## 3 Proposed Techniques
### Performance Assessment  
Data envelopment analysis (DEA) is one of the most classic techniques used to measure operational efficiencies among the so-called DMUs (decision management units). There are two common measures [27]: one is BCC (Banker, Charnes, Cooper) and the other is CCR (Charnes, Cooper, Rhodes). The selection of input and output variables is critical to the efficiency measures and relative performances of the DMUs. Mathematically, operational efficiency for a specific DMU can be expressed as follows:  
\[Max\quad\eta_{k}=\frac{\sum u_{k}v_{k}}{\sum_{i}v_{i}x_{ik}+v_{k}},\ \textit{subject to}\ \eta_{k}\leq 1,v_{i},u_{r}\geq\varepsilon,\forall i,r, \tag{17}\]  
\begin{table}
\begin{tabular}{c c c} \hline \(c_{1},c_{2}\) & **Relationship** & **Explanation** \\ \hline +, + & Pure competition & Both suffer from each other’s existence \\ +, - & Predator-prey & Entity 1 serves as direct food to entity 2 \\ \(-\), - & Mutualism & The case of symbiosis (win-win) \\ +, 0 & Amensalism & Entity 1 suffers from the existence of entity 2, who is impervious to what is happening \\ \(-\), 0 & Commensalism & Entity 1 benefits from the existence of entity 2, who \\  & & nevertheless remains unaffected \\
0, 0 & Neutralism & No interaction between each other \\ \hline \end{tabular}
\end{table}
Table 2: Relationship description according to the signs of interaction parameters.  
where \(v_{i}\) and \(u_{r}\) are the weights of the input (\(x_{ik}\)) and output (\(y_{rk}\)) variables, \(\varepsilon\) is called non-Archimedean small number, an extremely small positive value that is usually represented by \(10^{-6}\), and \(i\), \(r\), and \(k\), respectively, represent indices for input, output, and DMU. The parameter \(v_{ko}\) is used to control variable returns to scale (VRS) in BCC or constant returns to scale (CRS) in CCR (\(v_{ko}=0\)). For the input-oriented DEA, CCR can be replaced by solving the following formula [28,30]:  
\(Max\quad\sum_{r}u_{r}y_{rk}\), subject to \(\sum_{i}v_{i}x_{ik}=1\), \(\eta_{k}\leq 1\), \(v_{i}\), \(u_{r}\geq\varepsilon\), \(\forall i,r\). Based on dual theorem in linear programming, the dual form can be solved as follows:  
\[\begin{array}{l}Min\ \eta_{k}=\theta-\varepsilon[\sum_{i}s_{ik}{{}^{-}}+\sum_{r}s _{rk}{{}^{+}}]\,\ subject\ to\ \eta_{k}s_{ik}{{}^{-}},s_{rk}{{}^{+}}\geq 0,\forall i,r\\ \sum_{k}\lambda_{k}x_{ik}-\theta x_{ik}+s_{ik}{{}^{-}}=0,\ \sum_{k}\lambda_{k}y_{rk}-s_{rk}{{}^{+}}=y_{rk},\ s_{ik}{{}^{-}},\ s_{rk}{{}^{+}},\ \lambda_{k}\geq 0,\end{array} \tag{18}\]  
where \(s_{ik}{{}^{-}}\) and \(s_{rk}{{}^{+}}\) represent the slack (input excess) and the surplus (output shortfall), and \(\theta\) is a constant ratio of the reduction of input variables used for achieving an efficient DMU.  
The main differences between CCR and BCC are VRS or CRS. In simple words, CCR derives operational efficiency (OE) defined by the weighted output over the weighted input. To improve the CRS assumption in CCR, BCC separates OE into two multiplicative parts: scale efficiency (SE) and technical efficiency (TE). Scale efficiency is the ratio of existing inputs (or outputs) of DMUs to the inputs (or outputs) of optimal production scale. Specifically, \(\sum_{k}\lambda_{k}\) can be used to justify the trends of returns to scale: \(\sum_{k}\lambda_{k}<1\) means increasing returns to scale (IRS), \(\sum_{k}\lambda_{k}=1\) means constant returns to scale (CRS), and \(\sum_{k}\lambda_{k}>1\) indicates decreasing returns to scale (DRS). If a DMU achieves Pareto efficiency, \(\eta_{k}=1\), it means no adjustment is required (\(s_{ik}{{}^{-}}=s_{rk}{{}^{+}}=0\)). Otherwise, the required adjustments for an inefficient DMU (\(\eta_{k}<1\)) are \(x_{ik}{{}^{*}}=\theta x_{ik}-s_{ik}{{}^{-}},y_{rk}{{}^{*}}=y_{rk}+s_{rk}{{}^{+}}\), where \(x_{ik}\) (\(x_{ik}{{}^{*}}\)) and \(y_{rk}\) (\(y_{rk}{{}^{*}}\)) are the input and output variables before (after) adjustment; \(s_{ik}{{}^{-}}\) and \(s_{rk}{{}^{+}}\) are the desired adjustments.