Evaluation of Regional Water Use Efficiency under Green and Sustainable Development Using an Improved Super Slack-Based Measure Model

Abstract

Enhancing water use efficiency (WUE) is essential for the sustainable and green development of water utilization. The conventional Super Slack-Based Measure (CSSBM) model is commonly employed to measure WUE, however, it is prone to underestimating WUE due its exaggeration of the slack variable. Recognizing the need to deal with problems involving the slack variable without limitation, we propose an improved Super-SBM (ISSBM) model that assigns an upper bound to the slack variables. In addition, the general deprivation index (GDI) of water resource exploitation is then introduced as the output indicator representing the social equality, resulting in a comprehensive set of output indicators related to the economy, society, and ecological environment. The ISSBM and CSSBM models were applied to determine the WUE in Guangdong province, China from 2009 to 2018, and the results indicate that the WUE calculated via CSSBM exhibited relatively extreme performance (i.e., the high and low values were greater than 2 and less than 0.1, respectively), while the ISSBM-estimated WUE showed relatively stable performance (i.e., the majority of the city’s WUE was located in the range between 0.5 and 1). The WUE determined from the output indicators involving GDI thus demonstrated stronger discriminating power compared to that without GDI. Furthermore, the spatial pattern of WUE in Guangdong province presents an essentially radial distribution, with high WUE located in Pearl River Delta and low WUE located North, East, and West of Guangdong. These results verify that the proposed ISSBM model can obtain a relatively appropriate WUE and could potentially be applied to other regions.

1. Introduction

Water resources are significant natural resources and are necessary for both human life and for the progress of society and the economy [1]. However, global water resource scarcity poses a great threat to the future development of society and the economy. The Food and Agriculture Organization and the World Water Council have reported that 40% of the world’s population is facing fresh water shortages, and this is expected to increase to 67% by 2050 [2]. The increase in fresh water scarcity is a major threat for humans, and the sustainable utilization of water resources is crucial to overcoming this problem [3,4]. The United Nations General Assembly has implemented the Sustainable Development Goals (SDGs) for 2015–2030 in order to address global challenges, including air pollution, energy and food security, and water shortages [5,6]. In particular, Goal Six fully describes targets for water resources, among which target 6.4 emphasizes that in order to address water scarcity, water use efficiency (WUE) must substantially increase by 2030. Water resources alone cannot produce any outputs without others inputs (e.g., labor and capital stock) in the production process [7]. Thus, the definition of water use efficiency (WUE) in this paper mainly refers to the degree of resource utilization in the production process, where water, labor, and capital are inputs and socioeconomic development benefits and discharge of waste water are outputs. High WUE indicates that more socioeconomic development benefits are obtained using less water resources and other resources while releasing less discharge in terms of water pollution [8]. Therefore, improving WUE is essential to reducing water scarcity tensions and achieving sustainable development [9].

Much attention has been focused on understanding the status of WUE. Furthermore, WUE evaluation belongs to the class of multi-input/output problems [7]. Presently, Stochastic frontier analysis (SFA) and Data envelopment analysis (DEA) are the most prevalent approaches to calculating WUE, as these have advantages when dealing with multi-input/output problems [10]. As a parametric method, SFA must specify a stochastic frontier production function, and it can be a challenge to determine the form of the production function for different production processes [11]. As for DEA, it is a non-parametric method, and as such its major advantage compared with SFA is that it does not assume a production function [12]. Therefore, DEA is employed to determine WUE in this paper. Following the proposal of the first DEA model by Charnes [13], extensive studies have contributed to numerous extensions (

Table 1. Key literature on the development of DEA.

Author(s) and Year	Research Content	Contributions
Charnes et al. (1978) [13]	New definition of efficiency related to multiple inputs and outputs, and derivation of the first proposed CCR model.	Innovative work in the domain of DEA.
Charnes et al. (1985) [27]	Construction and analysis of the Pareto-efficient frontier production function.	Development of the additive DEA model to directly deal with input excesses and output shortages without scalar measures.
Pastor et al. (1999) [28]	Determination of a solution to the Russell graph measure for interpretative and computational difficulties.	New DEA global efficiency measure.
Tone (2001) [29]	Derivation of a slack-based measure (SBM) for DEA efficiency, and comparison with related models.	Proposal of SBM to directly deal with input excesses and output shortfalls with scalar measures.
Tone (2002) [30]	Derivation of a super-efficient slack-based measure.	Proposed super-efficient approach effectively discriminates efficient DMUs.
Tone (2003) [31]	Derivation of SBM model that simultaneously copes with desirable and undesirable outputs.	Modified SBM model to account for undesirable outputs.
Tone et al. (2020) [32]	Derivation of a modified model that combines the SBM and Super-SBM.	Proposed model can simultaneously measure SBM and Super-SBM efficiency scores.

), focusing on overcoming the corresponding deficiencies. Such examples include the development from radial to non-radial models, as well as from the slack-based measure (SBM) to Super-SBM. Advantages of these developments include not requiring a specific production functional form and the prior assignment of input and output weights, and have popularized these models for the evaluation of WUE in both developed and developing countries, including Italy [14,15], the USA [16], South Africa [17], the Palestinian Territories, [18] and China [19]. These numerous studies have proven the suitability of the DEA model for the evaluation of WUE across the globe. Despite the ability of the Super-SBM model to overcome DEA’s failure to fully rank all Decision-Making Units (DMUs), as efficient DMUs are all equal to 1, it can exaggerate the slack variables of input and output as it automatically optimizes the operations via linear programming. This consequently lead to underestimating the WUE [20]. In addition, research on social equality indicators for the evaluation of WUE using the DEA model is lacking, and thus current indicators cannot fully reflect the core concept of sustainable development from the overall perspective of the whole economy, society and eco-environment.

As the largest developing country, China’s water resources are characterized by large total amounts, low per capital availability, and an uneven spatiotemporal distribution [21]. This intensifies the conflict between water supply and demand. Moreover, inefficient water use and water pollution have degraded the self-renewing ability of water resource systems in recent decades [22]. The constraint of fresh water resources is of great concern for the social and economic development of the country. In order to overcome these issues, the Chinese government has implemented a set of water-saving measures and environmental regulations, aiming to ease tensions related to water utilization and pollution [23]. Furthermore, the Fourteenth Five-Year Plan in China emphasized that green development, as characterized by efficient, harmonious, and sustainable growth, is required for China [24]. In the context of green development proposed by the Fourteenth Five-Year Plan, the evaluation of WUE must be determined by three components, namely, the economy, society, and the eco-environment. Existing studies related to WUE have contributed to identifying the current status of WUE in China. However, the current literature is generally limited to industry [25] and agriculture [10] at the provincial level, while comprehensive WUE at the prefecture level, particularly the overall WUE required to enhance the economy, society, and eco-environment, remains unclear. Thus, there is a great need to comprehensively and intensively explore WUE from the perspectives of the economy, society, and the eco-environment at the prefecture level in China in order to propose a constructive policy for local governmental departments [26].

In order to overcome the limitations of the current literature, this study aims to improve the conventional Super-SBM (CSSBM) by assigning an upper bound to the slack variables. Taking Guangdong province in China as an example, the Improved Super-SBM model (ISSBM) is employed to measure WUE under the conditions of green and sustainable development. The objectives of this study are as follows: (1) to construct an ISSBM and demonstrate its advantages over the CSSBM model; (2) to improve the input and output indicators of the ISSBM model based on the economy, society, and the eco-environment; and (3) to calculate and analyze the WUE of Guangdong using the ISSBM model. Our findings support a comprehensive understanding of the status of WUE in Guangdong province and lay the foundation for accurate WUE measurements in other regions similar to Guangdong province, China in the context of green and sustainable development.

2. Methodology and Data

2.1. Conventional Super-SBM without a Set Slack Limit

As a non-parametric mathematical programming method, the DEA is able to evaluate a set of homogeneous DMUs with multiple inputs and outputs [33]. Assume there are n DMUs (DMU_j, j = 1, …, n) at each period, whereby each DMU contains m inputs $X=\left(x_{ij}\right)\in R^{m\times n}$, s₁ desirable outputs $Y^g=\left(y_{rj}^g\right)\in R^{s_1\times n}$, and s₂ undesirable outputs $Y^b=\left(y_{kj}^b\right)\in R^{S_2\times n}$; moreover, suppose that X > 0 and Y > 0, that is, that the dataset is positive. The production possibility set P can then be defined as $P=\left\{\left(X,Y^g,Y^b\right)|x\ge X\lambda ,y^g\le Y^g\lambda ,y^b\ge Y^b\lambda ,\lambda \ge 0\right\}$.

Several methods have been proposed in order to deal with the undesirable outputs, as described in the following: (i) the undesirable outputs are regarded as inputs [34]; however, this assumption contradicts the real production process, as the desirable outputs are accompanied by undesirable outputs [33]; (ii) the directional distance function can be applied to simultaneously increase the desirable output and reduce the undesirable output [35]; however, the evaluation results may vary for the same DMU with different directional distance functions. In addition, the choice of a directional distance function relies heavily on subjective judgment [33]; lastly, (iii) the undesirable outputs can be treated as desirable outputs by transforming them into new formations using either the reciprocal or multiplication method. The former employs the reciprocal of the undesirable output [36], while the latter first multiplies the undesirable output by (−1) and subsequently defines the translated threshold required to make negative variables positive [37]. However, it is difficult to define the suitable translated threshold for the multiplied method, while the reciprocal method is relatively simple and practical; thus, this study employs the reciprocal method to deal with undesirable outputs.

We integrate the reciprocal method with the approach proposed by Tone to define the efficiency of the objective DMU (DMU₀) [31]:

$$\rho =\min \left(\frac{1-\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{s_i^{-}}{s_{i0}}}{1+\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{g+}}{y_{r0}^g}+{{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{b+}}{y_{r0}^b}\right)}\right)$$

(1)

$$s.t.\{\begin{array}{l}{x}_0=X\lambda +s^{-}\\ y_0^g=Y^g\lambda -s_g^{+}\\ y_0^b=Y^b\lambda +s_b^{+}\\ 0\le s^{-},s_g^{+},s_b^{+}\\ 0\le \lambda \end{array}$$

(2)

where $\rho$ is the DMU₀ efficiency, s₁,s₂ indicate the number of expected and unexpected outputs, respectively, $x_0,y_0^g,y_0^b$ indicate the input, expected output, and unexpected output, respectively, of the objective DMU, vectors $s^{-},s_g^{+},s_b^{+}$ indicate the input, expected output and unexpected output, respectively, of the slack variables, and $\lambda$ is an intensity variable for each DMU and is used to connect the inputs and outputs.

The SBM model returns an efficient value between 0 and 1 for the evaluated DMUs when the DMU lies on the frontiers of the production possibility set without input and output slack variables, the DMU is efficient and the value is equal to 1, and the inefficiency value is less than 1 [29]. For the efficient DMUs, we are unable to further discriminate those that are superior. In order to overcome this problem, the proposed Super-SBM model can further calculate the value for the efficient DMUs, with the inefficient DMUs maintaining their original value from the SBM model [30]. The objective and programming functions of the Super-SBM model can be described as follows:

$$\delta =\min \left(\frac{1/m\cdot {{\displaystyle \sum }}_{i=1}^m{\overline{x}}_i/x_{i0}}{1/s\cdot {{\displaystyle \sum }}_{r=1}^{S_{}}{\overline{y}}_r/y_{r0}}\right)$$

(3)

$$s.t.\{\begin{array}{l}{\displaystyle {\displaystyle \sum }_{j=1\left(j\ne 0\right)}^n}{\lambda }_j{x}_j\le \overline{x}\\ {\displaystyle {\displaystyle \sum }_{j=1\left(j\ne 0\right)}^n}{\lambda }_j{y}_j\ge \overline{y}\\ \lambda \ge 0,\overline{x}\ge x_0,0\le \overline{y}\le y_0\end{array}$$

(4)

where $\delta$ is the DMU₀ efficiency and ($\overline{x},\overline{y}$) is the reference point of the objective DMU ($x_0,y_0$).

2.2. Improved Super-SBM with Set Slack Limit

The WUE evaluations in most previous studies may not be accurate, as the DEA automatically assigns the weights to each input and output, resulting in the large reduction (enhancement) of DMU inputs (outputs) [20]. In the SBM model, this problem typically reflects the input (output) slack variables. In order to solve this issue, Liu and Tone introduced the concept of artificially assigning a weight to the slack variables [38]. This was further developed to take into account subjective weights based on the importance of the inputs (outputs) [39,40]. However, the DEA approach relies on a benchmark to evaluate each DMU whereby each DMU corresponds to a specific benchmark. If only weights for the objective function are determined, this fails to fundamentally change the benchmark for inefficient DMUs. More specifically, previous WUE evaluations may be incorrect only due to assigning artificial weights to slack variables in the objective function. To avoid the large reduction (enlargement) of inputs (outputs), the input (output) slack variables must reflect the actual conditions as much as possible. However, this has been barely mentioned in the existing literature.

The slack variables mainly reflect the distance between the evaluated DMU and the effective DMU during a certain period. Thus, we can attempt to determine a relatively reasonable range for the slack variables in order to reflects the gap between the evaluated DMUs and the best DMUs by employing lower and upper bounds for the slack variables. The lower bound should be greater than or equal to zero based on the slack variable definition, although the upper bound of a slack variable does not stipulate a specific value at definition. Therefore, determining the upper bound is key to constructing the slack variable range. In order to determine the upper bound of slack variables, our proposed approach follows the previous work of [41]. The proposed methodology is presented in Figure 1.

The above-mentioned parameter t is a scalar variable, and is introduced to transform the fractional program into a linear program [29]. The improved SBM model is defined as follows:

$$\theta =\min \left(\frac{1-\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{s_i^{-}}{s_{i0}}}{1+\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{g+}}{y_{r0}^g}+{{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{b+}}{y_{r0}^b}\right)}\right)$$

(5)

$$s.t.\{\begin{array}{l}{x}_0=X\lambda +s^{-}\\ y_0^g=Y^g\lambda -s_g^{+}\\ y_0^b=Y^b\lambda +s_b^{+}\\ 0\le s^{-},s_g^{+},s_b^{+}\le UB\\ 0\le \lambda \end{array}$$

(6)

where $\theta$ indicates the efficiency of DMU₀, UB represents the upper bound set of the slack variables, and the other parameters follow the implantation of Formulas (1) and (2).

We subsequently constructed an improved Super-SBM model based on the improved SBM model. The proposed ISSBM model was then applied to calculate the value of the DMUs.

2.3. Study Area

Guangdong Province, China, has 21 prefecture-level cities, which can be divided into the Pearl River Delta (PRD), Western Guangdong (WG), Eastern Guangdong (EG), and Northern Guangdong (NG) regions according to their socioeconomic development level and geographical location (Figure 2). This region belongs to the subtropical monsoon climate designation; a large amount of precipitation leads to abundant surface water resources in Guangdong province, while there is uneven spatiotemporal distribution of water resources [42]. Furthermore, following the implementation of the “reform and opening” policy, Guangdong province has experienced rapid economic development, and its GDP ranks first in China after 1988 [43,44]. However, the PRD accounts for 62% and 80% of Guangdong’s population and GDP, respectively. This regional disparity within Guangdong Province remains today, causing a discrepancy in natural resources use efficiency, including water resource use efficiency. Moreover, a conflict between water supply and demand exists in certain cities within Guangdong Province.

2.4. Data

In production processes, water resources need to be combined with others inputs (e.g., labor and capital stock) in order to produce outputs, among which the outputs contain expected and unexpected outputs (e.g., GDP and wastewater). Previous studies related to WUE have commonly chosen assets, labor, and water use as input variables and GDP and wastewater as outputs [45,46,47]. Considering the availability of data and the purpose of our research, this study selected five input and three output indicators (Figure 3) according to the rule of thumb that the number of DMUs should be at least twice the number of inputs and outputs [48]. Unlike previous studies, this paper employs the intensity of variables rather than their total amounts. Compared with total amounts, the intensity of variables better reflects the actual performance of inputs and outputs at particular technological levels. Specifically, the five input indicators containing water-related and water-unrelated variables were the primary, secondary and tertiary industry water use per CNY 10,000 GDP, capital stock per CNY 10,000 GDP, and labor per CNY one million GDP, respectively. The GDP per water use, social equality, and emission of wastewater per CNY 10,000 GDP were employed as the desirable and undesirable output indicators, respectively. With the exception of social equality, all indicators were collected from editions of the Guangdong Statistical Yearbook and Guangdong Water Resources Bulletin released for 2009–2018, and were subsequently converted into average indicators to represent the intensity of the variables. The summary statistics of the inputs and outputs are reported in

Table 2. Summary statistics of inputs and outputs of DEA model in Guangdong province.

Year	Variable	Water Inputs			Non-Water Inputs		Desirable Outputs		Undesirable Output
		PIWGDP	SIWGDP	TIWGDP	LGDP	CSGDP	GDPWC	Social Equality	WWEGDP
2009	Mean	1206.70	85.50	83.91	23.36	6053.42	90.73	0.37	22.83
	SD	410.68	62.56	40.08	10.67	2479.44	110.30	0.20	6.95
2010	Mean	1048.33	73.31	73.22	19.77	5583.91	103.77	0.28	20.26
	SD	388.52	54.78	32.88	8.26	2265.49	122.94	0.20	6.63
2011	Mean	938.03	63.47	64.13	17.09	5140.15	120.38	0.27	16.91
	SD	350.88	46.90	29.35	7.17	2060.63	141.83	0.17	4.31
2012	Mean	853.64	54.90	57.37	15.49	4997.75	134.71	0.53	16.74
	SD	337.53	43.6	24.82	6.45	2004.21	159.82	0.20	3.88
2013	Mean	784.06	48.87	49.48	13.65	4617.06	149.65	0.25	14.46
	SD	320.57	36.27	19.89	5.58	1712.03	173.66	0.17	3.02
2014	Mean	774.03	44.99	45.87	12.57	4462.08	161.88	0.27	13.51
	SD	324.14	33.61	17.63	5.06	1651.52	186.54	0.19	3.21
2015	Mean	726.12	40.42	42.29	11.83	4357.56	174.01	0.24	12.67
	SD	302.30	28.74	16.02	4.76	1596.15	200.13	0.17	3.07
2016	Mean	650.18	37.54	38.32	10.99	4187.86	191.67	0.34	12.21
	SD	265.77	26.69	14.51	4.35	1536.83	222.22	0.19	3.07
2017	Mean	643.49	35.41	33.92	10.41	4073.08	211.50	0.26	11.42
	SD	250.11	25.09	12.74	4.38	1544.31	255.85	0.16	3.11
2018	Mean	589.23	30.01	30.77	9.86	3989.06	228.05	0.36	11.03
	SD	218.17	21.33	10.90	4.13	1530.36	267.04	0.18	3.17

Note: The unit of PIWGDP, SIWGDP, and TIWGDP is m³/10⁴ CNY, the units of LGDP, CSGDP, GDPWC and WWEGDP are person/million CNY, CNY, 10⁴ CNY/m³, m³/10⁴ CNY, respectively, and social equality is a comprehensive index without a unit.

.

The social equality indicator generally reflects the fairness and well-being of humans in terms of social economic development. In order to characterize this indicator, we introduced the general deprivation index (GDI). Deprivation theory was initially proposed by Norris in 1979 to deal with social inequality [49]. The GDI was subsequently applied to measure the deprivation intensity based on the concept of deprivation, and has been widely applied to evaluate social equality from different perspectives [50,51], including recent applications in water resources exploitation (WRE) [52]. Due to its potential in measuring WRE inequality, we employed the GDI to represent social equality related to WUE (the higher the GDI, the lower the social equality). The reader can refer to the aforementioned article for details on the GDI calculation [52]. Data on the selected variables used to calculate the GDI were collected from editions of the Guangdong Statistical Yearbook and Guangdong Water Resources Bulletin released during 2009–2018 (

Table 3. Summary statistics of GDI index variable.

Variable	Definition	Unit	Min	Max	Mean	SD
Per capita water resources	$\frac{\mathrm{TWR}}{\mathrm{TP}}$	m3	138.30	8524.40	2360.30	2029.50
Per capita water consumption	$\frac{\mathrm{TWC}}{\mathrm{TP}}$	m3	163.20	826.50	463.60	160.60
Urbanization rate	$\frac{\mathrm{UP}}{\mathrm{TP}}$	%	34.40	100.00	61.90	20.10
Sewage treatment rate	$\frac{\mathrm{TWW}}{\mathrm{TWWE}}$	%	20.80	99.10	86.30	11.20
Water utilization rate	$\frac{\mathrm{TWC}}{\mathrm{TWR}}$	%	5.82	100.00	38.10	0.32
Per capita GDP	$\frac{\mathrm{TGDP}}{\mathrm{TP}}$	CNY	7637.90	141,744.10	41,652.40	30,611.60
Water consumption per CNY 10,000 of GDP	$\frac{\mathrm{TWC}}{10,000\cdot \mathrm{TGDP}}$	m3	9.00	671.00	163.40	129.90
Water consumption per CNY 10,000 value added by industry	$\frac{\mathrm{TWC}}{10,000\cdot \mathrm{IAV}}$	m3	5.00	370.00	70.80	67.80
Water consumption per mu of irrigated farmland	$\frac{\mathrm{TWC}}{\mathrm{IFL}}$	m3	380.00	1004.00	728.30	128.10
Waste water emission per CNY 10,000 of GDP	$\frac{\mathrm{WWE}}{10,000\cdot \mathrm{TGDP}}$	m3	5.20	47.50	17.80	7.90

Note: mu is a unit of area (=0.0667 ha); the meaning of the abbreviations are as follows: TWR, TWC, UP, TP, TWW, TWWE, TGDP, IAV, IFL, and WWE represent Total Water Resources, Total Water Consumption, Urban Population, Total Population, Treatment of Waste Water, Total Waste Water Emission, Total Gross Domestic Product, Industrial Added Value, Irrigated Farmland, Waste Water Emission, respectively.

).

3. Results

3.1. Estimated WUE Using the Conventional Super-SBM Model

The estimated WUE for the 21 prefecture-level cities in Guangdong province was determined using the CSSBM model from 2009 to 2018 (Figure 4). For most cities (located in the western Guangdong (WG), northern Guangdong (NG), and western Guangdong (EG)), the mean WUE is less than 0.5, with only five cities (located in the PRD) exhibiting values greater than 1. This suggests that cities with the lower WUE occupy a relatively greater proportion than those with a high WUE, while geographic location and socioeconomic development may have a greater impact on the WUE. Note that several of the estimated WUE values are relatively extreme (e.g., Shenzhen, Guangzhou and Zhuhai have a markedly high WUE, while Shaoguan, Meizhou, and Heyuan have extremely low values). This reflects the disadvantage of CSSBM whereby the slack variables are fully determined by the automatic optimization. In addition, the box length of several cities (e.g., Zhongshan, Maoming and Yangjiang) is relatively long, highlighting the fluctuations in WUE for these cities from 2009 to 2018. This can be attributed to a relatively lower estimated WUE due to an exaggeration of the slack variable in certain years for the aforementioned three cities, causing further large fluctuations in the WUE. Several outliers can be observed (plus signs above or below the boxes) in Figure 4, indicating that a deviation exists in between the estimated WUE determined by the selected model and the actual WUE.

In order to analyze the regional disparity of the estimated WUE, we classified Guangdong province into four regions (PRD, WG, NG, and EG; see Figure 1) based on the criteria proposed by the Guangdong Provincial Government. The PRD exhibits the maximum mean WUE from 2009 to 2018, followed by NG, WG, and EG, further confirming that the geographic location and socioeconomic development level of a city is closely correlated to its WUE (Figure 5). However, all regions and the whole province exhibited mean WUE values less than 1 during study period. In particular, the values of WUE from EG and WG are generally lower than 0.2. In addition, there exist marked fluctuations between 2016 and 2017 for all regions. The reason for this may again be exaggerated slack variables, which are highly sensitive to the original data in the absence of a constraint. According to the principle of the SBM model, larger slack variables will result in a smaller WUE.

3.2. Estimated WUE Using the Improved Super-SBM Model

Figure 6 depicts the estimated WUE of the 21 prefecture-level cities in Guangdong Province from 2009 to 2018 using the ISSBM model. The WUE values of Guangzhou, Shenzhen, Zhuhai, Foshan, and Dongguan are greater than 1, while the WUE values of most cities are inefficient, ranging between 0.5 and 1, which accounts for 76% of cities. Moreover, all cities exhibit a relatively narrow interquartile range of WUE (represented by the box plots in Figure 6), although several outliers can be observed. From the perspective of regional disparity, the PRD exhibits the greatest value, while other regions are below the average of the whole province (Figure 7). This implies that the WUE is somehow positively correlated with socioeconomic development level and geographic location. Furthermore, the values of WUE are generally stable for the PRD; the reason for this is that the efficiency value determined by the DEA model is a relative efficient value, and the value reflects valid efficiency when it is equal or greater to 1; otherwise, it reflects invalid efficiency. If a city has valid efficiency, it essentially represents a benchmark for other cities with invalid efficiency. Generally, the valid efficiency is slightly greater than 1. In the PRD, most cities have valid efficiency, and thus become benchmarks for the other cities of Guangdong Province during 2009–2018. Thus, the WUE of the PRD demonstrates a stable trend, while there are slight fluctuations in the EG and WG regions. In NG, the WUE exhibits a U-shaped trend, initially decreasing from 2009 to 2016 and subsequently increasing between 2016 and 2018. Compared with the results shown in Figure 5, there is a relatively steady fluctuation from 2009 to 2018 in Figure 7, indicating that the ISSBM model is more robust than the CSSBM model.

3.3. Comparison of CSSBM and ISSBM WUE Estimates

The comparison of estimated WUE between the 21 prefecture-level cities in Guangdong province from 2009 to 2018 via the CSSBM and ISSBM models is depicted in Figure 8. The majority of observations are located to the left of the diagonal (and above), indicating that the WUE estimated by the ISSBM model generally exceeds that determined by the CSSBM model. This is further confirmed by Figure 4 and Figure 6, which imply that the CSSBM model may underestimate value of cities with inefficient WUE due to exaggerated slack variables. The DMUs on the diagonal are efficient, which means that the WUE of the DMUs are same when the DMUs are efficient calculated by the CSSBM and ISSBM models. The reason for this is that the slack variables of efficient DMUs are zero for both models, as the difference in WUE between the CSSBM and ISSBM derives from the slack variable. It is worth noting that the average estimations of WUE were less than 1 and showed marked variations between 2016 and 2017 for four regions when using the CSSBM model, while the ISSBM model presents a relatively steady fluctuation and slight increasing trend from 2009 to 2018, with the sole exception of the U-shaped trend in NG. This suggests that the ISSBM results are relatively more stable than the those of the CSSBM.

Furthermore, in order to demonstrate the importance of considering the GDI of water resource exploitation as a social equality indicator, in this paper we calculated the standard deviation (SD) of WUE from 2009 to 2018; a higher SD indicates that the WUE has a stronger degree of discriminating power between cities. From the

Table 4. Standard deviation of WUE evaluation results determined with and without the GDI.

Year	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
GDI	0.35	0.32	0.44	0.42	0.48	0.48	0.45	0.46	0.36	0.36
Non-GDI	0.49	0.48	0.42	0.40	0.27	0.26	0.27	0.33	0.26	0.26

Note: Non-GDI represents the evaluated scope without the social equality indicator.

, the SD with the GDI indicator exceeds that without in most years, which indicates that the model considering GDI as an output indicator has stronger discriminating power than the model that does not consider the GDI. This is helpful for identifying the disparity in WUE between cities and effectively classifying cities in terms of WUE.

3.4. Spatiotemporal Distribution of WUE in Guangdong Province

We further analyzed the spatiotemporal distribution of estimated WUE using the ISSBM model. In order to facilitate analysis, we selected four research periods (2009, 2012, 2015 and 2018) for subsequent discussion. In addition, WUE levels were divided into five classes following the Jenks natural breaks classification using ArcGIS10.6. Figure 9 demonstrates the spatiotemporal distribution of WUE among the 21 prefecture-level cities in Guangdong province. As depicted in Figure 9, the value of WUE shows an increasing trend from the global perspective. For example, the scope of low values is 0.26~0.36 in 2009 and 0.34~0.63 in 2018. Specifically, certain cities in the PRD, such as Guangzhou, Foshan, Dongguan, Shenzhen, and Zhuhai, exhibit high WUE in 2009, while most cities in Western, Eastern, and Northern Guangdong are associated with low WUE. The number of cities with high WUE increased from 2012 to 2015, while the number of cities with low WUE decreased, particularly in Yangjiang (YJ) and Maoming (MM), which had high WUE values during 2012~2015. In 2018, the WUE value increased for all cities, while the spatial pattern essentially shows a radial distribution with high WUE in the PRD and low WUE in EG, WG, and NG.

In general, the PRD, especially Shenzhen, Dongguan, and Zhuhai, maintained high WUE throughout the research period, while Northern Guangdong exhibited poor performance. This indicates the occurrence of spatial disparity in WUE in Guangdong Province due to geographical location and socioeconomic development.

4. Discussion

Previous evaluations of WUE have generally focused on the economy and ecological environment due to the deteriorating water ecological environment resulting from rapid and rough economic development [53]. Economy-focused evaluations of WUE place great importance on the pursuit of rapid economic development, while environmental effects are understudied. Thus, most studies have only considered one desirable output, namely, economic output, with wastewater seen as an inevitable result of production processes [54] However, increasing attention has been focused on the environment in recent years. The discharge of wastewater is regarded as an undesirable output, and has gradually begun to be considered in evaluations of WUE. In order to satisfy the demands of the economy and society for high-quality development, the indicators of estimated WUE should be fully extended to the three aspects of economy, society, and the eco-environment [55]. Society generally reflects the fair treatment and well-being of humans. This study used the GDI related to water to represent social equality. As shown in Table 4, it reveals that when the output indicators contain the three aspects of the economy, society, and the eco-environment, the resulting WUE values have stronger discriminating power. Other indexes can be integrated into the inputs and outputs as necessary, according to the specific socioeconomic development stage under study.

The WUE values of the 21 prefecture-level cities in Guangdong province from 2009 to 2018 were investigated using the CSSBM and ISSBM models. Unlike CSSBM, the ISSBM model artificially assigns an upper bound to the slack variables. The CSSBM-estimated WUE is consistently lower than that of the ISSBM model, with the exception of the efficient DMUs on the diagonal of Figure 8. This indicates the tendency of the CSSBM model to excessively underestimate the WUE of the 21 prefecture-level cities examined during the study period.

Taking the slack variable of the input in 2009 as an example (

Table 5. Comparison of original data and data with constrained and unconstrained slack variables for 2009.

City	PIWGDP			SIWGDP			TIWGDP			LGDP			CSGDP
	OD	SUC	SC	OD	SUC	SC	OD	SUC	SC	OD	SUC	SC	OD	SUC	SC
GZ	733	121	121	140	0	0	23	0	0	8	0	0	0.73	0	0
SG	1663	11	193	168	147	29	70	31	6	24	12	3	0.70	0	0.11
SZ	1076	0	0	13	11	11	25	16	16	8	1	1	0.46	0.13	0.13
ZH	412	199	199	24	0	0	40	0	0	8	0	0	0.58	0	0
ST	1013	0	174	31	18	0	86	62	13	23	16	4	0.94	0.51	0.10
FS	1170	0	0	63	0	0	52	0	0	7	0	0	0.32	0	0
JM	1909	1182	178	79	69	7	71	54	6	17	11	1	0.68	0.37	0.07
ZJ	848	0	168	42	31	19	95	75	24	27	20	5	0.47	0.11	0.02
MM	922	0	176	43	32	16	82	60	10	28	21	5	0.66	0.26	0.13
ZQ	858	0	65	105	94	10	72	51	4	29	23	2	1.33	0.96	0.10
HZ	1422	465	195	69	57	0	62	39	14	17	10	5	0.41	0	0.04
MZ	1462	1013	0	220	214	44	128	117	8	42	39	7	0.62	0.43	0
SW	1084	486	116	97	90	14	155	141	27	31	26	5	0.25	0	0.03
HY	2165	1815	205	238	234	27	146	138	15	32	30	3	0.44	0.29	0.04
YJ	923	203	84	22	13	0	96	79	12	31	25	4	0.5	0.2	0
QY	1545	955	229	43	36	0	93	79	20	25	20	6	0.61	0.36	0.13
DG	960	0	0	53	0	0	45	0	0	11	0	0	0.19	0.1	0.10
ZS	1504	489	60	98	86	4	40	16	0	13	5	0	0.53	0.09	0
CZ	1105	711	165	78	73	12	101	91	14	29	26	4	0.67	0.5	0.06
JY	1181	717	191	42	36	0	117	106	20	32	28	5	0.85	0.65	0.09
YF	1375	0	152	119	101	25	155	122	25	39	29	6	0.66	0.07	0.04

Note: OD, SC, and SUC represent original data, slack variables with constraint, and slack variables without constraint, respectively.

), the rationality of the aforementioned inference can be explained from the perspective of the slack variables. It can be seen that the unconstrained slack variables generally exceed those with an upper bound. The input slack variables represent the input redundancy, and reflect how inefficient the DMUs are [29]. In the CSSBM model, the slack variables are exaggerated (e.g., the input variable “primary industry water per CNY 10,000 GDP (PIWGDP) in Jiangmen (JM), Meizhou (MZ), Heyuan (HY), Qingyuan (QY)), resulting in much lower WUE values for the corresponding cities that deviate from their actual WUE status (Figure 4). In contrast, the slack variables determined by the ISSBM model are relatively reasonable, revealing the ability of this model to avoid excessively low estimations of WUE (Figure 6). The exaggerated slack variables obtained by the CSSBM model can be explained by Equation (1); specifically, the objective function that was used to solve the minimum value under constraint conditions requires the slack variables to be as large as possible for optimization. Thus, the CSSBM model consistently exaggerates the slack variables of inefficient DMUs, resulting in excessively low WUE values for inefficient DMUs. In the ISSBM model, the upper bounds of the slack variables are determined using our proposed method (see Section 2.2), which artificially imposes constraints in order to prevent the exaggeration of the slack variables due to automatic optimization. As depicted in Figure 6, the markedly lower DMU efficiency values in Figure 4 are relatively normal.

5. Conclusions

Enhancing WUE can overcome the bottleneck faced by sustainable and green socio-economic development. Moreover, accurate estimations of WUE are critical when designing targeted policies to confront such challenges. In the current study, an ISSBM model was proposed to calculate the WUE of the 21 prefecture-level cities in Guangdong Province from 2009 to 2018. We compared the results obtained by the CSSBM and ISSBM models to demonstrate the advantage of ISSBM over the CSSBM model. The spatiotemporal distribution of the WUE in Guangdong province was further analyzed. The following key conclusions can be drawn:

(1)

The ISSBM model is superior to the CSSBM model, as it avoids underestimation of the WUE. This is attributed to the ability of the ISSBM to artificially assign an upper bound to the slack variable, avoiding the excessive slack variables resulting from automatic optimization.

(2)

When the ISSBM model employs output indicators related to the economy, society, and the eco-environment, the estimations of WUE exhibit stronger discriminating power than when social equality is not considered as an output indicator.

(3)

Using the ISSBM model to estimate the WUE in Guangdong Province revealed that the PRD exhibits the highest WUE, while northern Guangdong exhibits the worst. This indicates the occurrence of a spatial spillover effect with respect to WUE in Guangdong province, which is due to the disparities in geographical location and socioeconomic development.

The ISSBM model proposed in the current study can effectively prevent the exaggeration of the slack variable, and can be applied to other scenarios (e.g., energy and land). However, the proposed five-step method used to determine the upper bound of the slack variables may not fully represent the optimal upper bound, as the statistical distribution of the collected data was not considered. For example, the average value of the top five large (small) variables was selected in order to determine the upper bound of the slack variables. The reason for taking the average was mainly to prevent extremely large or small values in the proposed five-step method. However, the values may not be optimal. Therefore, future research should focus on determining the optimal range of the slack variables, particularly while integrating interval and fuzzy approaches.