Ecological efficiency evaluation based on data envelopment analysis and a dual-objective model

Abstract

At present, for ecological efficiency evaluation, the traditional data envelopment analysis has the problem that the same model is difficult to take into account different proportions of economic and environmental efficiency analysis. This study innovatively proposes a dual-objective data envelopment analysis (DEA) ecological efficiency model that combines environmental efficiency and economic efficiency. This method is based on data inclusion analysis and addresses the limitations of traditional data envelopment analysis (DEA) in balancing economic and environmental efficiency ratios. The results showed that, compared to traditional methods, the new method considered cities with lower ecological efficiency more comprehensively. This was because it incorporated unexpected outputs, such as carbon emissions, and dynamic weight allocation. The provincial ENE was about 0.55 (new method), lower than the traditional data envelopment analysis’s 0.6, reflecting a more rigorous assessment of the model’s environmental impact. The environmental efficiency of a province was about 0.55, while the environmental efficiency of cities in the eastern, central, and western regions was about 0.75, 0.42, and 0.42, respectively. The environmental efficiency of cities in the north and south regions was around 0.35 and 0.73, respectively. The economic efficiency of the whole province was around 0.97, and the economic efficiency of the cities in the east, center, and west regions was around 0.99, 0.98, and 0.95, respectively, which were all higher than 0.95 and above. It demonstrated that the economic efficiency of the cities in the east, center and west regions was higher. The economic efficiency of cities in the north and south regions was around 0.965 and 0.995, respectively, and the economic efficiency of the province was higher at around 0.977. The ecological efficiency of the whole province was around 0.52. The ecological efficiency of cities in the east, center, and west regions was around 0.72, 0.41, and 0.42, respectively. The ecological efficiency of cities in the north and south regions was around 0.38 and 0.73, respectively. From 2020 to 2024, the changes in ecological efficiency in the province were more stable. The economic efficiency of all cities in the period from 2018 to 2020 was generally high, and some cities even reached a perfect score. It shows that the study proposes that the method can provide a new research idea for cracking the contradiction between resource environment and regional development.

Keywords

DEA model ecological efficiency evaluation data envelopment analysis economic efficiency environmental efficiency

Introduction

Ecological efficiency (ECE) is the ratio relationship between the environmental impact of a product system and the value of the system. It not only focuses on the efficiency of resource utilization, but also includes aspects such as greenhouse gas and pollutant emissions and resource consumption.¹ The goal of ECE evaluation is to maximize a product system’s performance value, including resource, production, delivery, and usage efficiency, as a quantitative management tool to lessen total environmental impacts.² Productivity increased during the industrial revolution. However, significant resource and ecological issues accompanied industrialization.³ Green tech innovation has arisen to achieve sustainable socio-economic growth. In this regard, determining the best way to gauge the effectiveness of green technology innovation in Chinese industrial firms is a crucial area of study. Chen W et al. created an evaluation index system with non-desired outputs (NDOs) and separated innovation efforts into two stages based on the innovation value chain. The findings proved that the efficiency gap was evident in various Chinese locations and that the outcomes transformation stage was more efficient than the technology development stage.⁴ Ren et al. proposed a matrix network method based on the global data envelopment analysis (DEA) framework, which can evaluate the efficiency of composite systems and subsystems, avoiding treating decision units (DMUs) as “black boxes.” The efficiency values were analyzed through various convergence tests. The empirical results indicated that the overall and regional eco-economic efficiency was low, and the eastern subsystem was leading. The center was economically and socially efficient but ecologically inefficient, and the opposite was true for the west. Overall and social efficiencies diverged and economic and ecological efficiencies stabilized.⁵ Network DEA unfolding is based on DMU internal structure simulation, which evaluates the effectiveness of systems with intricate internal structures. Based on pre-existing modeling assumptions in network DEA, You-Wei X et al. suggested a hybrid multi-period DEA model with feedback with the goal of exposing the internal structure of DMU systems and offering a cross-sectional evaluation of changes in DMU efficiency over time. The study proposed a binary heuristic algorithm to reduce the solution time complexity and maintain high accuracy, and proved its correctness and feasibility through research. Several comparative experiments verified the advantages of the model.⁶ In the minority areas of Yunnan, China, the ecological environment is fragile and the socio-economic development is insufficient. The study of the evolution of human-land systems can offer scientific direction for resolving the conflict between socio-economic development and environmental preservation as well as for fostering high-quality regional development. Tai L et al. developed an evaluation model using DEA based on the structure of the human-land system in order to examine the system’s evolution and the elements that have influenced it in Yunnan’s minority areas. From 1995 to 2020, the degree of coordinated development of the system increased, but the number of DEA failure areas increased after 2007, showing that the high input and high consumption pattern remained unchanged. The industrial waste utilization rate, total foreign trade, and urbanization rate were found to have a large impact on the efficiency of coordinated system development.⁷

To analyze the evolution of resource ECE and the pattern of heterogeneity in China, Tang et al. measured ECE from 2004 to 2017 and analyzed its evolution through the super-efficiency DEA model using resource cycle data from 26 provinces and municipalities. The results revealed that the ECE increased year by year, with an average annual increase of 1.5%, from inland to coastal growth. Although there was a strong correlation and clustering of ECE among provinces, the overall correlation was reduced by the radiation effect of high-level provinces. Regional differentiation in China decreased and spatial heterogeneity eased, but was offset by increased heterogeneity in the southwest.⁸ To more precisely evaluate ECE, Zhou et al. presented a novel DEA model that incorporates geographical interactions among DMUs and calculates the relative prices of all variables. The study proposed a model that included spatial correlations and addressed the interdependencies that were often neglected in traditional DEA models.⁹ Zhang et al. employed a system dynamics model to simulate the trend of environmental footprint evolution under various policy scenarios in an attempt to investigate regional variations in the ECE of maritime rangelands and provide countermeasures for sustainable development. The results showed that the ecological footprints of marine pastures were unbalanced at both the marine and provincial levels.¹⁰ Mariculture occupied an important position in the development of fisheries in Weihai City, and its ecological benefits directly affected the sustainable development of regional fisheries. Wu et al. used a three-stage DEA model as a non-expected output model to systematically evaluate the ECE of marine aquaculture in Weihai City. The findings demonstrated that environmental factors such government assistance, the degree of urbanization, and the amount of regional economic development all contributed to the overall ECE of marine aquaculture in Weihai City.¹¹

In summary, researchers have studied the evaluation index system, the DEA model, the model of spatial correlation, and the three-stage DEA model for ECE analysis. However, the application of ECE evaluation is not deep enough. Traditional DEA models have a key limitation in that they struggle to balance the proportional analysis of economic and environmental efficiency (ENE) within the same framework and are often viewed as independent objectives. This study innovatively constructs a dual-objective DEA model that integrates ENE and EE through a dynamic weight allocation mechanism. Unlike existing dual-objective studies, this model emphasizes real-time adjustments based on regional development priorities. Thus, the study suggests an ECE evaluation method based on the DEA model in an attempt to evaluate the ECE of various locations under the specified criteria of resource consumption, economic development, and environmental quality. The method innovatively combines ENE and economic efficiency (EE) to construct a dual-objective ECE model to evaluate and analyze the ECE of a certain province, which provides a technical basis for the effective utilization of resources.

This study’s article structure is as follows: The first section focuses on the process of ECE evaluation based on DEA model designed in this research. The second section describes the experimental validation based on the algorithm designed in the first section and analyzes the outcomes of the experimental data. Conclusions regarding the experimental results are made in the third section, which also outlines the design’s flaws and future development directions.

Methods and materials

The study proposes an ECE evaluation based on DEA modeling. Firstly, the DEA analysis in ECE evaluation is investigated. Second, an ECE evaluation model combining the integrated DEA model is proposed. A dual-objective ECE model combining ENE and EE is further proposed.

DEA studies in ECE evaluation

ECE evaluation refers to the quantitative analysis of the relationship between the environmental impacts and the economic value of products and services in an attempt to assess their performance in terms of environmental friendliness and EE.¹² ECE is centered on optimizing resource use, reducing environmental impacts and increasing the market value of a product or service. ECE describes the extent to which production activities create economic benefits while negatively impacting the environment.¹³ By improving ECE, both economic and environmental benefits can be realized. Therefore, ECE evaluation has become one of the hot spots of current research. As illustrated in Figure 1, the ECE evaluation process primarily consists of the following steps.

Figure 1.

ECE evaluation process.

The most effective method for conducting ECE evaluation is the DEA technique. By specifically taking into account the usage of various inputs (i.e., resources) and the production of multiple outputs (i.e., services), DEA is a strategy that may be used to assess the efficiency of multiple service units offering similar services.^14,15 By comparing DMUs using the same production method, the DEA approach’s core goal is to create an efficient production frontier. The efficiency values of all production units are measured relative to this frontier surface. Points located on the frontier surface are considered efficient, while points located in the upper-right region of the frontier surface have room to improve efficiency by reducing inputs.^16,17 DEA is a non-parametric method for evaluating efficiency in ECE evaluation. Its basic principle is to assess the relative efficiency level of each DMU by comparing its input indicator (InI) and output indicator (OI). In DEA, each DMU is regarded as a producer that produces a corresponding amount of output by consuming a certain amount of input. The goal of efficiency evaluation is to find those DMUs that can realize the maximum output under the given input conditions, which are called “efficient frontiers.”¹⁸ Figure 2 depicts the DEA analysis procedure.

Figure 2.

DEA analysis process.

In Figure 2, the evaluation target is determined first. Then the corresponding DMU is selected to construct the input-output index system. After selecting the DEA model, the DEA evaluation is carried out to determine whether the result is satisfactory or not. If unsatisfactory, the InI and OI are adjusted, the DEA model is selected again, and the operation is repeated until it is satisfactory. Then the evaluation results are analyzed and finished. The DMUs are set up to have n, and the input and output vector expressions are shown in equation (1).

{\begin{cases} x_{j} = {(x_{1 j}, x_{2 j}, \dots, x_{m j})}^{T} > 0 j = 1, 2, \dots, n \\ y_{j} = {(y_{1 j}, y_{2 j}, \dots, y_{m j})}^{T} > 0 j = 1, 2, \dots, n \end{cases}

(1)

In equation (1), $x_{i j}$ is greater than 0. Among them, i = 1, 2, ... , m. r = 1, 2, ... , s. Each DMU has m inputs and s outputs. $x_{i j}$ denotes the input of the $i$ th input of the $j$ th DMU. $x_{r j}$ denotes the amount of outputs of the $r$ th kind of the $j$ th DMU.

The Charnes-Cooper-Rhodes (CCR) model and the Banker-Charnes-Cooper (BCC) model are the two primary models for DEA. The basic idea of the CCR model is to find an optimal weight vector that allows all DMUs to achieve the maximum level of efficiency under given input and output conditions. The BCC model takes into account the variable scale efficiency, which is in line with the practical situation. Equation (2) illustrates how the study builds the CCR model using the efficiency index, or DMU goal function, as a constraint.

\min θ : s . t . {\begin{cases} \sum_{j = 1}^{n} x_{j} λ_{j} \leq θ x_{0} \\ \sum_{j = 1}^{n} y_{j} λ_{j} \geq y_{0} \\ λ_{j} \geq 0 \\ j = 1, 2, \dots, n \end{cases}

(2)

In equation (2), $λ_{j}$ and $θ$ denote the parameters. $j_{0}$ denotes the efficiency index of the first DMU. After that, the study uses DEA window (DEAW) analysis to analyze the ECE evaluation. DEAW analysis is a dynamic evaluation method. Based on the traditional DEA model, it evaluates the efficiency of DMUs over multiple time periods by introducing the concept of time windows. It allows the efficiency of DMUs to be analyzed dynamically in different time windows, thus better reflecting the change trend of DMU efficiency. Figure 3 indicates the primary steps.

Figure 3.

DEAW analysis.

In Figure 3, the InI and OI are first determined, and representative InI and OI are selected according to the research purpose and actual situation. According to the research needs, the appropriate length and number of time windows are set. The length of the time window can be determined according to the actual situation of the DMU and the purpose of the study. The input-output data of DMUs within different time windows are collected. Within each time window, the DMU is analyzed by DEA and its efficiency value is calculated. Finally, the efficiency values within different time windows are compared to analyze the trend of DMU efficiency.

Modeling of ECE evaluation combined with integrated DEA modeling

Traditional DEA suffers from the problem that the same model is difficult to take into account different proportions of economic and ENE analysis. The DEA model has significant advantages in ECE evaluation and can automatically assign optimal weights to multiple inputs and outputs. This avoids the subjective influence of human-determined weights, eliminates the need to standardize measurement units, and simplifies the evaluation process. In addition, the DEA model has high sensitivity and reliability, which can sensitively reflect the changes in the efficiency of DMUs, and the evaluation results have high credibility.^19,20 An example of DEA analysis is shown in Figure 4.

Figure 4.

DEA analysis example.

In Figure 4, (x)1 and (x)2 denote OI of equal size, and the OI is y. A, B, C, and D are the DMUs of four production possible set conditions. Points A, B, and C are connected to get a production frontier consisting of some DMUs. However, the traditional DEA in ECE evaluation has the problem that the same model is difficult to take into account different proportions of economic and ENE analysis. Therefore, the study constructs an integrated DEA model that combines environmental DEA with linearized simplicity using the transformation method. First, the study is set in the space of ECE evaluation. The input is $x_{i j} (i = 1, . . ., m)$ , the desired output (DO) is $y_{i r} (r = 1, . . ., s)$ , and the NDO is $x_{i j} (i = 1, . . ., m)$ . The possible set of outputs is shown in equation (3).

P o s s i b i l i t y (x) = {(y, z) : x o u t p u t (y, z)}

(3)

In equation (3), $P o s s i b i l i t y (x)$ denotes the output possible set. There are n DMUs in the output, and the evaluation corresponds to one DMU at a time. The environmental DEA technique is expressed as shown in equation (4).

\begin{array}{l} P o s s i b i l i t y (x) = {(y, z) : \\ \sum_{j = 1}^{n} λ_{j} x_{i j} \leq x_{i j 0}, i = 1, \dots, m \\ \sum_{j = 1}^{n} λ_{j} y_{r j} \geq y_{r j 0}, r = 1, \dots, s \\ \sum_{j = 1}^{n} λ_{j} z_{t j} = z_{t j 0}, t = 1, \dots, k \\ λ_{j} \geq 0, j = 1, \dots, n} \end{array}

(4)

In equation (4), $λ_{j}$ denotes the intensity variable. The directional distance function is the foundation upon which the conventional ECE model is built. The function expression is shown in equation (5).

{\vec{D}}_{directivity} (x, y, z; 0, y, z) = \max {θ : ((1 + θ) y, (1 - θ) z) \in P (x)}

(5)

In equation (5), ${\vec{D}}_{directivity} (x, y, z; 0, y, z)$ denotes the input-oriented function. At this point, the set of output possibilities is shown in equation (6).

T = {(x, y) : x output y}

(6)

In equation (6),

T

denotes the output possible set. The study sets the standard efficiency function as shown in equation (7).

S = {\begin{cases} 1 - {\vec{D}}_{directivity} (x, y; x, 0) \\ \frac{1}{1 + {\vec{D}}_{directivity} (x, y; 0, y)} \end{cases}

(7)

In equation (7), ${\vec{D}}_{directivity} (x, y; x, 0) \in [0, 1)$ , ${\vec{D}}_{directivity} (x, y; 0, y) \in [0, + \infty)$ . The larger this function is, the greater the efficiency. Pollutant output is also a factor to be considered in ECE evaluation, that is, ENE. The expression is shown in equation (8).

E = \min (1 - β)

(8)

In equation (8), $E$ represents ENE. When the DO increases, the objective function sets the EE, as shown in equation (9).

C = \min \frac{1}{1 + α}

(9)

In equation (9), $C$ represents EE. When considering both ENE and EE, the ability to evaluate desired and NDOs using ECE is shown in equation (10).

E C = 1 - {\vec{D}}_{directivity} (x, y, z; 0, y, z) = \min (1 - θ_{o})

(10)

In equation (10), $E C$ represents the integrated ECE. Since each efficiency evaluation corresponds to one DMU when considering environmental and EE, it is not possible to realize different DOs, NDO in the same model. Therefore, the study sets the variables to indicate the proportion of desired and NDOs that can be increased and decreased.²¹ The resulting ENE and EE objective function is described as shown in equation (11).

{\begin{cases} \min \frac{\sum_{t = 1}^{k} (1 - θ_{t})}{k} \\ \max \frac{\sum_{r = 1}^{s} (1 + θ_{r})}{s} \end{cases}

(11)

In equation (11), $θ_{r}$ and $θ_{t}$ denote the proportion of DO, NDO that can be increased. The integration obtains the comprehensive DEA model, as shown in equation (12).

E C = \min \frac{s}{\sum_{r = 1}^{x} (1 + θ_{r})} \times \frac{\sum_{i = 1}^{k} (1 - θ_{t})}{k}

(12)

The ECE objective function consists of a public integration of environmental and EE, as shown in equation (13).

{\begin{cases} C = s / (\sum_{r = 1}^{s} (1 + θ_{r})) \\ E = (\sum_{t = 1}^{k} (1 - θ_{t})) / k \\ E C = C \times E \end{cases}

(13)

In practical production processes, it is generally expected to achieve maximum DO and minimum NDO with constant input.^22,23 Therefore, the study further constructs a bi-objective CCR model. The optimization objectives such as DO and NDO are expressed as shown in equation (14).

\max \sum_{r = 1}^{s} α_{r}; \min \sum_{t = 1}^{k} β_{t}

(14)

In equation (14), $α_{r}$ denotes the DO efficiency value. $β_{t}$ denotes the NDO efficiency value. $λ_{j}$ denotes the weight of the input combination. In case of single objective, the study is processed using a linear weighted sum. The weights are assigned according to the importance of the objectives and this is converted to a single objective model as shown in equation (15).

\max h_{0} = \sum_{r = 1}^{s} μ_{r} α_{r} - \sum_{t = 1}^{k} ω_{t} β_{t}

(15)

In equation (15),

ω_{t}

is the prioritization degree of the NDO of the

t

th item.

μ_{r}

denotes the importance degree of the

r

th item DO.

h_{0}

denotes the efficiency value of the

j_{0}

th DMU after integrating the desired and NDOs.^24,25 The study constructs ECE evaluation system. Table 1 displays the InI and OI.

Table 1.

ECE evaluation system indicators.

Serial number	Indicator type	Index	Unit	Standardization method
1	Input indicators	Total energy consumption	10,000 tce	Min-Max normalization
2	Desired output	GDP	100 million CNY	Log transformation
3	Unexpected output	SO2 emissions	10,000 t	Z-score standardization
4	Unexpected output	Nitrogen oxide emissions	10,000 t	Z-score standardization
5	Unexpected output	Carbon emissions	10,000 t	Min-Max normalization
6	Environmental input	Resource recycling rate	%	Direct use (dimensionless)

In Table 1, the desired input variables for the study are total energy consumption and national labor force. The DO is gross domestic product, and the NDOs are SO₂ emissions and NOx emissions. The study will synthesize ECE evaluation to construct the corresponding system. The structure is shown in Figure 5.

Figure 5.

Corresponding system for comprehensive ECE evaluation.

In Figure 5, the visualized evaluation of ECE is divided into evaluation by region, year, average efficiency of each region, and indicator system. Evaluation by region and evaluation by region both require ENE evaluation and EE evaluation. Evaluation by year is to evaluate the efficiency of each region in a certain year as well as the cross-sectional comparison of each year in a region.

Results

To validate the proposed ECE evaluation method based on DEA modeling, an experiment is conducted to validate it. The corresponding design parameters and experimental data results are analyzed to verify the advantages and feasibility of the methodology and provide a reference for ECE evaluation.

DEA validation experiments in ECE evaluation

This study presents a comprehensive analysis of ECE evaluation experiments for cities in a province by selecting regional distributions in the east, center, west, north and south as well as the province as a whole. The figure shows the E1 (ENE) and C1 (EE) of different regions of the province as well as the whole province under the traditional method. Among them, Cities 1–3 are the main representative cities in the east, center, and west directions, respectively. Cities 4 and 5 are the main representative cities in the north and south directions, respectively. In Figure 6(a), the EI of the whole province is around 0.6. Among them, the E1 of City 1 is larger than the E1 of the province, which is around 0.83. The E1 of Cities 2 and 3 are smaller than the E1 of the province at around 0.45 and 0.5, respectively. In Figure 6(b), Cities 4 and 5 are smaller and larger than the E1 of the province at around 0.43 and 0.78, respectively. In Figure 6(c), the C1 of the province varies in the range of about 0.85–0.925. Among them, the C1 of City 1 is always larger than the C1 of the province, reaching a maximum of 1.00 in 2024. The C1 of City 3 is always smaller than the C1 of the province, varying around 0.80–0.81. City 2’s C1 varied similarly to the province’s C1. In Figure 6(d), the C1 of Cities 4 and 5 are similarly smaller and larger than the C1 of the province, respectively, at around 0.42 and 0.95. In summary, from 2018 to 2024, under the traditional ECE analysis method, the E1 and C1 of most cities are in a slightly improving trend.

Figure 6.

Under traditional methods, the E1 (ENE) and C1 (EE) of different regions and the entire province.

Figure 7 shows the ECE of different regions of the province as well as the province as a whole under the traditional method, synthesizing the ENE and EE. In Figure 7(a), the ECE for City 1 and the province is always greater than 0.8, indicating higher ECE. Its ECE for City 3 is around 0.73, which is less ecologically efficient. In Figure 7(b), the ECE of Cities 4 and 5 is in a stable or increasing trend from 2020 to 2024. Among them, the ECE of City 5 is around 0.98, with good ECE. In conclusion, under the traditional ECE analysis method, the ECE of City 1 and City 5 is better, and the ECE of the province is higher.

Figure 7.

ECE of different regions and the entire province under traditional methods.

Measurement statistics and analysis of ECE evaluation results

Figure 8 shows the E2 (ENE) and C2 (EE) of the different regions of the province as well as the province as a whole under the comprehensive efficiency analysis of the study. In Figure 8(a), the E2 of the province is around 0.55, and the E2 of Cities 1, 2 and 3 are around 0.75, 0.42, and 0.42, respectively. Compared with the traditional method, the research method comprehensively considers the smaller eco-efficient cities. In Figure 8(b), the E2 of Cities 4 and 5 are around 0.35 and 0.73, respectively. In Figure 8(c), the C2 of the province is around 0.97. The C2 of Cities 1, 2, and 3 are around 0.99, 0.98, and 0.95, respectively, which are all higher than 0.95 and above, showing that cities in the east, center, and west are more economically efficient. In Figure 8(d), the C2 of Cities 4 and 5 are around 0.965 and 0.995, respectively. The C2 of the whole province is higher at around 0.977. In summary, under the study of the comprehensive efficiency analysis method, the research method comprehensively considers cities with smaller ECE. The province’s E2 is lower and C2 is higher, which needs to focus on the improvement of ENE.

Figure 8.

Study the E2 (ENE) and C2 (EE) of different regions and the entire province under comprehensive efficiency analysis.

Figure 9 shows the ECE of the different regions of the province as well as the province as a whole under the study’s integrated ECE approach, which synthesizes ENE and EE. In Figure 9(a), the ECE of the province is around 0.52 after synthesizing the ENE and EE. The ECE of Cities 1, 2, and 3 is around 0.72, 0.41, and 0.42, respectively. In Figure 9(b), the ECE of Cities 4 and 5 is around 0.38 and 0.73, respectively. From 2020 to 2024, the change of ECE in the province is more stable.

Figure 9.

ECE of different regions and the entire province under the comprehensive efficiency analysis.

Table 2 illustrates the results of the DEAWs analysis of EE for the major representative cities in the east, center, west, north, and south for the years 2018–2024. City 1 maintains a high level of EE in 2021 and 2022, decreases slightly in 2023 (0.985), and rebounds in 2024 (0.988). City 2 shows a slight decrease in EE from 2018 to 2020, but remains at a high level (0.987–0.998). The years 2021 through 2024 show a continued but modest decline in EE (from 0.958 to 0.934). City 3 from 2021 to 2024 EE remains high in 2021 and 2022, but declines thereafter (0.963 in 2023 and 0.941 in 2024). City 4 continues to improve EE from 2018 through 2020, reaching full scores in 2019 and 2020. City 5 shows yearly increases in EE from 2018 to 2020, from 0.981 to 0.994. All cities are generally more economically efficient between 2018 and 2020, with some cities even reaching a perfect score. Cities’ EE generally remains high in 2021 and 2022, but declines in subsequent years.

Table 2.

EE DEAW analysis results of major representative cities in east, central, west, north, and south from 2018 to 2024.

Regional cities	2018	2019	2020	2021	2022	2023	2024
City 1	0.999	0.999	1	/	/	/	/
	/	0.999	0.988	1	/	/	/
	/	/	0.999	1	1	/	/
	/	/	/	0.999	0.999	0.985	/
	/	/	/	/	1	0.978	0.988
City 2	0.987	0.987	0.998	/	/	/	/
	/	0.996	0.977	0.974	/	/	/
	/	/	0.965	0.971	0.964	/	/
	/	/	/	0.958	0.954	0.953
	/	/	/	/	0.936	0.936	0.934
City 3	0.977	0.999	0.987	/	/	/	/
		0.997	1	1	/	/	/
	/	/	0.988	0.979	1
	/	/	/	0.974	1	0.961
	/	/	/	/	1	0.963	0.941
City 4	0.999	1	1	/	/	/	/
	/	0.996	0.989	0.987	/	/	/
	/	/	0.997	0.996	0.999	/	/
	/	/	/	0.978	0.997	0.989	/
	/	/	/	/	0.979	0.977	0.998
City 5	0.981	0.989	0.994	/	/	/	/
	/	0.982	0.996	0.997	/	/	/
	/	/	0.991	0.978	0.976	/	/
	/	/	/	0.974	0.988	0.952	/
	/	/	/	/	0.979	0.958	0.938

Table 3 shows the results of the dual target ECE window analysis for 10 cities from 2020 to 2024. These 10 cities are from two of the five regions: East, Central, Northwest, and South. For example, 1a and 1b represent two cities from the eastern region. The ECE values of most of the cities fluctuate during these 5 years, but the overall change is not significant. Some cities, such as City 2d, exhibit a downward trend, with their ECE value decreasing from 0.856 in 2020 to 0.684 in 2024. Meanwhile, the ECE values of City 1b and City 2a increase slightly over the same period. The ECE values of Cities 2b, 3a, 3b, 4a, and 4b show a decreasing trend over the 5 year period, indicating that these cities face some challenges in terms of ECE and need to take measures to improve them.

Table 3.

Analysis results of the dual-objective ECE window proposed in the study.

City	2020	2021	2022	2023	2024
1a	0.386	0.256	0.262	0.268	0.273
1b	0.294	0.200	0.272	0.281	0.282
2a	0.327	0.291	0.317	0.312	0.309
2b	0.856	0.742	0.775	0.734	0.684
3a	0.463	0.367	0.403	0.372	0.337
3b	0.625	0.524	0.496	0.470	0.460
4a	0.449	0.388	0.373	0.363	0.343
4b	0.524	0.399	0.445	0.419	0.396
5a	0.538	0.484	0.511	0.495	0.476
5b	0.321	0.272	0.292	0.298	0.303

To verify the flexibility of the dual-objective model, control experiments are conducted using a fixed-weight model (economic and ENE α = 0.5, β = 0.5), as shown in Table 4. The results show that the provincial ECE obtained by the traditional model is 0.65, 25% higher than the 0.52 obtained by the dual-objective model. This indicates that fixed weights overestimate economic efficiency. When α is adjusted to 0.3 (prioritizing the environment), the ECE of the dual-objective model drops to 0.48, indicating its sensitivity to policy priorities.

Table 4.

Control group experiment.

Model type	Index	Whole province	Eastern region	Western region	Northern region	Southern region
Fixed-weight model (α = 0.5, β = 0.5)	Environmental efficiency (ENE)	0.600	0.830	0.500	0.550	0.780
	Economic efficiency (EE)	0.970	0.990	0.950	0.965	0.995
	Ecological efficiency (ECE)	0.650	0.880	0.630	0.720	0.920
Dual-objective DEA model (α = 0.5, β = 0.5)	Environmental efficiency (ENE)	0.550	0.750	0.420	0.350	0.730
	Economic efficiency (EE)	0.977	0.990	0.950	0.965	0.995
	Ecological efficiency (ECE)	0.520	0.720	0.420	0.380	0.730
Dual-objective DEA model (α = 0.3, β = 0.7)	Environmental efficiency (ENE)	0.620	0.800	0.470	0.400	0.750
	Economic efficiency (EE)	0.920	0.950	0.900	0.910	0.960
	Ecological efficiency (ECE)	0.480	0.680	0.400	0.350	0.700

Discussion

To provide a new research idea to crack the contradiction between resource environment and regional development, the study proposed an ECE evaluation method based on the integrated DEA model. The results indicated that the dual-objective model demonstrated higher sensitivity to regional disparities. This flexibility was validated by the stable provincial ECE (0.52) from 2020 to 2024, contrasting with the fluctuating results of fixed-weight models. Cities 1–3 were the main representative cities in the east, center and west directions, respectively, and Cities 4 and 5 were the main representative cities in the north and south directions, respectively. Compared to the traditional method, the research method comprehensively considered cities with smaller ecological efficiency. From 2018 to 2024, under the traditional ECE analysis method, the E1 and C1 of most cities were in a slightly improving trend. Unlike the traditional DEA approach, which treated economic and ENE equally, the proposed framework enabled the weights to be adjusted dynamically. The ECE of City 1 and the province was always greater than 0.8, indicating high ECE. Its ECE for City 3 was around 0.73, which was less ecologically efficient. The ECE of Cities 4 and 5 was in a stable or increasing trend from 2020 to 2024. Under the study’s comprehensive efficiency analysis methodology, the research methods comprehensively considered cities with smaller ECE. The province had lower E2 and higher C2, which needed to be focused on the improvement of ENE. The ECE of Cities 4 and 5 was around 0.38 and 0.73, respectively. From 2020 to 2024, the changes in ECE in the province were more stable. All cities were generally economically efficient between 2018 and 2020, with some cities even achieving perfect scores. The EE of cities generally remained high in 2021 and 2022, but declined in the following years.

Conclusion

It can be concluded that it can provide reference for the government to formulate energy policy and planning, and promote the optimization and upgrading of energy industry structure. Simultaneously, it can offer businesses technical assistance to help them decrease environmental contamination and increase the efficiency of resource use. However, due to the diversity and complexity of data sources, there may be certain difficulties and errors in data acquisition and processing, which may have a certain impact on the accuracy of the evaluation results. It is necessary to further deepen the ways and methods of data acquisition in future research.

Footnotes

ORCID iD

Li Li

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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