# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 3 Methodology
### Compute VE and Ranking  
While the WASPS score primarily considers production aspects, VE incorporates cost considerations to achieve a well-rounded evaluation. The cost determination depends on the precast elements' square meters, assuming a thickness of 150 mm and a fixed HC width of 1200 mm. The depth of precast elements fluctuates depending on the specific span requirements. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Alternatives** & & & **Normalization** & & & \\
**to the** & **WASPAS** & **Cost (SAR/m2)** & **Cost/Max** & **VE** & **Normalized** & \\
**Supplier** & & **Cost/Max** & **Cost/Max** & **VE** & **VE** = \\ \hline A1 & 0.081 & 125 & 0.96 & 0.084 & 0.693 & 3 \\ \hline A2 & 0.067 & 130 & 1 & 0.067 & 0.550 & 5 \\ \hline A3 & 0.112 & 120 & 0.92 & 0.122 & 1.000 & 1 \\ \hline A4 & 0.067 & 95 & 0.73 & 0.092 & 0.754 & 2 \\ \hline A5 & 0.056 & 100 & 0.77 & 0.073 & 0.597 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Ranking of suppliers. The cost is determined depending on the bids submitted by the suppliers. Each cost is divided by the highest cost to normalize the cost values. Further, the quality weight is divided by the normalized cost to calculate the value of VE. This ratio is equivalent to the WASPAS score. For instance, if the WASPAS score for A4 is 0.067 and a normalized cost is 0.73, the VE score can be calculated as 0.067/0.73, yielding 0.092. This calculation is performed so that all suppliers can derive their corresponding VE scores. Then, the VE score is calculated in conjunction with the WASPAS scores, and the outcomes are presented in Table 16.  
The VE score shows each supplier's relative strength, with a higher score signifying a preferred choice. The last column of Table 16 displays the supplier ranking. In the precast industry, VE plays a pivotal role in selecting the most suitable supplier by striking a balance between various factors. The model's results, summarized in Table 16, provide a clear and quantitatively robust ranking of the supplier alternatives. The distribution of the final normalized Value Engineering (VE) scores, which range from 0.54 to 1.00, indicates that the framework is highly effective at discriminating between the performance of suppliers. A3 emerges as the definitively top-ranked alternative with a perfect normalized VE score of 1.00. Crucially, this is not a marginal victory; there is a substantial performance gap between the top suppliers. A3's VE score is 25% higher than the second-ranked supplier, A4 (VE score = 0.754), and 85% higher than the lowest-ranked supplier, A2 (VE score = 0.55). This significant quantitative differential underscores a clear and statistically meaningful preference for A3 based on the model's integrated assessment of quality, capacity, and cost. In contrast, A4 represents the \"value-for-money\" option, securing the second rank despite having a moderate production capacity by offering the lowest cost. The lower-ranked suppliers exhibit clear quantitative weaknesses. For example, A2's high cost is not justified by its capacity, resulting in the lowest VE score. This analysis demonstrates how the framework translates complex trade-offs into a single, decisive score. The robustness of these performance differentials and the stability of the final rankings are statistically interrogated in the subsequent Sensitivity Analysis (Section 4) and validated against external expert opinion (Section 5). This data-driven insight allows project managers to move beyond a simple ranking and make nuanced selection decisions. For instance, a manager could select A3 for critical projects and A4 for standard ones, thereby creating a flexible and cost-effective supplier portfolio. Furthermore, the results serve as a powerful tool for supplier development and negotiation. A project manager could leverage this data to approach Supplier A2 with evidence of its uncompetitive pricing or to negotiate better terms with Supplier A1 by highlighting its cost disadvantages relative to A4.