# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 3 Methodology
### Estimate Each Supplier's Qi Score Using the WASPS Method
The finding score for WASPAS for each supplier is displayed in Table 15.  
For a more granular analysis, a radar chart (Figure 2) is proposed to illustrate the performance profile of each supplier across the nine evaluation criteria. In a radar chart, each vertex represents a criterion, and the distance from the center to a vertex indicates the supplier's weighted score for that specific criterion (data from Table 13). This visualization allows for an immediate comparison of how suppliers perform on individual metrics. For example, a supplier with a large, well-rounded shape indicates strong performance across many criteria. In contrast, a supplier with a \"spiky\" shape excels in some areas but is weak in others. This detailed profile explains why a supplier achieved its final rank and provides \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** & **C7** & **C8** & **C9** & **WSM** \\ \hline A1 & 0.005 & 0.007 & 0.003 & 0.019 & 0.007 & 0.012 & 0.019 & 0.009 & 0.003 & 0.085 \\ \hline A2 & 0.004 & 0.006 & 0.003 & 0.016 & 0.006 & 0.010 & 0.016 & 0.007 & 0.003 & 0.070 \\ \hline A3 & 0.007 & 0.010 & 0.005 & 0.027 & 0.010 & 0.016 & 0.027 & 0.012 & 0.005 & 0.118 \\ \hline A4 & 0.004 & 0.006 & 0.003 & 0.016 & 0.006 & 0.010 & 0.016 & 0.007 & 0.003 & 0.070 \\ \hline A5 & 0.003 & 0.005 & 0.002 & 0.014 & 0.005 & 0.008 & 0.013 & 0.006 & 0.002 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Normalized weighted matrix of WSM. valuable insights for strategic decision-making. The identical nature of the curves for A2 and A4 is a direct result of their equivalent capacities. The radar chart shown in Figure 3 provides a multi-dimensional comparison of the five suppliers based on their normalized Weighted Product Model (WPM) scores across the nine distinct criteria. Each spoke of the chart represents a performance criterion (C1 through C9), with values farther from the center indicating a higher, more favorable score. Visually, the supplier with the largest enclosed area represents the best overall performer according to this model. From the chart, Supplier A3 (green) clearly stands out, exhibiting the most robust performance by consistently achieving the highest scores across nearly all criteria, particularly in C3 (Method of payment), C6 (Ease of communication), C7 (Quick response), and C9 (Technical expertise). In contrast, Supplier A5 (purple) demonstrates the weakest overall profile, with its shape being the most compressed towards the center. The chart also reveals that the performance profiles for Supplier A2 (red) and Supplier A4 (orange) are identical,  
Figure 3: Radar chart of supplier performance profiles and overall ranks for WPM. \begin{table}
\begin{tabular}{c c c c} \hline  & **WSM** & **WPM** & **WASPAS** \\ \hline A1 & 0.085 & 0.077 & 0.081 \\ \hline A2 & 0.070 & 0.064 & 0.067 \\ \hline A3 & 0.118 & 0.107 & 0.112 \\ \hline A4 & 0.070 & 0.064 & 0.067 \\ \hline A5 & 0.059 & 0.054 & 0.056 \\ \hline \end{tabular}
\end{table} 
Table 15: WASPAS score. as their lines overlap entirely. This visualization effectively highlights not only the overall ranking but also the specific strengths and weaknesses of each supplier, allowing for a more nuanced and granular assessment than a simple numerical score. To enhance the transparency and reproducibility of the research, this section provides a detailed, step-by-step explanation of the calculation process for the WSM, WPM, and the final WASPS scores. The calculations for Supplier A1 are used as a running example to illustrate how the data from various tables is substituted into the formulas. To calculate the WSM score for Supplier A1 (\(Q_{A}^{1}\)), we multiply each of the CQWs of the A1 values from Table 12 by the corresponding criterion weight from Table 5 and then sum the results.