Evaluation of the Utilization Efficiency of Water Resources in China Based on ZSG-DEA: A Perspective of Water–Energy–Food Nexus

The main resources needed for human survival are water, energy and food, and the research on the relationship among the three resources has become the research topic. Due to the shortage of natural resources, research on the efficiency of water–energy–food (WEF) nexus has become a hot issue among scholars and governments all over the world. The simple models cannot study the correlation among them; the methods of WEF nexus gradually shift from single to integrated model. The data envelopment analysis (DEA) model is the most simple and effective model, which can measure the efficiency value of each decision-making unit (DMU) and overcomes the shortcoming that the evaluation index system needs to give the weight. The DEA can calculate the efficiency value, but it cannot improve the efficiency value of DMU by changing the input. In this paper, the zero-sum gain (ZSG) DEA model is constructed based on zero-sum game theory. The initial efficiency values of 30 provinces in China are calculated, and each DMU is proportionally allocated according to the proportional subtractive method. After several iterations, the efficiency values of all DMUs reach 1, indicating that global optimization has been achieved. Under the condition of effectiveness, the initial input water resources are reconfigured. Finally, some conclusions are made, and optimization strategies are proposed for 30 provinces in China with low water resource utilization efficiency.


Introduction
The main resources needed for human survival are water, energy and food, and are critical for meeting the sustainable worldwide economic development [1]. Water-energy-food (WEF) nexus has become one of the important risks of sustainable economic development around the world. In 2015, the World Economic Forum ranked this risk as the first. Government departments pay more and more attention to the risk of WEF nexus. In the past, more and more governments and scholars have been paying attention to the links among the three. The interdependent and interactive feedback relationships of three resources are termed as WEF nexus. The exploitation and cleaning of fossil energy and the growth and processing of grain need a lot of water resources. Energy consumption in water resources production is mainly used for pumping and delivering water. Energy consumption in grain production and processing in mechanization, land preparation, fertilizer production, agricultural irrigation, food packaging, storage and other aspects. About 30% of energy is consumed in food processing and transportation. More than 70% of electricity is generated by burning coal, carbon dioxide emissions are among the highest in the world [2].
In terms of total water resources, China ranks sixth in the world. But it has less than a quarter of the world's water resources per person, making it one of the world's 13 waterscarce countries. With the cumulative impact of population increase, economic growth, ecological environment and other factors, the demand for water resources is increasing, and there are more and more contradictions among each other, making it more difficult to manage. Due to the influence of climate, topography and other factors, the amount of water resources in the region is extremely uneven, which leads to the increase of water cost and prominent contradiction of water resources [3]. Similarly, overall efficiency can be optimized by redistributing water from less efficient areas to more efficient ones. Water resource allocation is not between regions, more from the whole basin, involves the balance analysis of supply and demand of water resources. Water resource allocation is a typical multi-dimensional, multi-objective and complex group of semi-structured decision problem [4].
In China, there are eight major watersheds, such as the Yellow River, the Yangtze River, the Songhua River, the Liao River, the Huaihe River, the Pearl River and the Taihu Lake. They cover 45% of China's land area, support more than 90% of its population and economic output. Table 1 shows the drainage area, total water resources, water quality, population and gross domestic product (GDP) of China's eight major river basins.
In 2019, China's primary energy output reached a new historic peak of 3.97 billion tons of standard coal, up 5.1% year on year. Also, installed power capacity reached 2.01 billion kW. Refining capacity reached 860 million tons. Crude oil production growth turned positive from negative to 191 million tons, up 0.9%, which reversed the trend of continuous production declined since 2016. In 2019, China's annual net energy imports reached about 1 billion tons of standard coal, with the overall dependence on foreign countries at 21%. Coal imports, which use a lot of water to extract and produce, remained stable, with net imports of about 300 million tons. Natural gas imports grew at a slower pace, with net imports of 133 billion cubic meters, up 6.9% year on year, as unconventional gas extraction also consumes a lot of water.
From 2015 to 2020, China's annual grain output remained above 650 million tons, and consumption exceeded output. In 2020, grain consumption of China was about 740 million tons, leaving a gap of about 100 million tons, which needed to be imported from abroad. Taking into account the growth of population, development of animal husbandry and grain consumption for industry, grain consumption is expected to reach about 750 million tons in 2025, including over 600 million tons of grain consumption. Under the requirement of self-sufficiency in grain and absolute grain security, the total grain output of rice, wheat and corn should exceed 590 million tons. Including soybeans and other grain crops, the total grain production capacity of the 14th Five-Year Plan period should reach 650 million tons. According to the 14th Five-year Plan, by 2025, China will be better able to prevent floods and droughts, conserve and use water resources intensively and safely, China will also allocate water resources optimally, protect and manage river and lake ecosystems. And the country's water security capability will be significantly improved.
The rest of this paper is structured are follows. Section 2 conducts a literature review to reinforce our research motivation and contribution. In Sect. 3, we present the traditional DEA model and zero-sum gain (ZSG)-DEA model. In Sect. 4, the allocation scheme of water resources supply in each province of China is obtained through the model calculation. The allocation scheme of water resources is further analyzed, and the water resources are effectively allocated from the regional perspective to meet the global optimization. In Sect. 5, some conclusions are drawn and some future directions are pointed out.

Literature Review
Scholars have concluded that climate, population growth, economic growth and urbanization affected the coupling of WEF system and usually ignored the factor of the river basin [5]. The security of food, water and energy resources are understood for several major river basins worldwide. Usually, experts evaluate them using a questionnaire, expert rating, and give relevant suggestions [6]. Taniguchi and Makoto [7] studied the coordination and optimization of transboundary river basins between different South Asia from the perspective of WEF nexus. They also made an in-depth study of the problems in South Asia. Although government sectors promoted grain production through subsidies to ensure local food demand, the increase in grain production consumes water, which degrades the resource base and reduces the total and quality of water resources. Mroue et al. [8] studied the balance between the critical water demand industry and water consumption in the Heihe basin. He also used the graph theory to analyze the hydrological network relationship between users and countries along the Heihe basin. Some researchers analyzed a series of complex water resource management problems of agriculture in the high plains and constructed a framework for water resource management [9][10][11]. From the perspective of the WEF nexus, scholars analyzed the sustainable development of BRICS (Brazil, Russia, India, China, South Africa) nations [12]. They also constructed the food security index by the principal component analysis method, including agricultural machinery, land under grain production and agricultural added value [13]. Vito and Portoghese [14] analyzed food production problem in the Puglia area, and structured a comprehensive evaluation method to the quantitative calculation of irrigation efficiency. The results found that the region groundwater extraction cost and surface water are lower, often used by priority, but excessive use of groundwater will affect the region's ecological structure.
The river basin usually passes through many regions, the population, economy and culture of each region are different. Depending on the resource endowments, different region attaches different importance to water, energy, and food. The water resources of the downstream region/ countries are affected by the upstream region/countries [1]. For example, there are many biological species in the Yangtze River Basin, and the ecological environment is fragile. For the harmonious development of mankind and ecology, Chinese President Xi Jinping stressed that the Yangtze River has a unique ecosystem and is an important ecological treasure house in China, and a 10-year ban on fishing has been implemented. There are many factors that affect global ecological and environmental change. Global Catchment Initiative (GCI) has made an in-depth analysis of driving factors that cause global change and their impact on watershed economy [15]. Life cycle assessment has also been applied to the quantitative calculation of WEF nexus, which can effectively calculate the total water, virtual water and energy consumption of an industry [4,16,17]. Many articles used hydrological economic models to redistribute water resources in space and time, and gave a series of management schemes, economic values and policy choices [18]. It can measure and predict the amount of water by the hydrological model soil and water assessment tool, which is also an integrated model [19]. Taking Beijing as the case, they used quantitative research methods such as system dynamics or system optimization model to measure the internal relationship among the three, and gave some advice to the government department [2,20]. DEA is an ideal element allocation model, which can consider all input-output elements and achieve the optimal efficiency of the allocated object [21,22]. There are many papers that analyze water use efficiency by DEA model, Lins [23], Sun [24] and Miao [25] constructed environmental ZSG-DEA models to allocate China's energy conservation quotas and air pollutants emission rights. Wang et al. [26] also established a resource allocation model that joints the input and output orientation to allocate provincial GDP and quotas of energy consumption, coal consumption, and carbon emission in 2020.
The ZSG-DEA model was first constructed by Lins [23], the model was applied to sports ranking. There are many papers that analyze water use efficiency by DEA model, Lins [23], Sun [24] and Miao [25] constructed environmental ZSG-DEA models to allocate China's energy conservation quotas and air pollutants emission rights. Wang et al. [26] also established a resource allocation model that joints the input and output orientation to allocate provincial GDP and quotas of energy consumption, coal consumption, and carbon emission in 2020. A lot of reviews show that there are many studies on the allocation of provincial energy consumption, water resource, and food product, but few studies have attempted to focus on the coordinated allocation of the three elements [25,[27][28][29]. From the perspective of allocation principles and methods, most studies consider fairness and efficiency. DEA can associate the inputs of expected and unexpected outputs, and do not need to estimate the values of indicators [30,31]. Therefore, it is more objective than the allocation models based on indicators and nonlinear optimization, and the relevant research is more abundant [32]. The concept of zero-sum gain is introduced to allocate water resources, and the total amount of water resources is taken as the main constraint condition. From the perspective of efficiency and WEF nexus, we optimized the allocation of water resources in 30 regions of China.

DEA Model
The core idea of DEA model is to use input-output data to calculate the boundary of maximum output or minimum input, which is an effective method to evaluate the efficiency of multiple input-output decision-making units. Charnes et al. [33] first put forward the CCR (Charnes, Cooper, Rhodes) model with constant returns to scale. Then Banker et al. [34] developed the BCC (Banker, Charnes, Cooper) model considering the variable returns to scale, which can be divided into two types: output-oriented and input-oriented. The input-oriented BCC model used in evaluating the relative efficiency of the target DMU 0 via the basic DEA method can be express in the following formula (1) In the model, assuming that an evaluation system has N decision units of the same type, each decision unit has R input indicators and M output indicators. θ o is the relative efficiency of DMU o , λ i is the weight coefficient, x i and y i (i = 1, …, N) are the input and output amount of DMU i, respectively.
In some cases, the total amount of a certain input (or output) is fixed, and the inputs (or outputs) of each DMU are related to each other to ensure that the total amount remains unchanged. The core idea of the ZSG-DEA model is that the loss (or gain) of one player must be the gain (or loss) of other players, that is, the total return must be zero. However, the traditional DEA model can only give the relative efficiency of the initial state, but cannot make DMU integrate inputs (or outputs) to help it achieve DEA effectiveness. Under the strictest water resources management system, it is necessary to analyze the differential allocation of water resources. The traditional DEA model can only calculate the relative efficiency of the initial, but cannot help us realize the increase of DEA efficiency by adjusting the distribution results. (1)

The ZSG-DEA Model
To solve the water allocation issue, we use the ZSG-DEA model which is proposed by Lins [23]. After several iterations, each DMU achieves its valid boundary of efficiency.
In the input-oriented model, if DMU o is an invalid DMU, its ZSG-DEA efficiency value is θ o . The DMU o must reduce the usage of input x o . According to the ZSG-DEA model, an inefficient DMU unit must reduce a certain amount of input (or accept a certain amount of output) to become effective DEA. To keep the total amount of input (or output) unchanged, other DMU must accept a certain amount of input (or reduce a certain amount of output) in proportion to their initial input (or output) value.
In the input-oriented model, if the DMU o is a non-DEA effective decision unit, its ZSG-DEA efficiency value is φ o . To achieve DEA effectiveness, the model will reduce the input k of DMU by μ o = x ok (1 − φ o ), and distribute this reduction to other DMU in proportion (2).
In the model, all DMUs are reducing the proportion of input. After adjustment, the redistribution amount of input k to DMU i is the following formula (3).
The input-oriented BCC model is used in evaluating the relative efficiency of DMU o by the proportional increase strategy. Then the ZSG-DEA method can be expressed in the following formula (4). (3) revised, thereby keeping the total amount of x i unchanged and improving efficiency of all DMUs. In the original model, the invalid DMU is allocated its excess input in proportion to other DMUs. According to Eq. (4), some DMU may still fail to achieve DEA effectiveness. There are two solutions. One is the proportional subtraction formula proposed by Lins [23], and the other is the iterative method. The iterative method is adopted in this paper. Through multiple iterations, multiple redistribution of input k can be realized. Finally, all DMUs will reach the effective boundary. The result of multiple iterations is the optimal allocation of efficiency.
In this paper, ZSG-DEA model of Eq. (4) was used to redistribute water resources in 30 provinces of China. Figure 1 shows the ZSG-DEA unified effective boundary formation process. The initial efficiency value of DMU 1 is low. After two iterations, the input quota of DMU 1 continues to decline until it reaches a uniform effective boundary. The initial efficiency value of DMU 2 is 1. After two iterations, its input quota keeps rising and reaches a uniform effective boundary. DMU 3 does not reach the initial ZSG-DEA effective boundary, but its initial efficiency value is high. After the first iteration, its input quota increases significantly, making its efficiency value lower than the ZSG-DEA effective boundary after the first iteration. In the second iteration, its input quota must be reduced to achieve the unified ZSG-DEA effective boundary.

Background and Data Resources
According to the above analysis, the data required include water resources quantity (W), energy production (E), GDP and food production (F). In the paper, water resources are taken as model inputs, while energy output, GDP and food production are taken as model output variables. Water resource is the basic element of energy production, food growth and economic. The input of water resources in a certain region remains unchanged, and the higher the output of the three, the higher the utilization efficiency of water resources in the region; otherwise, the lower it is. DEA model is used to calculate the water efficiency of 30 provinces in China. We found that many provinces have low utilization efficiency of water resource. Then, ZSG-DEA model is used to redistribute water resources with low efficiency and repeated iterative calculations were carried out to make the efficiency values of all areas reach 1. In this case, the amount of water resources is the optimal allocation. The data sources are as follows: (1) The water resources quantity from 2014 to 2020 comes from China Statistics Yearbook (2015-2021). As shown in Fig. 2, Heilongjiang, Jiangsu, Inner Mongolia, Guangdong and Xinjiang consume the most water annually. Beijing, Tianjin, Hainan and Qinghai consume less water each year. Other provinces data are in the middle. The annual water consumption of each province is relatively stable, showing a decreasing trend year by year. The reason for higher water consumption in Inner Mongolia and Xinjiang is that they are resource-based regions, which consume a lot Fig. 1 Forming process of the uniform ZSG-DEA of water resources to exploit and produce energy, and also bring high GDP. Jiangsu and Guangdong belong to China's coastal areas, where the manufacturing industry is relatively developed. Water resources are mainly used in this industry, and water resources use efficiency is relatively high.
According to the policy of the 14th Five-Year Plan, the efficiency of water consumption in all provinces needs to be greatly improved, with the total water consumption per 10,000 yuan of GDP falling by 23%. Therefore, this paper uses the water resources supply of each region in 2020 as a reference, which is more convincing.
(2) The energy consumption of each province from 2015 to 2021 comes from China Energy Statistics Yearbook (2015-2021) and China Statistics Yearbook (2015-2021). Energy production is an important index reflecting the scale, composition and production results of energy production. According to the causes of energy, it is divided into primary energy (also known as natural energy) production and secondary energy (also known as artificial energy) production. The paper mainly collects the primary energy production of 30 provinces and cities, as shown in Fig. 3. Primary energy production refers to qualified products produced by enterprises producing primary energy during the reporting period through exploitation of existing natural energy resources in the 14th Five-Year Plan, energy production will increase by 10%.
(3) The food production of each province from 2014 to 2020 comes from China Statistics Yearbook (2012-2020). As shown in Fig. 4, Heilongjiang, Henan and Shandong are the main areas of grain production in China, with grain output increasing year by year. Hebei, Inner Mongolia, Jilin, Jiangsu, Anhui and Sichuan are in the second tier of grain production. From the national strategic point of view, Heilongjiang, Liaoning and Jilin are China's grain production bases. The amount of cultivated land must not be less than 1.8 billion mu. By 2025, grain output will increase by 15% and meet the requirements of the 14th Five-Year Plan, totaling 750 million tons. Grain production refers to the total amount of grain produced in a calendar year. It includes summer crops, early rice and autumn crops by harvest season, and cereals, legumes and tubers by crop variety.
(4) The GDP of each province from 2014 to 2020 comes from China Statistical Yearbook (2015-2021), and is converted into the value under the price level of 2015. It can be seen from Fig. 5 that GDP of different provinces and cities has shown an increasing trend in recent years. Among them, Jiangsu and Guangdong have the fastest economic development, because the manufacturing industry is relatively developed, which contributes the most to the regional economic development. At the same time, compared with Fig. 1, water consumption in the two provinces is also the largest. The GDP of each province in 2025 is forecasted according to its GDP in 2020 and annual GDP growth target in the 14th Five-Year Plan. The total GDP of 30 provinces in 2025 will be 1,289,698 billion yuan.

Results and Discussion
ZSG-DEA model of Eq. (4) was used to redistribute water resources in 30 provinces. The efficiencies are listed in Table 2. As we can see from Table 2, only 13 of the 30 provinces and cities have initial DEA efficiency value of 1, such as Beijing, Shanghai and Tianjin. There are 2 provinces and cities with efficiency values between 0.6 and 1, 5 provinces and cities with efficiency values between 0.5 and 0.6, and the rest provinces and cities with water resource efficiency values less than 0.5. The comprehensive efficiencies of water resources in Qinghai, Jiangxi, Guangxi, Guizhou and Yunnan provinces are low. It fully shows that the utilization efficiency of water resources in all provinces of China is seriously unbalanced, and there is still a big gap between the overall efficiency targets of water resources. To achieve the overall optimal efficiency of all provinces, it is necessary to reallocate water resources in all provinces. However, the efficiency value and relaxation variable of the traditional DEA model do not conform to the constraint of the established total amount. The paper introduces ZSG-DEA model to adjust the water resources quota of each province.
After three iterations, the water resource efficiency of all provinces is effective, and the value is equal to 1, as shown in Fig. 6. Theoretically, we can redistribute water resources across China's provinces. However, the allocation of water resources is mainly affected by river basins. As shown in Table 1, there are eight river basins in China. These basins affect the economic and demographic development of China's provinces. From a regional perspective, Heilongjiang, Jilin and Liaoning belong to the three provinces in northeast China, and are located near each other, mainly influenced by the Liao he River basin and Songhua River basin. The provinces of northeastern have been identified as China's most important grain production base. Grain growth is greatly constrained by water resources. Heilongjiang province's demand for water resources will reach 148.965 billion cubic There are five provinces in North China: Beijing, Tianjin, Hebei, Shanxi and Inner Mongolia. The water requirements of Beijing, Tianjin, Shaanxi and Hebei are 19.255, 13.18 and 34.526 billion cubic meters, respectively. Inner Mongolia is China's main coal production base, which will require 92.19 billion cubic meters of water. To solve the problem of water resources in North China, Beijing, Tianjin and Hebei will receive water from Jiangsu mainly through the South-to-North Water Diversion Project. The demand for water resources in Inner Mongolia can be replaced by water right trading. The water rights trading mechanism of water resources in northwest China has been relatively mature. In addition, agricultural water-saving measures can be used to replace agricultural water-saving into industrial water.
East and central of China are mainly influenced by the Yangtze River basin, from which a total of 10 provinces draws their water. Jiangsu, Zhejiang, Shandong and Henan have a high demand for water resources, which can be redeployed from the Yangtze River basin to meet the needs of industrial manufacturing. The demand for water resources in Jiangsu and Zhejiang reached 271.27 billion m 3 and 77.73 billion m 3 respectively, mainly due to the fact that two provinces are large in agriculture as well as industry. Jiangsu's GDP ranks first in China. It can allocate water resources from Hubei, Hunan and other provinces.
The overall utilization efficiency of water resources in 12 provinces of southwest, South and northwest China is not high, mainly due to the restriction of industrial structure.  Guangxi, Yunnan and Guizhou have developed tertiary industry, followed by primary and secondary industry, and their water demand is far less than that of the provinces in east China. Water resources from Guangxi can be diverted to Guangdong to meet its water demand. Water resources from Gansu, Qinghai, Xinjiang and other provinces are transferred to Inner Mongolia through allocation projects to meet the water needs of coal production and coal-chemical related industries in Inner Mongolia.

Conclusions
From the perspective of DEA value, the comprehensive efficiency value of water resources in Beijing and Tianjin reaches effective value 1. Compared with other provinces and cities, the water resource efficiency value is relatively low. The water resource efficiency values of some provinces are only between 0 and 0.5, such as Qinghai, Guangxi, Jiangxi. From Fig. 7, we can find that about 10 provinces need to make major adjustment. These provinces are mainly distributed near China's three major economic circles, which are the main undertakers of water resource consumption.
The main reason is unreasonable industrial structure and backward industrial technology. In this paper, ZSG-DEA model is used to allocate water resources in 30 provinces and regions of China from the perspective of improving distribution efficiency and watershed, and DEA effective water resources allocation scheme is obtained. But the results are far from the final answer to China's water shortages and efficient usage. The principle of fairness and efficiency must be considered in determining the distribution scheme. The distribution scheme presented can only satisfy DEA validity, but cannot reflect the fairness of distribution. As water resources are greatly affected by the basin where they are located, the basin will be affected by many other factors, and even affect the water supply of the basin.

Future Directions
It is very difficult to study the relationship between water, energy, and food resources in the framework of economy, environment, and society. Based on the equity perspective, the fairness interval of water resources allocation is determined. Then, aiming at improving DEA efficiency, fairness deviation index was added to the constraint conditions, and an allocation scheme with both fairness and efficiency could be obtained through programming solution.
Based on the paper, future research may focus on some aspects. On the one hand, the paper does not consider different industrial structures among the regions. We can choose an industry or agriculture in a high energy consumption, high water consumption industry, in-depth analysis the internal relationship of its water resources, energy, and food resources. On the other hand, we can try to combine the ZSG-DEA model with other quantitative models to study WEF nexus, such as system dynamics and full life cycle assessment model.