# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 3 Methodology
### Determine Quality Weight  
The weights of the significant criteria were computed using the SWARA method. The outstanding feature of the SWARA method is the prominence given to expert opinions. A team of selected experts from corresponding fields assigns weights to the provided criteria [37]. Experts are expected to utilize their implicit knowledge when ranking suppliers. In addition, the experts determine the importance of each criterion. The simplicity of this technique enables a team of experts to work seamlessly together on a joint project.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** & **C7** & **C8** & **C9** \\ \hline Exp. 1 & 2 & 3 & 1 & 7 & 4 & 6 & 8 & 9 & 5 \\ \hline Exp. 2 & 1 & 4 & 2 & 8 & 3 & 9 & 5 & 6 & 7 \\ \hline Exp. 3 & 3 & 2 & 4 & 5 & 1 & 7 & 9 & 8 & 6 \\ \hline Exp. 4 & 3 & 4 & 2 & 7 & 1 & 8 & 9 & 5 & 6 \\ \hline Exp. 5 & 3 & 4 & 1 & 8 & 2 & 9 & 7 & 6 & 5 \\ \hline Exp. 6 & 2 & 4 & 1 & 9 & 3 & 8 & 5 & 7 & 6 \\ \hline Exp. 7 & 2 & 3 & 1 & 8 & 5 & 7 & 6 & 9 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Criteria ranking by experts.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Expert** & **Sector** & **Position** & **Years of Experience** \\ \hline
**Exp. 1** & Governmental & Supplier relationship manager & 13 \\ \hline
**Exp. 2** & Private & Construction manager & 23 \\ \hline
**Exp. 3** & Private & Procurement manager & 18 \\ \hline
**Exp. 4** & Governmental & Supplier relationship specialist & 9 \\ \hline
**Exp. 5** & Governmental & Supply chain supervisor & 12 \\ \hline
**Exp. 6** & Private & Project manager & 12 \\ \hline
**Exp. 7** & Private & Project manager & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experts’ information about the first group.  
There are five significant steps involved in conducting an analysis using SWARA. First, the criteria requirements should be organized by their usefulness. The experts rank the defined criteria so that the most essential requirement is placed in the first position and the least essential requirement is placed in the last [38]. The second step is identified as calculating \(S_{j}\) (scientific criteria). This process involves experts determining the importance of a criterion (\(S_{j}\)) with a relative importance index (RII); the RII and \(S_{j}\) can be computed using the following Equations (1) and (2), respectively:  
\[RII=\frac{1n_{1}+2n_{2}+3n_{3}+4n_{4}+5n_{5}+6n_{6}+7n_{7}+8n_{8}+9n_{9}}{9(n_{ 1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{7}+n_{8}+n_{9})} \tag{1}\]  
\[S_{j}=\frac{RII_{j-1}-RII_{j}}{RII_{j}} \tag{2}\]  
where \(n_{1}\), \(n_{2}\), \(n_{3}\), \(n_{4}\), \(n_{5}\), \(n_{6}\), \(n_{7}\), \(n_{8}\), and \(n_{9}\) are the frequencies of options 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.  
Step three requires the SWARA users to determine the coefficient \(K_{j}\) using Equation (3).  
\[K_{j}=\begin{cases}1,&j=1,\\ s_{j}+1,&j>1.\end{cases} \tag{3}\]  
In step four, Equation (4) recalculates the weighting factors \(q_{j}\).  
\[q_{j}=\begin{cases}1,&j=1,\\ \frac{q_{j-1}}{k_{j}},&j>1.\end{cases} \tag{4}\]  
Lastly, the equation below is used to calculate the relative weighting factors of the evaluation criteria. The criteria weight (CW) can be calculated using Equation (5) [39].  
\[CW_{j}=\frac{q_{j}}{\sum_{k=1}^{n}q_{k}} \tag{5}\]  
The weightages for different supplier selection criteria were derived using the SWARA method. Table 5 summarizes the results obtained. The detailed calculations of the SWARA method are presented in Appendix A.