) of the fifth alternative supplier (\(NCS_{5}\)). The \(\overline{C}_{1}\) and \(NCS_{5}\) values were determined in Tables 10 and 11 to be 0.128 and 0.5, respectively. Thus, the \(CQW_{15}\) was 0.064 (\(CQW_{15}=0.128\times 0.5\)). Hence, the CQW matrix utilized in WASP is shown in Table 12. The values provide the precise weights allocated to each corresponding criterion. These \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Alternative** & **Capacity per Year** & **Capacity per Day (CS)** & **NCS** \\
**Supplier** & **(m\({}^{\textbf{3}}\))** & **(m\({}^{\textbf{3}}\))** & **NCS** \\ \hline
**A1** & 360,000 & 986 & 0.72 \\ \hline
**A2** & 300,000 & 822 & 0.6 \\ \hline
**A3** & 500,000 & 1370 & 1 \\ \hline
**A4** & 300,000 & 822 & 0.6 \\ \hline
**A5** & 250,000 & 685 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Normalization of PCA. criteria play a significant role in the decision-making process for selecting a precast supplier through the WASPS method. The resulting criteria quality weight (CQW) matrix, presented in Table 12, represents a pivotal output of the PCA-based analysis and the key innovation of this stage. Each value of CQWij quantifies the objective performance score of a specific supplier (j) on a specific criterion (i), derived directly from their production capacity. This matrix now serves as the core input for the subsequent aggregation phase of the framework. The next logical step is to systematically aggregate these individual performance scores, taking into account the relative importance of each criterion as determined by the SWARA method. For this purpose, the Weighted Aggregated Sum Product Assessment (WASPAS) method is employed. The rationale for selecting WASPS is its proven robustness in combining the strengths of both the Weighted Sum Model (WSM) and the Weighted Product Model (WPM) to provide a stable and comprehensive performance index (Qi) for each alternative. The following section details the application of the WASPS method to synthesize the CQW matrix and the SWARA weights into a final, ranked list of suppliers.