*3.1. FECO Measurement Method*

#### 3.1.1. Super-Efficient DEA

Data envelopment analysis is a typical class of nonparametric analysis, referred to as DEA analysis, which was proposed by Charnes et al. [36]. They studied the optimization of resource allocation in the production process by evaluating the relative efficiency ratio of inputs and outputs within each decision unit. In the production process, the ratio between the input quantity of resource consumption and the output quantity of the product determines the production efficiency value within the decision unit, and the weighting of the input and output values can be used to analyze multiple input and output problems. For the study of green issues, in the process of constructing the DEA model, pollution factor indicators and negative ecological indicators can be classified as non-desired outputs, and the DEA model will be based on the "asymmetric" curve measurement of each type of output to accurately estimate the eco-economic efficiency value. The DEA model will accurately estimate the eco-economic efficiency values based on "asymmetric" curve measures for each type of output, and through projection analysis, ensure sufficient output and appropriate inputs while strictly controlling the amount of undesired output [37]. The estimation of desired and undesired outputs in the production process is achieved by means of the radial measure of the curve and the inverse of the curve measure, respectively. The DEA is the curve radial measure, without function expressions and without hypothesis testing [38].

#### 1. Introduction of CCR-DEA model

The CCR-DEA model was proposed by Charnes et al. [39]; it is an input-oriented DEA model. The CCR model is the most basic DEA model with *n* DMU (*i* = 1, 2, ... , *n*), which satisfies the assumption of homogeneity and are all comparable. Each DMU has the same *t* inputs, and the input vector is:

$$\mathbf{x}\_{i} = (\mathbf{x}\_{1i}, \mathbf{x}\_{2i}, \dots, \mathbf{x}\_{ti})^T, \mathbf{i} = \mathbf{1}, \mathbf{2}, \dots, \mathbf{n} \ . \tag{1}$$

Each DMU has the same s outputs, then there is an output vector of

$$y\_i = (y\_{1i}, y\_{2i}, \dots, y\_{si})^T, i = 1, 2, \dots, n,\tag{2}$$

i.e., each DMU has the same *t* inputs and s output types. Where *xji* denotes the input quantity of the *i*-th DMU to the *j*-th DMU, and *yji* denotes the output quantity of the i-th DMU to the *j*-th DMU. In order to integrate all the DMUs in a uniform way, each input and output needs to be assigned a value, so that the weight vectors of the input and output are

$$v = \begin{pmatrix} v\_1, v\_2, \dots, v\_{\hat{l}} \end{pmatrix}^T,\tag{3}$$

$$\boldsymbol{\mu} = (\boldsymbol{\mu}\_1, \boldsymbol{\mu}\_2, \dots, \boldsymbol{\mu}\_r)^T,\tag{4}$$

where *vj* denotes the *j*-th type of input weight and *ur* denotes the rth type of output weight. At this point, the combined value of the *i*-th decision unit input is ∑*<sup>t</sup> <sup>j</sup>*=<sup>1</sup> *vjxji*, and the combined value of the output is ∑*<sup>s</sup> <sup>r</sup>*=<sup>1</sup> *uryri*, so the efficiency evaluation index of each DMUi is defined as

$$\mathfrak{ht}\_{\dot{\mathfrak{i}}} = \frac{\sum\_{r=1}^{s} \mathfrak{u}\_{r} \mathfrak{y}\_{\dot{\mathfrak{i}}}}{\sum\_{j=1}^{t} \mathfrak{v}\_{j} \mathfrak{x}\_{ji}},\tag{5}$$

$$\begin{cases} \max \mathbf{h}\_{i0} = \frac{\sum\_{r=1}^{i} \boldsymbol{\mu}\_{r} \mathbf{y}\_{i0}}{\sum\_{j=1}^{i} \boldsymbol{\upsilon}\_{j} \mathbf{x}\_{j0}}\\ \frac{\sum\_{r=1}^{i} \boldsymbol{\mu}\_{r} \mathbf{y}\_{i\bar{r}}}{\sum\_{j=1}^{i} \boldsymbol{\upsilon}\_{j} \mathbf{x}\_{j\bar{r}}} \le 1, i = 1, 2, \dots, n\\ \quad \boldsymbol{\upsilon} = \left(\boldsymbol{\upsilon}\_{1}, \boldsymbol{\upsilon}\_{2}, \dots, \boldsymbol{\upsilon}\_{\bar{\jmath}}\right)^{T} \ge 0\\ \quad \boldsymbol{\mu} = \left(\boldsymbol{\mu}\_{1}, \boldsymbol{\mu}\_{2}, \dots, \boldsymbol{\mu}\_{\bar{\jmath}}\right)^{T} \ge 0 \end{cases} \tag{6}$$
