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Explora: Environment
and Resource Evaluating agricultural efficiency and sustainability

evaluation. These studies provide substantial theoretical n
and practical support for promoting sustainable agricultural x s x 0
ii
development and optimizing resource utilization. i1
n
3. Model selection and variable selection y s y 0
ii

st.. i1 n (I)
3.1. DEA-BCC model i 1
The Charnes, Cooper, and Rhodes (CCR) model and the i1

BCC model are the primary divisions of the non-parametric i s , 0 s , 0 00
12 3,~,
analytical method, DEA. Charnes et al. introduced the i ,, n
16

CCR model, which was subsequently used by Banker et al.
20
to construct the BCC model. The fundamental principle where x and y denote the input and output variables,
i
i
of DEA is to determine the efficiency frontier by utilizing respectively, and γ , ϑ, s , and s denote the combination
+
−
i
specific input and output conditions, which represent the coefficients of the units, the efficiency evaluation index,
optimal production boundary for either cost minimization and the slack variables, respectively. In the context of Data
or output maximization. This frontier is used to assess the Envelopment Analysis (DEA), “s.t.” stands for “subject to,”
relative efficiency of decision-making units (DMUs). In which is used to introduce constraints in mathematical
this frontier, there are numerous DMUs that evaluate the models. The sentence describes the variables involved, such
efficacy of other DMUs in relation to the frontier. as input and output variables, combination coefficients,
The BCC model is a DEA model that is appropriate for efficiency evaluation index, and slack variables. A decision
examining the efficiency performance of decision units unit is considered DEA efficient when the efficiency
across various scales while accounting for scale effects. evaluation index equals one and both slack variables are
The efficiency frontier in this model is comprised of zero. If the efficiency index is less than one, the unit is
numerous decision units and is employed to evaluate the considered non-efficient. The decision unit is DEA efficient
+
-
relative technical efficiency (TE) of each decision unit. In when ϑ = 1 and s = s = 0, and non-efficient when ϑ <1.
particular, the BCC model assists us in comprehending the Second, for the sample set in Equation I with n
efficiency status of each decision unit in actual production decision units, each decision unit has m inputs and s
by calculating its TE, scale efficiency, and comprehensive outputs. Let Xi and Yi represent the input and output
efficiency. variables of the rth decision unit, respectively, as shown
The BCC model is implemented in this investigation in Equation II:
to measure the TE, scale efficiency [SE or k], and overall
efficiency [OE or θ] of agriculture in Shaanxi province, x x x, i 2 ,~, x T (II)

i
mi
i 1
using the DEAP2.1 software (The DEAP 2.1 software was y y y , ,~, y T

developed by the University of Maastricht, located in the i i 1 i 2 si
Netherlands). The precise formulas for these parameters where X and Y denote the input and output quantities.
are as follows: The weight vectors corresponding to the inputs and
ri
ji
• TE: quantifies the degree of rationality between inputs outputs are denoted by α and β, respectively, as shown in
and outputs. A value of 1 indicates that the TE has
achieved its maximum potential, while a value of 0 Equation III:
suggests that there is still space for improvement. T

• SE (k): a metric that assesses the logic of the input scale. , 2 ,~, 0 (III)
m
1

T
The scale is considered scale efficient when SE equals 1, , ,~, 0
and it is non-scale efficient when SE does not equal 1. 1i 2 s
• OE (θ): integrated TE, derived from TE × SE. A value The h represents the efficiency evaluation value for the
of 1 indicates that the decision unit is effective on kth decision unit, as expressed in Equation IV:
k
DEA, while a value of 0 indicates that it is effective on
non-DEA. T y k s y
h t 1 t k (IV)
3.1.1. Study of modeling equations k T x k m y
The model in this study uses the following linear i1 t k
programming equation (Equation I) for efficiency In the BCC model with constant returns to scale, the
calculations: ratio of the output β Y value to the input α X value of
Tk
Tk
Volume 2 Issue 1 (2025) 5 doi: 10.36922/eer.5129