## 4 Two Real Case Studies
### The First Case Study: University Departments
#### 4.1.1 Applying the Interactive Algorithm for the First Case Study
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**DMU\({}_{\mathbf{o}}\)**} & \multicolumn{2}{c}{**Target\({}_{1}\)**} & \multicolumn{2}{c}{**Target\({}_{2}\)**} & \multicolumn{2}{c}{**Target\({}_{3}\)**} & \multicolumn{2}{c}{**Target\({}_{4}\)**} & \multicolumn{2}{c}{**Target**} \\ \hline \multirow{4}{*}{DMU\({}_{05}\)} & Model 14 & 40 & 8 & 20 & 6 & DMU\({}_{03}\) \\ \cline{2-7}  & DM’s opinions & 40 & 8 & 20 & 6 & DMU\({}_{03}\) \\ \cline{2-7}  & \(\Delta_{\mathrm{f_{i}}}\) & 0 & 0 & 0 & 0 & - \\ \cline{2-7}  & Unsatisfied & 0 & 0 & 0 & 0 & - \\ \hline \multirow{4}{*}{DMU\({}_{06}\)} & Model 14 & 83 & 1 & 58 & 3 & DMU\({}_{07}\) \\ \cline{2-7}  & DM’s opinions & 83 & 11 & 58 & 3 & DMU\({}_{07}\) \\ \cline{2-7}  & \(\Delta_{\mathrm{f_{i}}}\) & 0 & \(-\)10 & 0 & 0 & - \\ \cline{2-7}  & Unsatisfied & 0 & 0 & 0 & 0 & - \\ \hline \multirow{4}{*}{DMU\({}_{16}\)} & Model 14 & 86 & 0 & 85 & 0 & DMU\({}_{13}\) \\ \cline{2-7}  & DM’s opinions & 186 & 20 & 85 & 10 & DMU\({}_{13}\) \\ \cline{2-7}  & \(\Delta_{\mathrm{f_{i}}}\) & \(-\)100 & \(-\)20 & 0 & \(-\)10 & - \\ \cline{2-7}  & Unsatisfied & 0 & 0 & 0 & 1 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of solving model 14 (Step 1 of STEM for p = 1) and DM’s opinions about them for three DMUs (related to the second interactive stage) in the first case study. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**DMU\({}_{\mathbf{o}}\)**} & \multicolumn{2}{c}{**I = 1**} & \multicolumn{2}{c}{**I = 2**} & \multicolumn{2}{c}{**I = 3**} & \multicolumn{2}{c}{**I = 4**} \\ \hline \multirow{4}{*}{DMU\({}_{05}\)} & \(\mathrm{f_{i}^{min}}\) & \(-\)40 & \(-\)8.000 & 18.000 & 6.000 \\ \cline{2-7}  & \(\mathrm{f_{i}^{*}}\) & \(-\)40 & \(-\)8.000 & 20.000 & 6.000 \\ \cline{2-7}  & \(\mathrm{\pi_{i}}\) & 0 & 0.000 & 0.006 & 0.000 \\ \cline{2-7}  & \(\mathrm{\beta_{1}}\) & 0 & 0.000 & 1.000 & 0.000 \\ \hline \multirow{4}{*}{DMU\({}_{06}\)} & \(\mathrm{f_{i}^{min}}\) & \(-\)83 & 11.000 & 40.000 & 2.000 \\ \cline{2-7}  & \(\mathrm{f_{i}^{*}}\) & \(-\)83 & \(-\)11.000 & 58.000 & 3.000 \\ \cline{2-7}  & \(\mathrm{\pi_{i}}\) & 0 & 2.000 & 0.008 & 0.167 \\ \cline{2-7}  & \(\mathrm{\beta_{1}}\) & 0 & 0.920 & 0.004 & 0.077 \\ \hline \multirow{4}{*}{DMU\({}_{16}\)} & \(\mathrm{f_{i}^{min}}\) & \(-\)186 & 20.000 & 80.000 & 5.000 \\ \cline{2-7}  & \(\mathrm{f_{i}^{*}}\) & \(-\)186 & \(-\)20.000 & 85.000 & 10.000 \\ \cline{1-1} \cline{2-7}  & \(\mathrm{\pi_{i}}\) & 0 & 1.000 & 0.001 & 0.100 \\ \cline{1-1} \cline{2-7}  & \(\mathrm{\beta_{1}}\) & 0 & 0.908 & 0.001 & 0.091 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calculating parameters for three DMUs to compose model 14 of step 1 of STEM (p = 1) (related to the second interactive stage) in the first case study. Non-radial model 14 for DMU\({}_{16}\) was then composed for the first iteration of step 2 of STEM. The results of solving this model showed that there was only one similar unsatisfied objective function (fourth objective function) in two consecutive steps of STEM. Therefore, the target of DMU\({}_{16}\) could not be considered as DMU\({}_{13}\). Therefore, the interactive algorithm was continued by asking DM to suggest a new target for each DMU\({}_{\text{o}}\). DM did not suggest new DMUs target for DMU\({}_{16}\) so there were no targets for DMU\({}_{16}\) in the FDH model. Then, DMU\({}_{\text{o}}\) (DMU\({}_{16}\)) from M\({}^{\prime}\) set was removed (M\({}^{\prime}=\varnothing\)). As there was no non-proceed DMUs and the process of targets determination for all DMUs had been carried out (M\({}^{\prime}=\varnothing\)), the interactive algorithm was finished. The results of applying the interactive algorithm for all DMUs are shown in Table 8.