## Abstract

Evaluating and improving water use efficiency is considered one of the main ways of tackling water shortage challenges in water-scarce cities. A useful indicator for evaluating industrial water use efficiency is the relative water use efficiency (RWUE). In this paper, an industrial RWUE evaluation scheme is proposed based on data envelopment analysis (DEA) theory. In this scheme, the RWUE is divided into overall efficiency (OE), pure technical efficiency (PTE), and scale efficiency (SE). In order to help decision-makers specify the focal industry of efficiency improvement, direct water use is distinguished from indirect water use. By employing this industrial RWUE evaluation scheme, this research calculated the industrial RWUEs for 25 representative industries of Beijing (1990–2010). Results show that the OE, PTE, and SE of Beijing have improved significantly. In the primary industry, the scale adjustment fundamentally lifted OE. For the secondary industries, there still exists much room for water use efficiency improvement in technical innovation. Some emerging tertiary industries replaced traditional tertiary industries as the most efficient water users. This study serves as a valuable reference for the implementation of the Strictest Administration of Water Resources (SAWR) of China, and provides policy-makers worldwide with a useful framework of understating industrial water use efficiency.

## Introduction

Water use efficiency was first proposed in the agriculture system. It is defined as the ratio of the amount of system output to the input or flux of water used in its production (Israelsen, 1932). In-depth research shows that the evaluation of the relative water use efficiency (RWUE) has been proven to be easier and practical in contrast with the absolute water use efficiency assessment (Zhou et al., 2008). The Chinese Government pays much attention to water use efficiency improvement but still lacks experience in implementing water resources management. In order to support robust water resources management, the State Council of China issued the Strictest Administration of Water Resources (SAWR) (State Council, 2010), in which specific restrictions were set for the total water use, the water use efficiency, and the total pollution discharge in water resources function areas. As one of the three restrictions, water use efficiency is the key to tackling the water shortage problems in water-scarce cities (Zhao et al., 2013). The restrictions are also called the three red lines that will be assessed once every five years based on specific indicators.

Beijing is a city suffering from extreme water shortage. For instance, Beijing's per capita water resources, 300 m3/capita/year, is one-thirtieth of the world's average value, far below the internationally recognized water stress threshold (1,700 m3/capita/year) (Falkenmark et al., 1989; Wang & Wang, 2005; Zhang et al., 2011). In spite of the extreme water pressure, Beijing's water use efficiency is unsatisfactory. In 2010, for example, the water use per million dollars GDP, the water use per agricultural value added, and the water use per industrial value added of Beijing were 175.05 m3/millions of US$, 5,880.48 m3/US$ and 150.51 m3/US\$, respectively (Beijing Statistical Information Net, 2010; Beijing Water Authority, 2010). Coupled with the trend that developed countries continuously transfer water-intensive products manufacturing to developing countries (such as China), it is a great challenge for Beijing to improve the water use efficiency and implement the SAWR. Since different water use industries have different production processes, improving water use efficiency essentially calls for cooperative efforts from different industries (Xu et al., 2005).

In order to solve the different water use efficiency management problems of different industries, this paper proposes an industrial RWUE evaluation scheme based on the data envelopment analysis (DEA). Moreover, this paper provides a robust investigation on the RWUEs of 25 representative industries of Beijing in 1990–2010. It will provide policy-makers with a useful framework of understating industrial water use efficiency and design specified efficiency improvement strategy in both qualitative and quantitative perspectives. The remainder of the paper is organized in the following way. Section 2 describes the industrial structure and water use status of Beijing; Section 3 provides details on the RWUE evaluation methodology; Section 4 presents the scheme's application to the 25 representative industries of Beijing (1990–2010); Section 5 discusses the implications for water resources management by taking into account the industrial structure regulation; and Section 6 includes the conclusions and limitations of this work.

## Methodology

### Basic model

DEA is a nonparametric method of measuring the relative efficiency of a decision-making unit (DMU), which has the incomparable advantage of not needing to reassign weights for multiple input and outputs (Charnes et al., 1978). Based on the DEA theory, RWUE is defined as the ratio of the minimum water input to the actual water input given a certain economic output.

Water input can be divided into direct water input and indirect water input. Direct water use is the volume of water directly used in production, such as the cooling water used in the steel industry, while indirect water is the embodied or virtual water use in the production of intermediate products (e.g., in the steel industry, the volume of freshwater that is used to produce the furnace equipment and transportation services). The sum of the direct and indirect water use equals the total water use (Chen, 2000). This division can help decision-makers to work out the efficiency difference between direct and indirect productions, which is important for water management decision-making. The minimum water input refers to the least water input that can be be used in producing the same economic output as the actual water input does.

RWUE includes three sub-concepts: overall efficiency (OE), pure technical efficiency (PTE), and scale efficiency (SE) (Lee, 2009). The OE is the ratio of the minimum water input on the efficient frontier to the actual water input under the same economic output. Therefore, the OE reflects the overall RWUE with constant returns to scale (CRS). Comparatively, when the returns to scale is variable, the measure of the OE becomes PTE. Thus, the PTE is a measure of how well water input is utilized compared to its maximum potential presented by the efficient frontier. An industry is considered as technically inefficient if it operates below the efficient frontier. The SE is related to the scale of the production. Scale inefficiency has two forms: decreasing returns to scale (DRS) and increasing returns to scale (IRS). DRS means that an industry is too large to take full advantage of its scale and has supra-optimum scale. In contrast, an industry experiencing IRS is too small for its scale to operations and, thus, operates at sub-optimum scale. An industry is scale efficient if it operates at CRS.

According to Lee (2009), the relationship of the three efficiencies is expressed as:
(1)
For simplification, it is presented as:
(2)

In terms of modeling object, DEA models can be classified into the input-oriented model and output-oriented model (Lee, 2009). This study selected the input-oriented model since we focused on the input water use efficiency during production. Various forms of DEA models have been reported in the literature, such as the CCR (Charnes, Cooper, and Rhodes) model, the BCC (Banker, Charnes, and Cooper) model, the PK (Pareto–Koopmans) model, the FDH (free disposal Hull) model, and the cross efficiency model (Charnes et al., 1985; Sexton et al., 1986; Thrall, 1999). In this paper, we chose the CCR model to measure the OE and BCC model to recognize inefficient elements from technical and scale aspects (PTE, SE).

### Evaluation index

The input and output indices (X, Y) of different industries (i.e., the primary, secondary, and tertiary industries) are determined based on the assessment indicators of the SAWR and data availability (Table 1) (Lai et al., 2006; Sun & Liu, 2009).

Table 1.

The RWUE evaluation indices.

Industry Input indices Output indices
Primary industry Proportion of fresh water use (%) Agricultural output value per cubic meter of fresh water (CNYa
Irrigation water per hectare (1,000 m3/ha) Primary industry output value per cubic meter of fresh water (CNY)
Effective irrigation area ratio (%)
Secondary industry and tertiary industry Percentage of industry water use (%) Direct income (CNY)
Direct fresh water coefficient (m3/10,000 CNY) Total income (CNY)
Total fresh water coefficient (m3/10,000 CNY)
Industry Input indices Output indices
Primary industry Proportion of fresh water use (%) Agricultural output value per cubic meter of fresh water (CNYa
Irrigation water per hectare (1,000 m3/ha) Primary industry output value per cubic meter of fresh water (CNY)
Effective irrigation area ratio (%)
Secondary industry and tertiary industry Percentage of industry water use (%) Direct income (CNY)
Direct fresh water coefficient (m3/10,000 CNY) Total income (CNY)
Total fresh water coefficient (m3/10,000 CNY)

a CNY is the standard currency symbol of the Chinese Yuan.

In the SAWR, there are three water use efficiency assessment indicators for Beijing: the water use per 10,000 CNY gross domestic products (GDP), the water use per 10,000 CNY industrial values added, and the descent proportion of the fresh water use in agriculture (Beijing Government, 2012). Our indices cover the latter two indicators. It should be noted that the direct water coefficient refers to the volume of fresh water use for per product or service in direct RWUE evaluation, while the total water coefficient is the total volume of fresh water use for per product or service in total RWUE evaluation. The total water coefficient equals to direct coefficient plus indirect coefficient. The direct wastewater discharge coefficient and total wastewater discharge are similar to them.

### The CCR model

The CCR model is used to calculate the OE. It assumes that there are n DMUs to be evaluated, each DMUj, uses m inputs and generates s outputs, and the returns to scale is constant. When the object DMU0 is under evaluation, the OE of the evaluated DMU0 equals to (Charnes & Cooper 1963):
(3)
where (x0,y0) is the actual input and output of the evaluated DMU0; is the actual input and output of one DMUj of all DMUs ; and are slack variables of DMU0 in which is the ith input redundancy and is the rth output deficiency; is the scale return combination coefficient of water inputs of DMUj. x, y, ε are known, θ, λ, S+, S are unknown.
The first two constraints of Equation (3) are set to ensure that the inputs and outputs of each DMU are enveloped in the possible production set T which is defined as:
(4)
where the envelope surface of T is the efficient production frontier.

The optimal solution of Equation (3) is θ0, λ0, S0+ and S0:

• when and , DMU0 is strongly efficient because both PTE and SE of DMU0 are efficient and achieve the best production states;

• when and at least one of is greater than zero, DMU0 is weakly efficient since PTE and SE of DMU0 cannot be efficient at the same time;

• when , DMU0 is inefficient, and neither PTE nor SE is efficient.

When DMU0 is inefficient, the projection approach could help to decrease inputs without outputs reduction in the input-oriented model, or increase outputs without inputs addition in the output-oriented model by the following equation:
(5)
where is the efficient input and output in terms of the actual input and output projected to the efficient production frontier. Therefore, input savings and output additions of can be estimated as:
(6)

### The BCC model

The PTE is estimated based on the BCC model which provides the variable returns to scale by adding the convexity constraint to , (Banker, 1984):
(7)
where is PTE of DMU0; . The optimal solution of this model is σ0, λ0, S0+, S0, whose implications can be deduced from the CCR model by analogy in Section 2.1.
The SE can be obtained from Equations (1) or (2):
(8)
• when , DMU0 is in the best scale condition which means the ratio of water input to output value is appropriate;

• when , the water input or output of DMU0 requires adjustments with reference to of the CCR model.

(9)

Whether the returns to scale is constant, increasing, or decreasing depends on whether is equal, less than, or greater than 1. The constant returns to scale means input and output change in the same proportion; the increasing returns to scale means the output changes faster than the input; and decreasing returns to scale means the output changes more slowly than the input.

## Result analysis

This paper applied the industry RWUE evolution scheme to the RWUE evaluation of 25 representative industries of Beijing from 1990 to 2010. In this section, data description and industry background of Beijing are first introduced, and the detailed result analyses of the primary, secondary, and tertiary industries are expanded, individually.

### Data description

Since 1949, two major economic regulations have been implemented in China. The first is the socialist transformation that occurred in the 1950s, and the second is the market-oriented reform between the 1980s and the 1990s (Liu & Li, 2002). In order to investigate the ‘natural’ correspondence between economic development and water use efficiency change, such human intervention periods were avoided so that the evaluation period of this research was chosen as 1990–2010. Moreover, all economy and water use data are cited from the Beijing Statistical Yearbook (Beijing Statistical Information Net, 2010) and Beijing Water Resources Bulletin (Beijing Water Authority, 2010). The 25 representative industries were extracted from the 44 major industries of China based on the latest National Industry Classification standards as well as the data availability after the years' industrial classification changes (National Bureau of Statistics of China, 2011) (Table 2). The price impact can be neglected in the RWUE evaluation scheme because it compares the relative efficiencies of different industries at the same time.

### Industry background of Beijing

#### Industrial structure

Figure 1 describes the industrial structure changes of Beijing in 1990–2010. Generally, the added values' proportions of the primary and secondary industries decline, while the proportion of the tertiary industry keeps rising. This tendency is consistent with the theory of industrial structure upgrading, which refers to that when the economy development reaches a certain level, the secondary industry would be replaced by the tertiary industry as the dominant industry. It also shows that the industrial structure of Beijing had been progressing in a positive tendency (Liu & Li, 2002).

At the same time, different industries went through different internal structure changes. For the primary industry, the proportion of farming reduced with the fishing and animal husbandry expansion, and grain crops declined while economic crops emerged. For the secondary industry, its internal structure change is elaborated in Figure 2. In the 1990s, the major secondary industries were light industry and low-tech heavy industry such as the 4th food manufacturing, the 6th paper industry, and the 9th chemical industry. Then with the industrial structure upgrading after 2000, infrastructure industry and high-tech industry grew quickly. For instance, the output proportions of the 14th transportation industry and the 18th electricity and heat production and supply industry increased, and the 16th electronic equipment manufacturing became the dominant industry with the maximum added value proportion.

Limited to data continuity, the internal structure change of the tertiary industry was only analyzed for the period of 2000–2010. In Figure 3, the added value proportions of traditional service industries, including the 19th transportation, warehousing and postal services, the 21st wholesale and retail industry, and the 22nd accommodation and catering industry, first decreased and then remained at 30% in total. In contrast, the emerging service industries, such as the 20th information and IT services, the 23rd financial industry, the 24th real estate industry, and the 25th business service, extended to an enormous scale in total, accounting for 70% by 2010. In the future, the industrial structure of Beijing is expected to be: to cultivate modern service industry and high-tech industry which will become dominant industries; modern manufacturing industry and infrastructure service industry will be highlighted; and urban industry and modern agriculture will be regarded as supplements (Beijing Municipal Commission of Development and Reform, 2007).

#### Water use

Figure 4 shows that Beijing's water use experienced an increasing-decreasing-stabilized change tendency. The total water use fell below 40 million m3 after 1996 and remained stable at 35 million m3 after 2002. Specifically, the agricultural and industrial water use decreased significantly, while the domestic and environmental water use rose. This reveals that the water use structure modification benefited from the industrial structure modification (Jia et al., 2004).

### RWUE in primary industry

As illustrated in Table 2, the primary industry is represented by one comprehensive industry, agriculture/forestry/animal husbandry/side-line production/fishing. Figure 5 shows that this representative industry's OE kept increasing and reached a strongly efficient position in 2010 (OE = PTE = SE = 1.0). Meanwhile, the PTE and the SE also reached the optimum by 2010. It is notable that Beijing's primary industry PTE always stayed at a very high level with a mean value of 0.85. Such good performances actually benefited from the clear agricultural zoning of the modern agriculture strategy and the ‘high-end’ industry development policy (Wang & Wang, 2009). Moreover, the rapid growth of the SE should not be overlooked. The reason behind it is that, in 1990–2009, the returns to scale of Beijing's primary industry kept decreasing due to agricultural scale reduction.

### RWUE in secondary industry

#### OE analysis

Figures 6 and 7 respectively summarize the direct and total OE of the secondary industry in 1990, 1992, 2000, 2005, and 2010. Generally speaking, except the 13th industry, all representative industries receive significant OE increases (direct and total). However, by 2010, only two industries reached direct OE efficiency (direct OE = 1), and six industries reached total OE efficiency (total OE = 1).

Furthermore, a detailed comparison between direct OE and total OE was conducted for the year 2010 (Table 3). It can help decision-makers to work out which water using section (i.e., direct or indirect) should be paid more attention in efficiency improvement. The comparison results were classified into three types as follows:

• Type I: the direct OE is better than the total OE. There are 11 industries in Type I, accounting for 64.71% of the secondary industries, characterized by low efficiencies. The 4th, 5th, 6th, and 8th industries are priority industries of the light industry; the 9th, 10th, 11th, 12th, 13th, 14th and 18th industries belong to traditional heavy industry. Their direct production utilized water more efficiently than the indirect processes so that the priority attention should be paid to the indirect production in the future (Wang, 2006). However, the direct efficiency improvement cannot be ignored since their direct OEs were relatively low compared with other industries of Type II and III.

• Type II: the direct OE is worse than the total OE. There are four industries in Type II accounting for 23.53% of the secondary industries utilizing input water more efficiently than those of Type I. Although they are water-intensive industries, they occupied the least GDP market share of Beijing. Moreover, Beijing only participated in the technology-intensive links rather than labor-intensive links such as transportation and technical deep processing so that they achieved relatively high efficiency (Xu et al., 2005). Further, future efforts should be paid to the direct water use production section, if it exists, to improve the OE.

• Type III: the direct OE and the total OE are ideal. The direct OE and the total OE of the 7th and 16th industries reached efficiency. The 7th wood industry accounted for no more than 1% of GDP of Beijing in 2010, while the 16th electronic industry developed rapidly with GDP proportion increase from 5% in 1994 to 15% in 2010. Moreover, the electronic industry usually uses a small amount of water in a super-efficient and high-tech way, so its OE had been efficient since 2000 compared with other secondary industries.

#### PTE and SE analysis

Figures 8 and 9 summarize the direct and total PTE and SE of the representative secondary industries in 1990, 2000, and 2010. From both direct and total perspectives, all industries' PTE and SE received increases with time. In particular, most industries got higher SE than PTE. Therefore, the overall inefficiency in these industries is primarily attributed to the technical inefficiency rather the scale inefficiency. This confirms the problem that the secondary industry of Beijing is ‘big’ but not ‘strong’, which was concluded by Zou & Ouyang (2008) as well.

From the output scale perspective, incoming was already satisfactory for most industries in 2010, especially in direct production. It means that the economic scale of these industries had been maximized through the vigorous economic development in the last two decades. However, managers have to divert attention to the technical development in order to improve water productivity. This is also forced by the water supply capacity and industrial scale limit of Beijing. Although it was previously proved that Beijing has achieved encouraging progress in water-saving through technical innovation (Yang et al., 2015), there is still much room for improvement in efficiency for more than half of the secondary industries under the existing production scale (Figures 8 and 9).

In order to find out the specialized water input adjustment strategies for different industries, the total OE of inefficient DMUs of the secondary industries in 2010 was projected (as shown in Table 4). For inefficient industries, the water use percentage and total fresh water coefficient were excessive and could be reduced with the proportion of . The decreasing return to scale means that, with water input decrease and water use coefficient decrease, the economic output decrease proportion was less than the input decrease so that reducing water input and water use coefficient will lead to economic output efficiency reduction, but the water-saving cost is considerable and worthwhile.

Table 2.

The number and industry names of 25 representative industries of Beijing.

Industry classification No. Industry name
Primary industry Agriculture/forestry/animal husbandry/side-line production/fishing
Coal mining and dressing industry
Metal mining and dressing industry
Food manufacturing
Textile industry
Leather, fur, feathers and their products and footwear industry
Wood processing and wood, bamboo, rattan, brown, grass products industry
Paper and paper products industry
Chemical materials and chemical products manufacturing industry
10 Non-metallic mineral products industry
11 Metal smelting and rolling processing industry
12 Fabricated metal products
13 General equipment manufacturing
Secondary industry 14 Transportation equipment Manufacturing
15 Electrical machinery and equipment manufacturing
16 Electronic equipment manufacturing
17 Instrument manufacturing
18 Electricity, heat production and supply industry
Tertiary industry 19 Transportation, warehousing and postal services industry
20 Information transmission, software and IT services industry
21 Wholesale and retail industry
22 Accommodation and catering industry
23 Financial industry
24 Real estate industry
Industry classification No. Industry name
Primary industry Agriculture/forestry/animal husbandry/side-line production/fishing
Coal mining and dressing industry
Metal mining and dressing industry
Food manufacturing
Textile industry
Leather, fur, feathers and their products and footwear industry
Wood processing and wood, bamboo, rattan, brown, grass products industry
Paper and paper products industry
Chemical materials and chemical products manufacturing industry
10 Non-metallic mineral products industry
11 Metal smelting and rolling processing industry
12 Fabricated metal products
13 General equipment manufacturing
Secondary industry 14 Transportation equipment Manufacturing
15 Electrical machinery and equipment manufacturing
16 Electronic equipment manufacturing
17 Instrument manufacturing
18 Electricity, heat production and supply industry
Tertiary industry 19 Transportation, warehousing and postal services industry
20 Information transmission, software and IT services industry
21 Wholesale and retail industry
22 Accommodation and catering industry
23 Financial industry
24 Real estate industry
Table 3.

Comparison between direct OE and total OE in 2010.

Type Percentage No. Industry name Direct OE Total OE
I. Direct OE is higher than total OE 64.71 Food manufacturing 0.25 0.03
Textile industry 0.46 0.06
Leather, fur, feathers and their products and footwear industry 0.85 0.36
Paper and paper products industry 0.69 0.31
Chemical materials and chemical products manufacturing industry 0.32 0.10
10 Non-metallic mineral products industry 0.34 0.14
11 Metal smelting and rolling processing industry 0.26 0.06
12 Fabricated metal products 0.78 0.58
13 General equipment manufacturing 0.39 0.19
14 Transportation equipment manufacturing 0.48 0.28
18 Electricity, heat production and supply industry 0.04 0.00
II. Direct OE is lower than total OE 23.53 Coal mining and dressing industry 0.94 1.00
Ferrous metal mining and dressing industry 0.24 1.00
15 Electrical machinery and equipment manufacturing 0.65 1.00
17 Instrument manufacturing 0.80 1.00
III. Direct OE is identical with total OE 11.76 Wood processing and wood, bamboo, rattan, brown, grass products industry 1.00 1.00
16 Electronic equipment manufacturing 1.00 1.00
Type Percentage No. Industry name Direct OE Total OE
I. Direct OE is higher than total OE 64.71 Food manufacturing 0.25 0.03
Textile industry 0.46 0.06
Leather, fur, feathers and their products and footwear industry 0.85 0.36
Paper and paper products industry 0.69 0.31
Chemical materials and chemical products manufacturing industry 0.32 0.10
10 Non-metallic mineral products industry 0.34 0.14
11 Metal smelting and rolling processing industry 0.26 0.06
12 Fabricated metal products 0.78 0.58
13 General equipment manufacturing 0.39 0.19
14 Transportation equipment manufacturing 0.48 0.28
18 Electricity, heat production and supply industry 0.04 0.00
II. Direct OE is lower than total OE 23.53 Coal mining and dressing industry 0.94 1.00
Ferrous metal mining and dressing industry 0.24 1.00
15 Electrical machinery and equipment manufacturing 0.65 1.00
17 Instrument manufacturing 0.80 1.00
III. Direct OE is identical with total OE 11.76 Wood processing and wood, bamboo, rattan, brown, grass products industry 1.00 1.00
16 Electronic equipment manufacturing 1.00 1.00
Table 4.

The input redundancy and scale returns of the secondary industry of 2010.

No. Industry name   Scale returns
Food manufacturing 6.15 239.73 Decreasing
Textile industry 2.52 187.27 Decreasing
Leather, fur, feathers and their products and footwear industry 0.54 75.27 Decreasing
Paper and paper products industry 1.71 51.52 Decreasing
Chemical materials and chemical products manufacturing industry 10.63 78.86 Decreasing
10 Non-metallic mineral products industry 4.44 78.25 Decreasing
11 Metal smelting and rolling processing industry 8.23 137.74 Decreasing
12 Fabricated metal products 0.60 48.48 Decreasing
13 General equipment manufacturing 3.04 45.54 Decreasing
14 Transportation equipment manufacturing 2.97 53.76 Decreasing
18 Electricity, heat production and supply industry 10.88 2.56 Decreasing
No. Industry name   Scale returns
Food manufacturing 6.15 239.73 Decreasing
Textile industry 2.52 187.27 Decreasing
Leather, fur, feathers and their products and footwear industry 0.54 75.27 Decreasing
Paper and paper products industry 1.71 51.52 Decreasing
Chemical materials and chemical products manufacturing industry 10.63 78.86 Decreasing
10 Non-metallic mineral products industry 4.44 78.25 Decreasing
11 Metal smelting and rolling processing industry 8.23 137.74 Decreasing
12 Fabricated metal products 0.60 48.48 Decreasing
13 General equipment manufacturing 3.04 45.54 Decreasing
14 Transportation equipment manufacturing 2.97 53.76 Decreasing
18 Electricity, heat production and supply industry 10.88 2.56 Decreasing
Fig. 1.

The industrial structure of Beijing in 1990–2010.

Fig. 1.

The industrial structure of Beijing in 1990–2010.

Fig. 2.

The representative secondary industrial structure of Beijing in 1990–2010.

Fig. 2.

The representative secondary industrial structure of Beijing in 1990–2010.

Fig. 3.

The representative tertiary industrial structure of Beijing in 2002–2010.

Fig. 3.

The representative tertiary industrial structure of Beijing in 2002–2010.

Fig. 4.

The water use structure of Beijing in 1990–2010.

Fig. 4.

The water use structure of Beijing in 1990–2010.

Fig. 5.

The RWUE of the primary industry in 1990–2010.

Fig. 5.

The RWUE of the primary industry in 1990–2010.

Fig. 6.

Direct OE of the secondary industry in 1990, 1997, 2000, 2005, and 2010.

Fig. 6.

Direct OE of the secondary industry in 1990, 1997, 2000, 2005, and 2010.

Fig. 7.

Total OE of the secondary industry in 1990, 1997, 2000, 2005, and 2010.

Fig. 7.

Total OE of the secondary industry in 1990, 1997, 2000, 2005, and 2010.

Fig. 8.

Direct PTE and SE in 1990, 2000, and 2010. Note: The peripheral number is industry number. 0–1 is the relative efficiency value ranges in bold. OE is drawn in an ascendant order.

Fig. 8.

Direct PTE and SE in 1990, 2000, and 2010. Note: The peripheral number is industry number. 0–1 is the relative efficiency value ranges in bold. OE is drawn in an ascendant order.

Fig. 9.

Total PTE and SE in 1990, 2000, and 2010.

Fig. 9.

Total PTE and SE in 1990, 2000, and 2010.

### RWUE in tertiary industry

For the tertiary industries, it is difficult to conduct a continuous efficiency analysis during a long time period. This is because of the significant changes in the industry classification according to the National Industry Classification. Therefore, we herein computed the direct OEs and indirect OEs in two years, 1990 and 2010 (Figures 10 and 11).

Fig. 10.

The tertiary industry's OEs of 1990.

Fig. 10.

The tertiary industry's OEs of 1990.

Fig. 11.

The tertiary industry's OEs of 2010.

Fig. 11.

The tertiary industry's OEs of 2010.

According to Figures 10 and 11, from 1990 to 2010, the OE efficient industry (i.e., finance and insurance industry) was replaced by the 20th information and IT industry and the 21st wholesale and retailing industry. It means that, with market requirement changes, emerging high-tech information services and modern commerce services gradually surpassed traditional industry to be the most efficient water users. However, huge efficiency gaps existed among different industries in the same year. Specifically, in 2010, the water use efficiency of traditional tertiary industry (transportation and catering) and some emerging industry (real estate) had the lowest efficiencies among representative tertiary industries, and the previously leading efficient industry (financial industry) fell behind the 20th and 21st industries in 2010. There are three main reasons for that. The first reason is that some basic service sectors are monopolized by the country-owned enterprises of China, such as transportation and financial industry. This places these sectors under the uncompetitive operation mechanism, causing water use inefficiency. Second, for small-scale industry (e.g., accommodation and catering industry), the industry admittance standard is low and operation supervision is not easily carried out, so water use efficiency cannot be guaranteed. The third reason is related to the incomplete industry admittance and supervision regulations.

The projection results for the inefficient DMUs in 2010 are shown in Tables 5 and 6. For direct production, the water use of the financial industry and business services should be reduced (Table 5). For indirect production, in spite of the wholesale industry, all tertiary industries have room for great efficiency improvement (Table 6).

Table 5.

The input redundancy and scale returns of the tertiary industry of 2010 (direct OE).

No. Industry name  Rank   Scale returns
19 Transportation, warehousing and postal services industry 0.06 Decreasing
20 Information transmission, software and IT services industry 1.00 Constant
21 Wholesale and retail industries 1.00 Constant
22 Accommodation and catering industry 0.06 Decreasing
23 Financial industry 0.09 0.76 Decreasing
24 Real estate industry 0.13 Decreasing
25 Leasing and business services 0.59 2.53 Decreasing
No. Industry name  Rank   Scale returns
19 Transportation, warehousing and postal services industry 0.06 Decreasing
20 Information transmission, software and IT services industry 1.00 Constant
21 Wholesale and retail industries 1.00 Constant
22 Accommodation and catering industry 0.06 Decreasing
23 Financial industry 0.09 0.76 Decreasing
24 Real estate industry 0.13 Decreasing
25 Leasing and business services 0.59 2.53 Decreasing
Table 6.

The input redundancy and scale returns of the tertiary industry of 2010 (total OE).

No. Industry name  Rank   Scale returns
19 Transportation, warehousing and postal services industry 0.07 0.86 Decreasing
20 Information transmission, software and IT services industry 0.34 1.70 Constant
21 Wholesale and retail industries 1.00 Constant
22 Accommodation and catering industry 0.04 0.60 Decreasing
23 Financial industry 0.29 8.52 Decreasing
24 Real estate industry 0.17 2.17 Decreasing
25 Leasing and business services 0.87 10.28 Decreasing
No. Industry name  Rank   Scale returns
19 Transportation, warehousing and postal services industry 0.07 0.86 Decreasing
20 Information transmission, software and IT services industry 0.34 1.70 Constant
21 Wholesale and retail industries 1.00 Constant
22 Accommodation and catering industry 0.04 0.60 Decreasing
23 Financial industry 0.29 8.52 Decreasing
24 Real estate industry 0.17 2.17 Decreasing
25 Leasing and business services 0.87 10.28 Decreasing

## Implications for water resources management

The above RWUE analysis proves that all the industries of Beijing achieved significant water use efficiency improvements from 1990 to 2010, but there are some deep-seated efficiency problems within inefficient industries. In order to effectively implement the SAWR as well as continuously support economic development, we proposed explicit efficiency improvement directions for different water-using industries, separately, as follows.

For the primary industry, highlighting virtual water importing and upgrading agricultural production can help to increase water conductivity. By 2007, the volume of the imported virtual water of Beijing was 237 million m3, accounting for 5.93% of the total fresh water use of Beijing. In consideration of this situation, virtual water trade serves as a key factor to improve efficiency by importing low-efficiency crops and developing high-efficiency agriculture (Wang et al., 2007). Moreover, promoting ecologic and tourism agriculture and broadening the foreign market with featured agricultural products can accelerate agricultural economic growth as well as increase the water use efficiency.

For the secondary industry, PTE should be given the priority in improving efficiency, and SE can be modified by taking into account the industrial structure regulations. Driven by the GDP-oriented development mode, some managers did not pay enough attention to technical innovation. However, based on our findings, more effort should be spent on technical aspects in both direct and indirect productions, for example, upgrading existing water-saving equipment and making use of unconventional water resources (i.e., recycled water, desalinated seawater, and rainwater). As for the scale modification, it is beneficial to encourage electronics, biomedicine, new energy, environmental protection industry and high-tech industry, and to eliminate the water-intense and low value-added industry, fostering certain famous brands instead of enlarging industry scales.

For the tertiary industry, the efficiency gaps among different industries can be made up by strengthening efficiency regulations and taking advantage of the market competition mechanism. Although the modern service industry has gradually become the dominant industry of Beijing, the water use efficiencies of some modern service industries were still inefficient, e.g., real estate industry and financial industry. It is necessary to tighten the industrial admittance criteria and strengthen operation supervision on water use efficiency for the traditionally scattered industry and some rapid-developing industries. Additionally, it is also important to employ the market competition mechanism to attract external high-efficiency projects, processes, and products, breaking the existing industrial monopoly.

## Conclusions and limits

In order to solve the differentiated water use efficiency management problems among economic industries, this paper proposed an industry RWUE evaluation scheme based on the DEA theory. This industrial RWUE evaluation scheme has two advantages for decision-making in water resources management, especially in implementing the SAWR. First, it can qualitatively specify an efficiency improvement emphasis among direct and indirect production processes from the technical and scale perspectives. Second, for each inefficient water-using industry, the industrial RWUE evaluation scheme can provide a quantitative input and output slack to enforce target assessment and fulfillment. As to the SAWR, two of its three water use efficiency assessment indicators were included in the input indices of the scheme. This can greatly facilitate policy implementation based on the industrial water efficiency assessment using the RWUE evaluation scheme.

Applying the RWUE evaluation scheme, this research evaluated the RWUEs of 25 representative industries of Beijing during 1990–2010. The main conclusions that can be drawn are as follows. (1) The RWUEs of all industries were markedly increased. (2) For primary industry, the future efficiency improvement can rely on importing virtual water and developing modern agriculture. (3) For secondary industry, the industrial production process (direct or indirect) plays an important role in water use efficiency. The future efficiency improvement emphases of secondary industry are technology innovation and scale modification under industrial structure regulations. (4) As for tertiary industry, some emerging industries replaced the traditional industries as the most efficient water users, but efficiency gaps existed among the industries. Attention should be paid by managers to legislation and supervision implementation, and market competition utilization in the future.

Regretfully, there are two limitations existing in this study. The first one is that it lacks the ability to add the absolute water use efficiency into the evaluation scheme. This is due to the restriction of the DEA method, in which the DEA can only calculate the relative efficiency. Moreover, the RWUE evaluation scheme is not robust enough to support the implementation of China's SAWR. This is because the scheme does not consider one indicator in the SAWR (i.e., the water use per 10,000 CNY GDP). In the future, further attempts should be made to deal with these limitations.

## Acknowledgments

This study was supported by the National Natural Science Foundation of China (Grant No. 51879010, 51479003) and the 111 Project (Grant No. B18006).

## References

References
Banker
R. D.
, (
1984
).
Estimating most productive scale size using data envelopment analysis
.
European Journal of Operational Research
17
(
1
),
35
44
.
Beijing Government
(
2012
).
Suggestions on Implementation of the Strictest Administration System of Water Resources
.
Beijing Municipal Commission of Development and Reform
(
2007
).
Guidance on the Industrial Structure Modification of Beijing
.
Beijing Statistical Information Net
(
2010
).
Beijing Statistical Yearbook
.
http://www.bjstats.gov.cn/tjsj/ (retrieved 31 January 2014)
.
Beijing Water Authority
(
2010
).
Beijing Water Resources Bulletin
. .
Charnes
A.
&
Cooper
W. W.
, (
1963
).
Deterministic equivalents for optimizing and satisficing under chance constraints
.
Operations Research
11
(
1
),
18
39
. doi.10.1287/opre.11.1.18.
Charnes
A.
,
Cooper
W. W.
&
Rhodes
E.
, (
1978
).
Measuring the efficiency of decision making units
.
European Journal of Operational Research
2
(
6
),
429
444
.
Charnes
A.
,
Cooper
W. W.
,
Golany
B.
,
Seiford
L.
&
Stutz
J.
, (
1985
).
Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions
.
Journal of Econometrics
30
(
1
),
91
107
.
Chen
X. K.
, (
2000
).
Shanxi Water Resource Input-Occupancy-Output Table and its Application in Shanxi Province of China
.
Thirteenth International Conference in Input-Output Techniques
,
Macerata
,
Italy
.
Falkenmark
M.
,
Lundqvist
J.
&
Widstrand
C.
, (
1989
).
Macro-scale water scarcity requires micro-scale approaches. aspects of vulnerability in semi-arid development
.
Natural Resources Forum
13
(
4
),
258
267
.
Israelsen
O. W
, . (
1932
).
Irrigation Principles and Practices
,
1st edn
.
John Wiley & Sons
,
New York
,
USA
,
422
pp.
Jia
S. F.
,
Zhang
S. F.
,
Xia
J.
&
Yang
H.
, (
2004
).
Effect of economic structure adjustment on water saving
.
Journal of Hydraulic Engineering
3
,
111
116
(in Chinese with English abstract)
.
Lai
H. L.
,
Wang
D. X.
&
Wu
D. F.
, (
2006
).
Comprehensive assessment indicator system for water resources and its development and use
.
17
(
1
),
95
101
(in Chinese with English abstract)
.
Lee
C. C.
, (
2009
).
Analysis of overall technical efficiency, pure technical efficiency and scale efficiency in the medium-sized audit firms
.
Expert Systems with Applications
36
(
8
),
11156
11171
. doi.10.1016/J.ESWA.2009.02.092.
Liu
W.
&
Li
S. R.
, (
2002
).
Industrial structure and economic growth
.
China Industrial Economy
5
,
14
21
(in Chinese with English abstract)
.
National Industry Classification Standard
(
2011
).
National Bureau of Statistics of China
.
http://www.stats.gov.cn/tjbz/hyflbz/ (in Chinese with English abstract).
Sexton
T. R.
,
Silkman
R. H.
&
Hogan
A. J.
, (
1986
).
Data envelopment analysis: critique and extensions
.
New Directions for Program Evaluation
1986
(
32
),
73
105
.
State Council
(
2010
).
Decision of the State Council and the Central Military Commission on Developing Water Conservancy Reforming of the People's Republic of China
.
State Council of the People's Republic of China
,
Beijing
,
China
.
Sun
C. Z.
&
Liu
Y. Y.
, (
2009
).
Analysis of the spatial-temporal pattern of water resources utilization relative efficiency based on DEA-ESDA in China
.
Resource Science
31
(
10
),
1696
1703
(in Chinese with English abstract)
.
Thrall
R. M.
, (
1999
).
What is the economic meaning of FDH?
Journal of Productivity Analysis
11
(
3
),
243
250
.
Wang
Q. S.
, (
2006
).
Beijing 11th Five-Year Plan Report Beijing: The 4th Meeting of the 12th Beijing People's Congress
(in Chinese)
.
Wang
H.
&
Wang
Y.
, (
2009
).
An input–output analysis of virtual water uses of the three economic sectors in Beijing
.
Water International
34
(
4
),
451
467
.
Wang
H. R.
,
Dong
Y. Y.
,
Wang
J. H.
,
Wang
Y.
&
Han
Z. X.
, (
2007
).
Distribution of virtual water of crops in Beijing
.
Environmental Science
28
(
11
),
2432
2437
(in Chinese with English abstract)
.
Xu
F. R.
,
Chen
L. T.
,
Zhang
C. L.
&
Sun
J.
, (
2005
).
Analysis on the relationship between industrial structure and water use in Beijing city
.
Journal of China Institute of Water Research and Hydropower Research
3
(
4
),
258
263
(in Chinese)
.
Yang
Z. W.
,
Liu
H. L.
,
Yang
T. T.
&
Xu
X. Y.
, (
2015
).
A path-based structural decomposition analysis of Beijing's water footprint evolution
.
Environmental Earth Sciences
74
(
3
),
2729
2742
.
Zhang
Z.
,
Yang
H.
&
Shi
M.
, (
2011
).
Analyses of water footprint of Beijing in an interregional input–output framework
.
Ecological Economics
70
(
12
),
2494
2502
.
Zhao
J. S.
,
Cai
X. M.
&
Wang
Z. J.
, (
2013
).
Comparing administered and market-based water allocation systems through a consistent agent-based modeling framework
.
Journal of Environmental Management
123
,
120
130
.
Zhou
P.
,
Ang
B. W.
&
Poh
K. L.
, (
2008
).
A survey of data envelopment analysis in energy and environmental studies
.
European Journal of Operational Research
189
(
1
),
1
18
.
Zou
D. T.
&
Ouyang
R. H.
, (
2008
).
Report on China Economic Development and Institutional Reform
.