# Robust Additive Value-Based Efficiency Analysis
## 5 Case Study concerning Evaluation of Healthcare System in Poland
### The Category of Financial Management  
In this section, we discuss the results attained at the level of financial management. Instead of comparing them to the outcomes at the comprehensive level, we emphasize how managers can use them to improve the relative efficiency of provinces. Similar improvement strategies can be designed for other categories or hierarchy nodes. Figure 12 presents the extreme and expected distances to the best province when limiting the scope to financial management. The most important result derived from their analysis is the division of provinces into efficient and inefficient. The minimal distance equals zero only for two units: POM and LBU. This means that they are the best performers among the sixteen voivodeships for at least one feasible weight vector. However, LBU \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \(ERAI\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** \\ \hline ZPM & 0 & 0.916 & 0.058 & 0.026 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ POM & 0 & 0.054 & 0.858 & 0.088 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ WM & 0 & 0 & 0 & 0 & 0 & 0.029 & 0.705 & 0.110 & 0.093 & 0.063 & 0 & 0 & 0 & 0 & 0 & 0 \\ PDL & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.003 & 0.179 & 0.096 & 0.075 & 0.403 & 0.142 & 0.102 & 0 \\ LBU & 0 & 0.030 & 0.084 & 0.882 & 0.004 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ WLKP & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ KP & 0 & 0 & 0 & 0 & 0 & 0 & 0.212 & 0.272 & 0.182 & 0.087 & 0.247 & 0 & 0 & 0 & 0 \\ MAZ & 0 & 0 & 0 & 0 & 0 & 0.932 & 0.013 & 0.046 & 0.009 & 0 & 0 & 0 & 0 & 0 & 0 \\ LBL & 0 & 0 & 0 & 0 & 0 & 0.049 & 0.036 & 0.294 & 0.206 & 0.177 & 0.176 & 0.049 & 0.013 & 0 & 0 \\ DSL & 0 & 0 & 0 & 0 & 0 & 0.039 & 0.039 & 0.399 & 0.201 & 0.070 & 0.142 & 0.064 & 0.019 & 0.026 & 0.001 & 0 \\ OPO & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.010 & 0.990 \\ LDZ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.120 & 0.059 & 0.085 & 0.159 & 0.281 & 0.296 & 0 & 0 \\ SL & 0 & 0 & 0 & 0.004 & 0.996 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ SW & 0 & 0 & 0 & 0 & 0 & 0 & 0.194 & 0.077 & 0.069 & 0.215 & 0.311 & 0.134 & 0 & 0 & 0 & 0 \\ MLP & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.023 & 0.011 & 0.043 & 0.450 & 0.473 & 0 \\ PKR & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.005 & 0.012 & 0.190 & 0.369 & 0.414 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Distribution of ranks for Polish vivodeships when considering inhabitants’ health improvement level. has slightly better maximal and expected distances to the best province than POM. When looking at their inputs and outputs within the financial category, they perform equally well (51.3) on output \(F_{3}\). It is the best value among all provinces. Moreover, the other two financial factors are greater for LBU, confirming that it transforms more beds (input \(F_{2}\)) into a more significant profit (output \(F_{1}\)). These two voivodeships should serve as ultimate peers for the remaining inefficient units in terms of financial management. Among them, the overall good performers are WLKP (\(Ed^{F}=0.1689\)) and MLP (\(Ed^{F}=0.2328\)). They do not optimize one specific input or output, but perform decently on all indicators. In the optimistic, pessimistic, and expected scenarios, SL attains the least favorable results with the significantly greatest distances to the best province. In turn, KP  
Figure 11: The Hasse diagram of the necessary efficiency preference relation when considering inhabitants’ health improvement level.