## 3 A New Hybrid Technique for Finding DMU Targets in Non-Radial FHD Models
### The Interactive Algorithm  
In this section, an algorithm is proposed to find DMU targets in non-radial FDH models. The interactive algorithm (the first part of proposed hybrid technique) contains two interactive stages. The purpose of the first interactive stage is to determine efficient DMUs and their targets. The second interactive stage determines the target of other DMUs using STEM. DMU targets are found through solving three non-radial FDH models in interactive algorithm. Applied models are obtained based on ASBM. Classical DEA models have been created based on decreasing inputs and increasing outputs. Moreover, only one variable has been defined for decreasing all inputs and only one another variable has been defined for increasing all outputs in classical radial models. However, in non-radial classical models, different variables have been defined separately for decreasing each input, and different variables have been defined separately for increasing different outputs. In addition, all DMUs in the research area should be considered, and the relationship \(n\geq 3(m+s)\) existes between the number of DMUs (n), number of inputs (m), and number of outputs (s) parameters. In this regard, the main improvements that are obtained from solving DEA models relates to non-efficient DMUs. Therefore, decreasing the number of DMUs may increase the number of efficient DMUs [38]. In DEA models, choosing appropriate inputs and outputs is an important step which may significantly affect the efficient frontier. In this regard, inputs and outputs should be relevant to the research area, gathering related data for DMUs should be possible, and experts should confirm them. It is considerable that using real data is preferred rather than gathering from experts' opinions. However, if gathering real data is not impossible, experts' judgment is used. In this situation, experts should have enough information about the problem. As classical DEA models are created based on decreasing inputs and increasing outputs, this subject should be considered for selecting inputs and outputs as well. Moreover, all DMUs in the research area should be considered, and the establishment of the relationship \(n\geq 3(m+s)\) between inputs, outputs, and DMU numbers is recommended. As a matter of fact, in situations where \(n<3(m+s)\), the number of efficient DMUs may be increased. Therefore, a set of non-duplicated DMUj, j = 1,..., n, that utilizes m positive inputs, \(x_{ij}\), i = 1,..., m, to produce s positive outputs, \(y_{ij}\), r = 1,..., s, are considered. Moreover, objective functions \(e_{i}\), l = 1,..., m + s, and decision making variables, \(u_{v}\), \(v\) = 1,..., n + m + s are defined as  
\((e_{1}(u),\ldots,e_{m}(u),e_{m+1}(u),\ldots,e_{m+s}(u))=\)  
and \((u_{1}\),..., \(u_{n}\), \(u_{n+1}\),..., \(u_{n+m}\), \(u_{n+m+1}\),..., \(u_{n+m+s})=(\lambda_{1}\),..., \(\lambda_{n}\),s\({}_{1}\),..., s\({}_{m}\), t\({}_{s}\)), respectively. \[\text{u}\in\text{s}=\left\{\text{u}\left| \begin{array}{c}\sum_{j=1}^{n}\lambda_{j }=1,\,\lambda_{j}\in\{0,1\},\,j=1\ldots\text{n},\\ \sum_{j=1}^{n}\lambda_{j}x_{ij}\leq\theta_{i}x_{\text{io}},\,0\leq\theta_{i} \leq 1,\,i=1\ldots\text{m},\\ \sum_{j=1}^{n}\lambda_{j}y_{ij}\geq\varphi_{i}y_{\text{ro}},\varphi_{\text{r}} \geq 1,\,r=1\ldots\text{s}.\end{array} \right.\right\}.\]  
After the solving of non-radial model 12 for DMU\({}_{j}\); \(j=1,\,\ldots,\,n\), M (the members of M set are DMUs that lay on the efficient frontier) and M\({}^{\prime}\) sets (the process of targets determination of M\({}^{\prime}\) set members should be carried out through the second interactive stage of the interactive algorithm) are defined as \(\text{M}=\left\{\text{DMU}_{j}\middle|Z_{j}^{\text{o}}=0,\,\forall j\right\}\) and \(\text{M}^{\prime}=\left\{\text{DMU}_{j}\middle|\text{DMU}_{j}\
otin\text{M}, \,\,\forall j\right\}\), respectively. It is considerable that DMU\({}_{j}\); \(j=1,\,\ldots,n\) of non-radial model 12 is efficient if \(Z_{j}^{\text{o}}=0\).