## 4 Two Real Case Studies
### The Second Case Study: Operations Strategies of Fars Province Pharmaceutical Distributing Companies
#### 4.2.2 The Main Results of Applying Extended RBA for the Second Case Study  
As described in Appendix A.2 (Appendix A.2), through applying the interactive algorithm for the second case study, non-radial FDH models 12, 13, non-radial FDH model 14 of step 1 of STEM (p = 1), and non-radial model 14 of step 2 of STEM (p = 1) should be solved 13, 11, 11, and 5 times, respectively. So, finding targets of 40 mixed 0-1 LP models were required. The target of these non-radial FDH models could be obtained using extended RBA through two target finding stages (Figure 2). In Appendix A.2, applying extended RBA for solving three of these non-radial FDH models (models 12-14 for DMU\({}_{05}\) of the second case study) are described. \begin{table}
\begin{tabular}{p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt}} \hline \hline \multirow{2}{*}{**DMU\({}_{o}\)**} & \multirow{2}{*}{**Member of M set**} & **Obtained Target by Solving of Step 1 of STEM Model** & **Obtained Target via DM’s** & **Obtaining DM’s Target** & **Related Interactive Stages of the Interactive Algorithm** & **Case** \\ \hline DMU\({}_{01}\) & \(\surd\) & - & - & - & As DMU was a member of M set, target was itself & 1 \\ \hline DMU\({}_{06}\) & \(\surd\) & & & & & \\ \hline DMU\({}_{02}\) & & & & & & \\ \hline DMU\({}_{03}\) & & & & & & \\ \hline DMU\({}_{05}\) & \(\times\) & DMU\({}_{01}\) & DMU\({}_{01}\) & \(\surd\) & The best compromise solution via DM’s opinions was found in step 1 or 2 of STEM & 2 \\ \hline DMU\({}_{09}\) & & & & & & \\ \hline DMU\({}_{11}\) & & & & & & \\ \hline DMU\({}_{12}\) & & & & & & \\ \hline DMU\({}_{04}\) & & & & & & \\ \hline DMU\({}_{08}\) & \(\times\) & DMU\({}_{01}\) & DMU\({}_{06}\) & \(\times\) & The best compromise solution was not found because there was only one similar unsatisfied objective function in the step 1 and first iteration of step 2 of STEM & 3 \\ \hline DMU\({}_{13}\) & & & & & & \\ \hline DMU\({}_{10}\) & \(\times\) & DMU\({}_{01}\) & DMU\({}_{06}\) & \(\times\) & Compromise solution was not found because calculating value of beta 1 (l = 1,..., 5) were not possible for the first cycle of step 2 of STEM & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: The brief of applying the interactive algorithm for finding DMU targets (the second case study). The detail results of applying extended RBA (Figure 2) to solve non-radial FDH models 12-14 for DMU\({}_{07}\) of the second case study (related non-radial FDH models in the interactive algorithm) are described in Appendix A.2 (Appendix A). Each target of model was found using two target finding stages for DMU\({}_{07}\) of the second case study considering related conditions. \(x_{i0}=x_{ij}\), \(i=1,\ \ldots,3\), and \(y_{ro}=y_{ij}\), \(s=1,\ 2\ (j=1,\ \ldots,\ 13)\) were firstly defined for DMU\({}_{0}=\) DMU\({}_{07}\). Applying extended RBA for non-radial FDH models 12 and 13 (Appendix A, Appendix A.2), showed that \(S_{step\ 0\ \text{of}\ \text{STEM}}=\{\text{DMU}_{01},\text{DMU}_{02},\text{DMU}_{05}, \text{DMU}_{06},\text{DMU}_{07}\}\) and some non-radial FDH models had alternative targets. Applying extended RBA for non-radial FDH model 14 (Appendix A, Appendix A.2), showed that \(S_{step\ 1\ \text{of}\ \text{STEM}}=\{\text{DMU}_{01},\text{DMU}_{02},\text{DMU}_{0 5},\text{DMU}_{06},\text{DMU}_{07}\}\) and DMU\({}_{01}\) was the only target (Table A9). By solving step 1 of the STEM model (non-radial FDH model 14), DMU\({}_{01}\) was obtained as the DMU\({}_{07}\) target (Appendix A, Table A10). However, the obtained target via [PERSON]'s opinions was DMU\({}_{06}\). A compromise solution was not found because no feasible integer solution could be found in the first iteration of step 2 of STEM. It is mentionable that the results obtained from solving of all non-radial FDH models 12-14 for the second case study DMU\({}_{07}\) using extended RBA were the same as the results obtained from solving of mentioned models using regular approaches.