# Robust Additive Value-Based Efficiency Analysis
## 5 Case Study concerning Evaluation of Healthcare System in Poland
### Comprehensive Evaluation of the Quality of Healthcare Systems
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**Voivodeship** & **ZPM** & **POM** & **WM** & **PDL** & **LBU** & **WLKP** & **KP** & **MAZ** & **LBL** & **DSL** & **OPO** & **LDZ** & **SL** & **SW** & **MLP** & **PKR** \\ \hline ZPM & N & & P & P & & & P & P & N & P & P & P & P & P & P & P \\ POM & N & N & N & P & P & P & N & N & N & N & N & N & N & N & N & N \\ WM & P & & N & P & & P & P & P & N & N & P & P & P & P & P \\ PDL & P & & P & N & & & & P & P & P & P & P & P & P & P & P \\ LBU & N & P & N & N & P & P & N & N & N & N & N & N & N & N & N & N \\ WKKP & N & P & N & N & P & N & P & N & N & N & N & N & N & N & N & N \\ KP & P & P & N & P & P & N & P & P & N & N & P & N & P & P & P & P \\ MAZ & P & & P & P & & & P & N & P & P & P & P & P & P & P & P \\ LBL & P & & P & P & & & P & P & N & P & P & P & P & P & P \\ DSL & & & P & & & & P & P & N & P & P & P & P & P & P & P \\ OPO & P & & & P & & & P & P & N & P & P & P & P & P & P \\ LDZ & P & P & P & & & P & P & P & P & P & N & P & P & P & P & P \\ SL & P & P & P & & & P & & P & P & P & P & N & P & P & P & P \\ SW & P & P & P & & P & P & P & P & N & P & P & P & P & P & P \\ MLP & P & P & P & & P & P & P & P & P & P & P & P & N & P & P \\ PKR & P & P & P & P & P & P & P & P & P & P & P & P & P & P & N & P \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The necessary (N) and possible (P) efficiency preference relations for pairs of Polish vivodeships in the comprehensive analysis of the healthcare system. \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 & 0 & 0.594 & 0.144 & 0.095 & 0.072 & 0.065 & 0.028 & 0.002 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ POM & 0.577 & 0.303 & 0.120 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ WM & 0 & 0 & 0 & 0.029 & 0.192 & 0.210 & 0.191 & 0.183 & 0.103 & 0.042 & 0.030 & 0.020 & 0 & 0 & 0 & 0 \\ PDL & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.002 & 0.009 & 0.072 & 0.114 & 0.443 & 0.288 & 0.072 \\ LBU & 0.050 & 0.226 & 0.724 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ WLKP & 0.373 & 0.471 & 0.156 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ KP & 0 & 0 & 0 & 0.248 & 0.245 & 0.174 & 0.162 & 0.099 & 0.039 & 0.023 & 0.010 & 0 & 0 & 0 & 0 & 0 \\ MAZ & 0 & 0 & 0 & 0 & 0.101 & 0.161 & 0.215 & 0.171 & 0.220 & 0.096 & 0.033 & 0.003 & 0 & 0 & 0 & 0 \\ LBL & 0 & 0 & 0 & 0.033 & 0.084 & 0.151 & 0.149 & 0.158 & 0.256 & 0.104 & 0.044 & 0.017 & 0.004 & 0 & 0 & 0 \\ DSL & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.003 & 0.022 & 0.042 & 0.140 & 0.325 & 0.468 \\ OPO & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.001 & 0.017 & 0.217 & 0.311 & 0.453 \\ LDZ & 0 & 0 & 0 & 0 & 0.007 & 0.028 & 0.069 & 0.139 & 0.360 & 0.278 & 0.090 & 0.027 & 0.002 & 0 & 0 \\ SL & 0 & 0 & 0 & 0.007 & 0.010 & 0.028 & 0.032 & 0.041 & 0.120 & 0.150 & 0.184 & 0.335 & 0.068 & 0.022 & 0.003 \\ SW & 0 & 0 & 0 & 0.096 & 0.227 & 0.190 & 0.146 & 0.195 & 0.098 & 0.04 For pairs of vovodeships that are not related by the necessary preference, it is worth analyzing the pairwise efficiency outranking indices (see Table 5). For some, one province proves better for most scenarios (see, e.g., ZPM and PKR with \(PEOI^{I}(ZPM,PKR)=99.4\%\) or MAZ and MLP with \(PEOI^{I}(MAZ,MLP)=99.3\%\)). For other pairs, the shares of feasible scenarios confirming the preference in both directions are more balanced (see, e.g., MAZ and LBL with \(PEOI^{I}(MAZ,LBL)=53.4\%\) and \(PEOI^{I}(LBL,MAZ)=46.6\%\), or PKR and SL with \(PEOI^{I}(PKR,SL)=47.6\%\) and \(PEOI^{I}(SL,PKR)=52.4\%\)).