## 3 Research Methods
### Data Envelopment Analysis--BCC Model and Super-Efficiency SBM Model  
When used for efficiency analysis, the DEA method includes several classic models such as BCC, CCR, FG, and ST. Among them, the BCC model and the CCR model are the most commonly used. The BCC model was proposed by [PERSON], [PERSON], and [PERSON] in 1984. The BCC model is not strict on the assumption of constant scale return but adopts a dynamic scale return form. The result is the Crste of each decision unit (DMU). DMU is the abbreviation for decision-making unit, referring to the object being evaluated in the DEA model. Crste, Vrste, and Scale are three key indicators in the Data Envelopment Analysis (DEA) model. Crste stands for Constant Returns to Scale Technical Efficiency, Vrste stands for Variable Returns to Scale Technical Efficiency, and Scale stands for scale  
Figure 2: Diagram of the research framework.  
efficiency. These indicators are used to evaluate the efficiency performance of DMU. The mathematical model of BCC is expressed in Equation (1).  
\[\left\{\begin{array}{c}\min\left[\theta-\varepsilon\big{(}e_{m}^{T}S^{-}+e_{S}^ {T}S^{+}\big{)}\right]\\ \sum_{i=1}^{n}X_{i}\dot{\Lambda}_{i}+S^{-}=\theta X_{0}\\ \sum_{i=1}^{n}Y_{i}\dot{\Lambda}_{i}-S^{+}=Y_{0}\\ \sum_{i=1}^{n}\dot{\Lambda}_{i}=1\\ S^{+}\geq 0,S^{-}\geq 0,\dot{\Lambda}_{i}\geq 0,i=1,2,\ldots,n\end{array}\right. \tag{1}\]  
where \(\theta\) is the efficiency index of DMU, \(\dot{\Lambda}\) represents the weight, and \(\varepsilon\) is a non-Archimedean infinitesimal quantity greater than zero. Here, \(e_{m}^{T}=(1,\,1,\,\ldots,\,1)\)\(TeE^{m}\), \(e_{S}^{T}=(1,\,1,\,\ldots,\,1)\)\(TeE^{s}\), and \(S^{+}\) are input slack variables and output slack variables, which represent input redundancy and output deficiency, respectively. DMU\(i_{0}\) is valid when \(\theta_{0}=1\) and \(S^{-}=S^{+}\). When \(\theta_{0}<1\) and at least one of \(S^{-0}\) or \(S^{+0}\) is not 0, DMU\(i_{0}\) is invalid.  
The analysis results of the data envelopment model typically have multiple DMUs with a computational efficiency value of 1. In other words, there are relatively more efficient DMUs. Under this premise, it is impossible to judge the medium-efficiency difference and score ordering of these efficient DMUs. Therefore, some scholars have made new assumptions about the judgment range of the efficiency value. Specifically, the efficiency value can be greater than or equal to 1 and is termed super-efficient. In addition, [PERSON] has solved the problem of how to sort the decision-making target units when the efficiency result value is greater than 1. Specifically, a super-efficiency SBM model was proposed based on the BCC model. Under conditions of an unchanged Vrste, the SBM super-efficiency model is shown in Equation (2).  
\[\left\{\begin{array}{c}\min\left[\theta-\varepsilon\big{(}e_{m}^{T}S^{-}+e_ {S}^{T}S^{+}\big{)}\right]\\ \sum_{i=1,j\
eq i_{0}}^{n}\dot{\Lambda}_{i}+S^{-}=\theta X_{0}\\ \sum_{i=1,j\
eq i_{0}}^{n}Y_{i}\dot{\Lambda}_{i}-S^{+}=Y_{0}\\ S^{+}\geq 0,S^{-}\geq 0,\dot{\Lambda}_{i}\geq 0,i=1,2,\ldots,n\end{array}\right. \tag{2}\]  
In the above formula, the meanings of the symbols are the same as those for the BCC model. Under the super-efficiency model, when \(\theta_{0}\geq 1\) and \(S^{-0}\) or \(S^{+0}=0\), DMU\(i_{0}\) is considered DEA efficient. DMU\(i_{0}\) is considered DEA inefficient when \(\theta_{0}<1\).