## 5 Case Study
### Sensitivity Analysis  
The ELECTRE-MOr method also allows sensitivity analyses, varying the cut-off level and verifying the distribution of alternatives [70]. Table 13 exposes the sensitivity analysis, with the consolidated classification of the alternatives after variation \(\lambda\). To verify more demanding and flexible scenarios, the following values were used for the cut-off level \(\lambda\): 0.75; 0.85; 0.9; 0.95 and 1).  
After the sensitivity analysis, we verified that the results presented by the proposed methodology are coherent. As the \(\lambda\) value was increased (making the analysis more demanding), there was a downward trend of alternatives in classes A and B, that is, military personnel who would be promoted by merit or time of service, and an increase of alternatives distributed in classes C (not promoted). Analyzing the most flexible scenario (cut-off level equal to 0.75), we observed that only 13.3% of the officers would not gain promotion.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Alternatives** & **Class** \\ \hline OF9 & \\ OF10 & \\ OF17 & \\ OF20 & A \\ OF23 & \\ OF25 & \\ \hline OF1 & \\ OF2 & \\ OF3 & \\ OF4 & \\ OF6 & \\ OF7 & \\ OF8 & \\ OF11 & \\ OF14 & B \\ OF15 & \\ OF12 & \\ OF21 & \\ OF24 & \\ OF25 & \\ OF28 & \\ OF30 & \\ \hline OF5 & \\ OF12 & \\ OF13 & \\ OF16 & \\ OF18 & C \\ OF22 & \\ OF27 & \\ OF22 & \\ \hline \hline \end{tabular}
\end{table}
Table 12: Consolidated classification of alternatives, with a cut-off level of 0.8.  
In addition, we observed that, for the most demanding case possible, with \(\lambda\)=1, all officers were allocated to the lower class. Thus, the sensitivity analysis provided additional information to the decision-maker because it verified the changes in the distributions of the alternatives when the cut-off level was varied (from 0.75 to 1). With this analysis, the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Lambda**} \\ \hline  & & & & & **0.75** & \\  & & & & & **0.8** & \\
**0** & & & & & **0.85** & **1** \\  & & & & & **0.9** & \\  & & & & & **0.95** & \\ \hline OF1 & B & B & C & C & C & C & C \\ OF2 & B & B & B & A & A & C \\ OF3 & B & B & B & A & A & C \\ OF4 & B & B & A & C & C & C \\ OF5 & C & C & C & C & C & C \\ OF6 & B & B & A & C & C & C \\ OF7 & B & B & C & C & C & C \\ OF8 & B & B & A & A & C \\ OF9 & A & A & A & C & C & C \\ OF10 & B & A & C & C & C & C \\ OF11 & B & B & A & A & C \\ OF12 & B & C & C & C & C & C \\ OF13 & B & C & C & C & C & C \\ OF14 & B & B & B & C & C & C \\ OF15 & B & B & C & C & C & C \\ OF16 & B & C & C & C & C & C \\ OF17 & B & A & C & C & C & C \\ OF18 & C & C & C & C & C & C \\ OF12 & B & B & A & C & C & C \\ OF20 & A & A & A & C & C & C \\ OF21 & B & B & C & C & C & C \\ OF22 & B & C & C & C & C & C \\ OF23 & A & A & A & C & C & C \\ OF24 & B & B & A & C & C & C \\ OF25 & B & B & A & A & A & C \\ OF25 & B & A & A & C & C & C \\ OF27 & C & C & C & C & C & C \\ OF28 & B & B & A & A & A & C \\ OF22 & C & C & C & C & C & C \\ OF30 & B & B & B & C & C & C \\  & & & & & & 0.00\% \\  & & & & & & 20.00\% \\ Class A & 10 & & & & & 20.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.67\% \\  & & & & & & 53.33\% \\ Class B & 76 & & & & & 20.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.00\% \\  & & & & & & 0.67\% \\ Class C & 13.33\% & 26 & & & & 80.00\% \\  & & & & & & 80.00\% \\  & & & & & & 100.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 13: Sensitivity analysis of the result, varying the cut-off level.  
decision maker can make decisions based on more flexible or rigorous scenarios at the discretion of the Naval High Administration. In other words, the decision maker can use the variation of \(\lambda\) and, consequently, of the distributions, as a way to prioritize alternatives that remain in the higher classes with the increase of the cut-off level.