## 4 Case Study
### Stage A: Efficiency Evaluation by B-DEA Model  
To evaluate the efficiency of locations, this stage applied the B-DEA model discussed in Section 3.1. First, ten experts with at least eight years of experience in renewable energy, marine climate and public policy development were selected to contribute to this study. There are seven quantitative indicators defined by relevant research and expert opinion [17; 52; 53; 54]. These indicators are divided into two groups as inputs and outputs of the B-DEA model. The inputs include bathymetry (m), distance to shore (km), and distance to the grid (km). These factors directly affect the cost of installation and maintenance and transmission power loss. Therefore, the smaller value of these metrics, the higher efficiency of WWS. Meanwhile, the population density in the adjacent residential area (people/km\({}^{2}\)) as well as the energy potential related indicators of locations, such as average wind speed (m/s), annual average power density (W/m\({}^{2}\)), and wave height (m), are outputs. As shown in Table 4, the data of inputs and outputs were collected from online renewable energy databases, such as the International Renewable Energy Agency database [55; 56]. Figure 4: The proposed feasible locations for WWS in Vietnam. Based on the collected data, the procedure of the B-DEA model, as mentioned in Section 3.1, was applied. This study assumed that experts are more concerned with gains than losses (\(\Theta>0.5\)), and \(\mu=2.25\), \(\alpha=0.85\), \(\beta=0.92\) in the B-DEA model [10]. Then, the B-DEA model (7) was solved with a different value of \(\Theta\) by Lingo solver 19.0.53. The results of B-DEA's model are presented in Table A2 in Appendix A. Based on efficiency corresponding to different values of \(\Theta\), locations were ranked as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Location** & **Bathymetry** & **Distance to** & **Distance to** & **Average Wind** & **Annual Average** & **Wave** & **Population Density of the** \\  & **(m)** & **Shore (km)** & **Grid (km)** & **Speed (m/s)** & **Power Density** & **Height (m)** & **Adjacent Residential Area** \\ \hline WWS-1 & 40 & 77.34 & 99.44 & 7.40 & 447.14 & 0.9 & 99.62 \\ WWS-2 & 25 & 90.80 & 91.94 & 7.61 & 454.05 & 1.1 & 99.37 \\ WWS-3 & 44 & 90.20 & 118.39 & 7.61 & 454.05 & 1.1 & 87.67 \\ WWS-4 & 52 & 98.40 & 98.47 & 7.61 & 454.05 & 1.1 & 96.78 \\ WWS-5 & 69 & 73.63 & 86.49 & 7.27 & 376.72 & 1.1 & 80.88 \\ WWS-6 & 91 & 96.12 & 112.63 & 7.27 & 376.72 & 1.2 & 97.99 \\ WWS-7 & 99 & 99.02 & 99.10 & 6.85 & 318.33 & 1.4 & 94.66 \\ WWS-8 & 535 & 67.66 & 100.24 & 6.85 & 318.33 & 1.4 & 66.62 \\ WWS-9 & 439 & 90.01 & 132.21 & 7.07 & 344.87 & 1.4 & 88.70 \\ WWS-10 & 2057 & 89.88 & 96.00 & 7.07 & 344.87 & 1.4 & 90.46 \\ WWS-11 & 2152 & 85.55 & 96.82 & 6.17 & 248.00 & 1.4 & 96.19 \\ WWS-12 & 635 & 100.76 & 109.07 & 6.17 & 248.00 & 1.6 & 93.16 \\ WWS-13 & 131 & 23.70 & 98.01 & 6.17 & 248.00 & 1.5 & 91.90 \\ WWS-14 & 43 & 104.08 & 105.50 & 6.19 & 219.74 & 1.3 & 98.50 \\ WWS-15 & 40 & 98.02 & 121.95 & 6.19 & 219.74 & 1.3 & 126.72 \\ WWS-16 & 23 & 31.95 & 117.76 & 6.19 & 219.74 & 0.7 & 102.65 \\ WWS-17 & 24 & 76.49 & 129.76 & 6.19 & 219.74 & 0.8 & 78.75 \\ WWS-18 & 24 & 94.23 & 161.85 & 6.38 & 261.99 & 0.8 & 97.35 \\ WWS-19 & 42 & 78.83 & 158.20 & 6.38 & 261.99 & 0.7 & 123.08 \\ WWS-20 & 26 & 65.16 & 71.59 & 6.38 & 261.99 & 0.3 & 66.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The quantitative indicators of the B-DEA model. Figure 5: WWS location ranking with different values of \(\Theta\). The first finding from the ranking results is that WWS-12 has the highest efficiency without being affected by \(\Theta\). Meanwhile, at the bottom of the rankings, the performance of WWS-12 and WWS-14 positions is also unchanged by the psychological behavior of the decision maker. Meanwhile, at the bottom of the rankings, the efficiency of WWS-16 and WWS-20 positions remained unchanged as decision makers place more emphasis on gains.