Environmental Production Technology

Assume there are n DMUs. Any DMU_j(j = 1,2, . . . n) uses m inputs to produce s desirable outputs. The ith input and rth output of DMU_j are denoted as x_ij and y_rj. Then the production possibility set (PPS) of DMU₀ (subscript 0 indicates the DMU being evaluated) based on the constant return to scale (CRS) assumption is expressed as follows:

(1)

From PPS Equation 1, we see that inactivity is always possible, while the finite amount of inputs should produce finite outputs not beyond the best production possibility combination. Following the idea in Fare et al. (1989), we assume β is a positive value and rewrite the PPS as:

(2)

PPS (Equation 2) is equivalent to PPS (Equation 1). However, undesirable outputs should be considered in PPS in environmental efficiency measurement. We define that the best DMU should maximize desirable output and minimize undesirable output. Denote the tth undesirable output of DMU_j as $y\mathit{tb}\text{,t=1,}\dots \text{,w}\text{.}$ Then, the PPS for any DMU₀ can be written as:

(3)

PPS (Equation 3) expresses the PPS while considering undesirable output based on constant returns to scale in which the variable 0 ≤ β^b ≤ 1 and 0 ≤ β. It is important to point out that the desirable outputs and undesirable outputs are evaluated using different variables. Also, the PPS (Equation 4) based on the variable returns to scale (VRS) assumption is formulated as follows:

(4)

Nonradial DDF

Based on the definition of PPS (Equation 3), we can construct a nonradial DDF model similar to that in Zhou et al. (2012) based on CRS to measure the performance on undesirable outputs together with that of desirable outputs. Different from the radial DDF in Chung et al. (1997), the performance of undesirable and desirable outputs are each calculated in nonradial way.

(5)

In model (Equation 5), ${\beta }_0^{}$ denotes an increase in desirable output and ${\beta }_0^b$ denotes a decrease in undesirable output. The environmental efficiency of DMU_o is defined as the optimal value $\frac{1-{\beta }_0^{b*}}{1+{\beta }_0^{*}}$. A DMU_o is environmentally efficient if and only if ${\beta }_0^{*}=0$ and ${\beta }_0^{b*}=0$.

However, the aforementioned nonradial DDF model is a nonlinear program that is difficult to resolve by using existing software. Some researchers changed the optimal function into an additive formula like ${\beta }_0^{}+{\beta }_0^b$ to convert the nonradial DDF result to a linear program. Based on the optimal values obtained, they use a second step to calculate the environmental efficiency by $\frac{1-{\beta }_0^{b*}}{1+{\beta }_0^{*}}$. Unfortunately, the environmental efficiency score obtained in this way might not be the global optimum solution (Wang et al., 2016).

Nonradial DDF based on SOCP

As shown in the research of Sueyoshi and Sekitani (2007), a nonlinear programming solution can be transformed into a linear program in the form of SOCP (see Appendix). Model (Equation 5) can be formulated into an SOCP as follows:

(6)

Model (Equation 6) is a linear programming SOCP form in which four slacks $d\mathit{tb}$, $d\mathit{iX}$, $d_0^{\psi }$, $d_0^{\delta }$ are used in the constraints for transform them into equation. The environmental efficiency of DMU₀ is ${\psi }_0^{\text{*}}$, and DMU₀ is CRS efficient if and only if ${\psi }_0^{\text{*}}=1$. It is obvious that the aforementioned nonradial DDF model is constructed based on the CRS assumption in which the scale of DMUs is assumed to be unchanged. Also, we can construct the nonradial DDF based on the VRS assumption as follows:

(7)

As the transformation ${\tau }_j^{}={\mathrm{lgr;}}_j{\delta }_0$ is used above, the additional constraint ${\displaystyle {\sum }_{j=1}^n{\tau }_j^{}}-{\delta }_0=0$ is equivalent to ${\displaystyle {\sum }_{j=1}^n{\mathrm{lgr;}}_j^{}}=1$. Based on model (Equation 7), the environmental efficiency of DMU₀ is ${\theta }_0^{\text{*}}$, and it is VRS efficient if and only if ${\theta }_0^{\text{*}}=1$.

A Numerical Example

In this section, a simple example is constructed to illustrate the use of the new models. Assume there are five DMUs, each produces one desirable output and one undesirable output by using a single input. All data are illustrated in Table 1:

Table 1.

Numerical Example With Five DMUs.

We calculate the efficiency of the five DMUs listed in Table 1 by using the traditional nonradial DDF and the model (Equation 6) based on SOCP, respectively. As mentioned earlier, the traditional way to calculate a nonradial DDF solution is to replace the $\mathit{Min}:{\theta }_0^{*}=\left(1-{\beta }_0^{b*}\right)/\left(1+{\beta }_0^{*}\right)$ by $\mathit{Max}:{\beta }_0^{b*}+{\beta }_0^{*}$. From the efficiency results shown in Table 1, we can find that the efficiency scores obtained by the two models are the same. This equivalence means that the objective function $\mathit{Max}:{\beta }_0^{b*}+{\beta }_0^{*}$ used in the traditional nonradial DDF solution is equal to the function for calculating the efficiency $\mathit{Min}:{\theta }_0^{*}=\left(1-{\beta }_0^{b*}\right)/\left(1+{\beta }_0^{*}\right)$ in some cases.

Next, we consider another numerical example with six DMUs and the data in Table 2.

Table 2.

Numerical Example With Six DMUs.

In Table 2, an additional DMU F is considered. Then, we can find that a difference in the efficiency scores of DMU E calculated by the traditional and new presented models. By using the models in Zhou et al. (2012), DMU E attains a higher optimal objective value ${\beta }_0^{b*}+{\beta }_0^{*}=0.8$, while the environmental efficiency score increases from 0.519 to 0.556. It is noteworthy that the increase of efficiency score is unreasonable because the PPS of DMUs in Table 1 is dominated by the set for DMUs in Table 2. That means the objective function $\mathit{Min}:{\theta }_0^{*}=\left(1-{\beta }_0^{b*}\right)/\left(1+{\beta }_0^{*}\right)$ for DMUs in Table 1 should be no smaller than that of Table 2. On the other hand, the new model (Equation 6) does maintain the consistency of computed results, based on which the efficiency score of DMU E is still 0.519. The aforementioned simple numerical examples illustrate the difference between our new model based on SOCP and the traditional approach; in the next section, we apply our approach to real-life data.

Empirical Study With Chinese Iron and Steel Industry Data

The Chinese iron and steel industry has grown remarkably in past 30 years; it is now the worldwide leader in the production of crude steel and it consumes about 15% of China’s national total energy. At the same time, the Chinese iron and steel industry is one of the major emitters of waste water, waste gas, and waste solids. Following China’s green development strategy and objective in the national “13th Five-Year Plan”(2016–2020), all the iron and steel makers need to shift their work from developing production to increasing environmental efficiency. In this section, we measure the environmental efficiency of 30 major steel makers in China using data for the year 2010.

Data and measures

In China, many small and medium size steel makers with heavy pollution have already merged or shut down in recent years. For this reason, we select a sample of 30 major steel makers which, combined, account for 51.3% of the national total crude steel production. All the data are gathered from China’s Iron and Steel Industry Annual Report (2011) and the China Iron and Steel Statistics Annual Report (2011).

Three indicators are used to illustrate the inputs in the production process: (X₁) Labor: the total number of full-time employees, (X₂) Energy consumption: the tons of coal equivalent of energy consumed, and (X₃) Sintering iron ore consumption: the tons of main material consumed in production. Three desirable outputs are selected to show the outputs of every steel maker: (Y₁) pig iron production: the tons of primary iron production, (Y₂) crude iron production: the tons of primary steel production, and (Y₃) finished steel production: the tons of finished steel production. Three undesirable outputs are considered to analyze the environmental efficiency performance: ( $Y_1^b$) waste water: the tons of waste water emitted, ( $Y_2^b$) Waste gas: the tons of waste gas emitted, and ( $Y_3^b$) waste solids: the tons of solid waste emitted. Descriptive statistics of the steel makers in the sample is shown in Table 3.

Table 3.

Descriptive Statistics of 30 Major Chinese Iron and Steel Makers.

Environmental efficiency measurement

For evaluating the performance on energy utilization and pollution treatment for Chinese iron and steel industry, we use the new presented nonradial DDF models to calculate the environmental efficiency of selected iron and steel sectors. The environmental efficiency results for the 30 major iron and steel makers are listed in Table 4. The environmental efficiency scores were calculated using both CRS and VRS models, and the efficiency results for desirable and undesirable outputs are shown as ${\beta }_0^{*}$ and ${\beta }_0^{b*}$, respectively. Based on CRS, more than half (17 of 30) of the steel makers are efficient based on nonradial DDF, while the others need to improve their performance by increasing desirable outputs or decreasing undesirable outputs. The scores of the inefficient steel makers show their space for performance improvement. Xinyu Iron & Steel, for example, gets an efficiency score of 0.942, which means it needs to improve its performance a relatively small amount to become efficient. In contrast, for some DMUs, such as Baotou Iron & Steel, the managers need to do much work regarding both desirable and undesirable outputs; Baotou’s environmental efficiency score of only 0.402 means it needs to increase its performance by 59.8% to become efficient. The technical efficiency results calculated by the VRS-based approach are shown in the last three columns of Table 4. We can find that most of the DMUs (22 in 30) are technically efficient, with only eight steel makers are technically inefficient. When we look at the results using the CRS approach, we find that the condition for inefficient DMUs is different. Wuhan Iron & Steel, for example, obtains an efficiency score of 0.458 based on CRS, while it is efficient based on VRS. It is clear that Wuhan Iron & Steel performed very well in technical efficiency, but it needs to change its scale efficiency to become efficient.

Table 4.

Environmental Efficiency Scores of 30 Chinese Steel and Iron Makers.

The efficiency results for desirable and undesirable outputs were determined by the new nonradial DDF method and are shown as ${\beta }_0^{*}$ and ${\beta }_0^{b*}$ in Table 4. Based on the efficiency results of the CRS model, the inefficient DMUs can be divided into three categories corresponding to their performance on desirable and undesirable outputs. Some inefficient steel makers perform poorly regarding desirable output, such as Xinyu Iron & Steel and Anyang Iron & Steel; they need to improve their desirable outputs by a proportion of ${\beta }_0^{*}$ while maintaining their undesirable outputs. Some other iron and steel makers, such as Panzhihua Iron & Steel and Lingyuan Iron & Steel, need to decrease their undesirable outputs by ${\beta }_0^{b*}$ with the present level of desirable output production. The others, such Baotou Iron & Steel and Jinan Iron & Steel, need to both increase desirable outputs and decrease undesirable outputs to achieve optimal performance improvement. Based on the VRS model, we can find that all the inefficient DMUs only need to decrease undesirable outputs to become efficient, which means that all the DMUs are technically efficient regarding desirable outputs.

Moreover, we can calculate the type of returns to scale by comparing the efficiency scores obtained based on CRS and VRS. From the last column of Table 5, we can find that all the iron and steel makers can be divided into three classes based on having Increasing Returns to Scale (IRS), Decreasing Returns to Scale (DRS), and Constant Returns to Scale (CRS). All the iron and steel makers which are efficient based on the CRS approach must be optimal in both technical and scale efficiency, and they have the CRS property. In our application study, all the inefficient DMUs perform poorly in scale efficiency and need to change their scale. Two steel makers, namely, Shuicheng Iron & Steel and Huibei Iron & Steel, exhibit DRS and need to decrease their scale to attain better scale efficiency. Most of the DMUs, however, exhibit IRS. For these steel makers, such as Baotou Iron and Steel and Lingyuan Iron & Steel, their inefficiency is partially or totally caused by their relative small scale.

Table 5.

Efficiency Results and Type of RTS of 30 Chinese Steel and Iron Makers.

Furthermore, we also calculate the target values for the inefficient DMUs to use for improvement. Based on the CRS DEA approach, the targets for the inefficient steel makers are shown in Table 6, and these targets should be used for increasing both technical and scale efficiency. Take Baotou Iron & Steel for example; it needs to increase pig iron production, crude iron production, and finished steel production to 995, 1,037, and 978, respectively, and reduce waste water, waste gas, and waste solid to 394, 779, and 10,449,413, respectively, in order to become efficient.

Table 6.

Improvement Target Values for Inefficient Steel Makers Based on CRS Model.

Environmental Efficiency Scores

This article constructs nonradial DDF models to measure environmental efficiency and applies them to evaluate the performance of 30 major Chinese iron and steel makers. The models allow evaluation of the environmental efficiency of DMUs considering the performances regarding both desirable and undesirable outputs. Different from the existing nonlinear nonradial DDF models, our new models use linear programming based on the idea of SOCP. Another advantage of our models is that they show the performance regarding desirable and undesirable outputs separately; this level of detail allows inefficient DMUs to obtain target values for both desirable and undesirable outputs to improve their performance to full efficient.

The empirical results indicate the environmental efficiency of the 30 major iron and steel makers considering three desirable outputs (pig steel, crude iron, and finished steel), together with emissions of three undesirable outputs (waste water, waste gas, and waste solids). Nearly half of the evaluated steel makers (13 in 30) are inefficient regarding technical efficiency or scale efficiency. Some of them, such as Baotou and Wuhan Iron & Steel, perform poorly with an environmental efficiency lower than 0.5. All the inefficient steel makers can be divided into three categories based on the results: Some of them need to improve their performance by increasing production of desirable outputs, while the majority needs to improve their performance by decreasing the emission of undesirable outputs by maintaining or increasing the production of desirable outputs.

By calculating the type of returns to scale, we can find that most of the inefficient steel makers exhibit increasing returns to scale. That means the inefficiency of these iron and steel sectors is caused by their small size to some extent. Moreover, the new presented models supply improvement targets for all the inefficient iron and steel makers to reach efficiency based on the performance and the existing production level of every sector.

Policies for Efficiency Improvement

Based on the empirical study, we can find that it is necessary for the government to improve the policies of efficiency. Several policies for improving the environmental efficiency of China’s iron and steel industry should be described as following:

Policy 1: The overall efficiency of China’s iron and steel industry is relatively low, while some of the major iron and steel sectors emit too much pollution at the present level of production. More attention should be paid to decrease the emission of all kinds of pollution through improving environmental efficiency or decreasing the production scale.

Policy 2: Many iron and steel makers attain relatively low environmental efficiency scores, which means that the iron and steel makers with a heavy negative influence on the environment. The large iron and steel factories should be moved out from major cities in China, as they are no longer welcome in the population centers.

Policy 3: There are significant differences on the performance of environmental efficiency between different iron and steel sectors in China. It is a possible way to improve the performance of the industry by decreasing the pollution emissions of poor performed sectors while maintaining or increasing the present level of products. Exactly values of pollution emission and products should be provided by the managers to guide the operation and allocation of resource.

Policy 4: The managers of steel industry should make different plans for improving the efficiency of poor performance steel makers based on the efficiency results rather than decrease emission of pollution only, because there are obvious differences between the performances of different steel makers and the reasons of inefficient results.

Policy 5: Expanding scale and consolidation may be good selections for resolving the problem for some steel makers as most of the steel maker are increasing return to scale or CRS.

Then, we conclude the major policies of China’s iron and steel industry during 2010 to 2018 and list them in Table 7. By comparing with the five policies mentioned earlier, we can find that most of the existing policies are focusing on controlling the emission of iron and steel industry by improving production efficiency or decreasing production scale (Policy 1). Some of them could improve the industry structure by adjusting the location or scale of iron and steel sectors (Policies 2 and 5). However, there are inadequate policies to guide the resource allocation or reallocation among different iron and steel sectors. Besides, we also find that nearly all the policy focus on guiding the action of whole industry, but few of them could consider individual characteristics.

Table 7.

Major Policies of China’s Iron and Steel Industry During 2010 to 2018.