# Multicriteria Decision Making and Its Application in Geothermal Power Project
## 4 Case Study
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Physical Suitable** & **Socioeconomic Suitable** & **Technical Suitable** \\  & **Area (PSA)** & **Area (SSA)** & **Area (TSA)** \\ \hline Physical suitable area (PSA) & (1,1,1) & (1,2,3) & (3,4,5) \\ Socioeconomic suitable area (SSA) & (1/3,1/2,1) & (1,1,1) & (4,5,6) \\ Technical suitable area (TSA) & (1/5,1/4,1/3) & (1/6,1/5,1/4) & (1,1,1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fuzzy comparison matrices. The maximum individual values are calculated as follows in order to guarantee complete randomness amongst the criteria:  
\[S1=(1\times 2\times 4)^{1/3}=2 \tag{26}\]  
\[S2=(1/2\times 1\times 5)^{1/3}=1.36 \tag{27}\]  
\[S3=(1/4\times 1/5\times 1)^{1/3}=0.37 \tag{28}\]  
\[\sum S=S1+S2+S3=3.73 \tag{29}\]  
\[\omega_{1}=\frac{2}{3.73}=0.54 \tag{30}\]  
\[\omega_{2}=\frac{1.36}{3.73}=0.36 \tag{31}\]  
\[\omega_{3}=\frac{0.37}{3.73}=0.1 \tag{32}\]  
\[ \begin{bmatrix}1&2&4\\ 1/2&1&5\\ 1/4&1/5&1\end{bmatrix} \times \begin{bmatrix}0.54\\ 0.36\\ 0.1\end{bmatrix} = \begin{bmatrix}1.66\\ 1.13\\ 0.31\end{bmatrix}  \tag{33}\]  
\[\frac{ \begin{bmatrix}1.66\\ 1.13\\ 0.31\\ 0.54\\ 0.36\\ 0.1\end{bmatrix} }{ \begin{bmatrix}1.66\\ 1.13\\ 0.31\end{bmatrix} }= \begin{bmatrix}3.07\\ 3.14\\ 3.1\end{bmatrix}  \tag{34}\]  
Based on the number of main criteria, the authors get \(n=3\); \(\lambda_{max}\) and \(CI\) are calculated as following:  
\[\lambda_{max}=\frac{3.07+3.14+3.1}{3}=3.1 \tag{35}\]  
\[CI=\frac{\lambda_{max}-n}{n-1}=\frac{3.18-3}{3-1}=0.05 \tag{36}\]  
To calculate \(CR\) value, we get \(RI=0.52\) with \(n=3\). \[CR=\frac{CI}{RI}=\frac{0.05}{0.52}=0.0962 \tag{37}\]  
the consistency ratio, \(CR=0.0962\leq 0.1\), so there is no need to re-evaluate. The pair-wise comparison is then shown in Table 5 between the three main criteria being assessed in the case study. The weight of criteria for each sub-criterion after applying the weighting of the three main criteria accordingly is shown in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Criteria**} & **Physical Suitable** & **Socioeconomic Suitable** & **Technical Suitable** \\  & **Area (PSA)** & **Area (SSA)** & **Area (TSA)** \\ \hline Physical suitable area (PSA) & \(1\) & \(2\) & \(4\) \\ Socioeconomic suitable area (SSA) & \(1/2\) & \(1\) & \(5\) \\ Technical suitable area (TSA) & \(1/4\) & \(1/5\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Real number priority. The WASPAS approach is a unique combination of weighted sum model (WSM) and weighted product model (WPM). Due to simple mathematics operations and the capability to give more accurate results as compared to the individual WSM and WPM methods, the WASPAS model is now being chosen as an efficient decision-making tool in an MCDM model. In this work, a WASPAS model is applied to rank five potential locations. The results of the normalized matrix, weighted normalized matrix, and exponentially weighted matrix for the WASPAS model are displayed in Tables 7-9, based on the factors of 0.5, 0.5 of the alpha and beta values of the WSM and WPM methods, accordingly. The final ranking function value \(\text{S}_{\text{i}}\) was identified by using weighted sum mode \(\text{S}_{\text{i1}}\) (WSM) and weighted product model \(\text{Q}_{\text{i2}}\) (WSM), as can be seen in Table 10. From the results in Figure 4, the three highest suitable locations were DMU5, DMU4, and DMU2, with scores of 0.9870, 0.9118, and 0.8892, respectively. Therefore, Quang Tri (DMU5) is the optimal location, based purely on methodology calculations. For sensitivity analysis, a modification in the coefficient \(\lambda\) was conducted (coefficient \(\lambda\) is fixed in the range of 0.1, 0.2, 0.3,..., 1). The ranking results for varying \(\lambda\) values are exhibited in Figure 5. The results show that the values of the coefficient \(\lambda\) do not affect the change in the rank of the alternative.