Running Efficiency and S&T Contribution to Regional Wastes' Treatment in China based on Parallel and Two-stage DEA models

In this study, we apply parallel and two-stage DEA models to measure the running efficiency and S&T contribution to regional wastes' treatment in China. The process of harshly development in industry often sacrificed natural living environment of human being. Because of greenhouse effect, poor air and water quality, improper disposed solid waste and other environmental pollution problems, regional environment are bearing tremendous pressure. To relieve pressure on environment and keep sustainable development in China, decision makers begin to focus on the optimal measures of ecological environment. A novel parallel and two-stage DEA models were applied to evaluate the efficiency of regional wastes' treatment in China. While the status of wastes can be divided into three types, i.e. waste water, gas and solid wastes, we classified different types of treatments into three modes. Then, the multiple parallel DEA methodology is applied to calculate the treatment efficiency of these three modes of wastes' treatment in 30 provincial regions in China. Taking S&T inputs as a pivotal effect on wastes' treatments, two-stage DEA model was applied to calculate S&T contribution rate to wastes' treatment in 30 provincial regions in China. Based on the calculation results, decision making information can be drawn for each region in China and.


INTRODUCTION
Since 1970s, the old Soviet mode had been applied which mainly enlarged the inputs, especially labor and capital, in China and had already pushed China's economy development. In that process, natural environment and limited resources were sacrificed to pursue economy's rapid development. With the influence of global greenhouse effect and serious pollution, decision makers began to transfer traditional production mode into environmental friendly development mode and emphasis on the capability of wastes' treatments. Generally, based on the status of wastes, we can classify wastes into three different modes, i.e., waste gas, waste water and solid wastes. The treatments of the three types of wastes are pivotal measures to build regions with more environmentally friendly.
Water quality management issues were discussed in Oregon, USA and proposed constructive measures to enhance the capability of waste water's treatment (Sharon et al., 1991). At the same time, other two types of wastes, waste gas and solid wastes, also take important roles in ecological environment. A coordination of Energy-Economy-Environment System should be expressed by the close relationship between energy, economy and environment (Heshan et al., 2011). The evaluation of wastes' treatment should be applied to identify the development level of ecological optimization. Many statistical methodologies can be applied to calculate ecological indicators (Paul, 1996). In fact, the treatment processes of waste gas, waste water and solid wastes are parallel systems where little interaction exists among those three systems. At the same time, all three processes cover the major aspects of wastes' treatment. Based on the parallel structure of three types of wastes' treatment, we applied parallel DEA to calculate the running efficiency and provide regional information of wastes' treatments to the decision makers. To identify the effect of S&T on wastes' treatment, two-stage DEA model was applied to measure the contribution of S&T to wastes' treatments.

Structure and indexes of wastes' treatments:
In general, we candivide all of wastes in three types, denoted as waste gas, waste water and solid wastes. To optimize the eco-environment, we also should apply Table 1: Indexes for each of waste treatments   Treatment   Indexes  ---------------------------------------------------------------------------------------------------------------------------------------------------------------------Inputs Outputs Waste gas treatment Total volume of industrial waste GasEmission (100 million cu.m) Number of facilities for treatment of waste gas (set) Volume of industry sulphur dioxide removed (10 000 tons) Volume of industrial Soot Removed (10 000 tons) Volume of industrialDust removed (10 000 tons) Waste water treatment Total volume ofwaste water discharge in industry (10 000 tons) Number of facilities fortreatment of waste water (set) Consumption waste water discharge (10 000 tons) Industrial waste water meeting dischargeStandards (10 000 tons) Solid wastes treatment Volume of industrial solid wastes Produced (10 000 tons) Volume of industrial solid wastes utilized (10 000 tons) Volume of industrial solid wastes in stocks (10 000 tons) Volume of industrialsolid wastes treated (10 000 tons) corresponding treatment measures in these three types wastes (Xiong et al., 2007;Kai-ya et al., 2005). Because three types of wastes are existed in different forms, the treatment of them is expressed as parallel measures. Then, we divided the optimization of ecoenvironment into three parallel processes, i.e., waste gas treatment, waste water treatment and solid wastes' treatment (Yong and Qing, 2005). If we take each of waste treatment as a sub-system, there are multiple indexes can be listed to measure the efficiency of each process of waste treatments (Yao-bin et al., 2005) in the view of multiple inputs and outputs. The indexes can be shown on Table 1. For waste gas treatment, we use 1 input and 4 outputs index to interpret the sub-system's efficiency. For waste water treatment, we design 2 inputs and 2 outputs to explain the efficiency of sub-system. For solid wastes' treatment, we apply 1 input and 3 outputs to measure the sub-system's efficiency. Multiple parallel DEA model: DEA model CCR (Charnes et al., 1978) was applied an optimal linear programming formula to calculate efficiency of DMUs. Suppose we have n DMUs and that kth k DMU (k = 1, 2, …, n) has m inputs, denoted as ik x (i = 1, 2, …, m) and s outputs, denoted as rk y (r = 1, 2, …, s). The traditional CCR DEA model can be expressed by the following formula (1): By calculating with DEA models, the optimal weights can be allocated for each DMU, denoted as * * * * 1 2 ( , ,..., ) , which guarantee the kth DMU with the maximum efficiency value. If the objection of model (1) equals to 1, then the DMU is denoted as DEA efficient DMU. If the objection of model (1) is less than 1, then the DMU is denoted as DEA inefficient DMU. DEA models have obvious advantages in measure the performance of multiple inputs and outputs system. However, traditional DEA models take system as a black box and ignore the internal structure of system.
In general, the inside of DMU can be classified in different structures and the internal structure can affect the overall efficiency of whole system. For each of subsystems, its efficiency has close relationship to overall efficiency. In this study, we will use the DEA model to deal with parallel sub-system structures.
To overcome the shortcomings of traditional DEA models, parallel DEA model (Chiang, 2009) was proposed for measuring the relationship between subsystems and DUM. Firstly, we will explain the parallel structure. For each of DMUs, there are q sub-systems, denoted as sub-system 1, sub-system 2, ..., sub-system q. For each of sub-systems, we use p ik X and p rk Y to express the ith input and rth output, respectively, of the pth subsystem. The relative inefficiency of a set of n DMUs, each has q parallel sub-systems can be calculated by following formula: The above model (2) should be calculated for n times to obtain the inefficiency slacks of systems as well as their sub-systems. However, the inefficiency slacks is not equal to inefficiency scores because is not equal to 1 for kth DMU with wth sub-systems. Therefore, the inefficiency score should be calculated by S k w should be divided by ∑ =1 and the efficiency score should be: Calculation and results: Based on those indexes listed on Table 1, we collect 30 provinces corresponding  (2). There are 14 regions, occupied 47%, who reached 1 as overall efficiency value. Those regions are executed well in the eco-environmental optimization. Among these efficient regions, Beijing, Tianjin and Zhejiang are advanced developed regions which have large amount of inputs in treatments process, i.e., emission of waste gas, discharged waste water and produced solid wastes. The main reason of high performance of eco-environmental optimization in the three regions is the capability of treatments for those three types of wastes. Therefore, the three regions have the characteristics of large inputs and lager outputs.
For Jilin, Heilongjiang, Fujian and Hainan, they are efficient regions too. Those regions are middle developed regions. Heilongjiang and Jilin locate in the northeast part of China. Although these regions are industry basement in 1980s, the center of industry development has transferred into coastal regions. Therefore, the transformation relieved the pressure of

S&T CONTRIBUTION TO WASTES' TREATMENTS
With the rapid change and development of society, S&T has become the pivotal power for pushing the development of regional economy. However, the traditional regional strategy was focus on the development of industry but ignore the protection of environment. Therefore, the traditional S&T inputs were designed for stimulate the development of industry (Wang et al., 1997). With the development of regional eco-construction, more of S&T inputs for optimizing eco-environment are proposed. In the view of regional eco-construction, the impact of S&T inputs on environmental emission and treatment were measured in this study. Based on the chain relationship between S&T inputs, environmental emission and environmental treatment, addictive two-stage DEA model was applied to calculate the impact efficiency of S&T inputs on environmental emission and treatment (Rongchao, 2007).At the same time, we can obtain the impact relationship between S&T inputs and regional ecoenvironmental optimization.

Basic structure of S&T's effect on wastes' treatment:
To identify the influence of S&T to ecoenvironment optimization, we divided the whole process into two connected stages. Taking related S&T indexes as inputs and wastes emission indexes as outputs in the first stage, we can identify the "wastes producing stage" the first stage. Then, the second stage is "wastes' treatments stage" which takes wastes emission as inputs and treated wastes as outputs and corresponding indexes is same as the indexes mentioned in Section II. The wastes emission indexes are same as the inputs on Table 1. Therefore, the two stages are connected by intermediate indexes. The structure can be shown in Fig. 1. Number of facilities for treatment of waste gas (set) Volume of industry sulphur dioxide removed (10 000 tons) Volume of industrial soot removed (10 000 tons) R&D expenditure (million RMB) Volume of industrial dust removed (10 000 tons) Full-time equivalent of R&D Personnel (10 000 man-years) Total volume of waste water Discharge in Industry (10 000 tons) Number of facilities for treatment of waste water (set) Consumption waste water discharge (10 000 tons) Industrial waste water meeting discharge standards (10 000 tons) R&D Project (item) The number of national science and technology achievement award (item) Volume of industrial solid wastes produced (10 000 tons) Volume of industrial solid wastes utilized (10 000 tons) Volume of industrial solid wastes in stocks (10 000 tons) Technical contracts number (item) Volume of industrial solid wastes treated (10 000 tons) Table 3, we will propose S&T indexes as inputs. Based on the principle of scientific, comprehensive, operational and obtainable and referenced on related references, six indexes can be listed as the S&T indexes in the left column on Table 3.

Two-stage DEA methodology:
We suppose there are n DMUs and each DMU j (j = 1, 2, …,n) has m inputs, denoted as x ij (i = 1, 2, …, m). Through the first stage, we get s outputs, denoted as z tj (t = 1, 2, …,s). Because the second system follows the first system, the outputs of the first system become the inputs of the second system. Through the second system, there are p outputs produced, denoted as y kj (k = 1, 2, …, p).
A two-stage DEA model was proposed based on CRS (Constant Return to Scale) model (Chen et al., 2009;Sexton and Lewis, 2003), which can be expressed as follow for DMU j0 as formula (3), where 1 w and 2 w are user-specified weights for subsystem 1 and subsystem 2 respectively and 1 w + 2 w = 1. The value of By changing the value of α,β, we can study the sensitivity of the overall efficiency scores to α,β. To determine the efficiency for each stage, we propose the following procedure. Chen et al. (2009) calculated either the first stage's efficiency (θ 1 j ) or the second stage's efficiency (θ 2 j ) first, then derive the efficiency of the other stage. The following model determines the first stage's efficiency (θ 1 j ) while maintaining the overall efficiency score at o θ calculated from model (3): The efficiency for the second stage then is calculated as: For the second stage's efficiency ( 2 o θ ), we can calculate from model (6) The efficiency for the first stage then is calculated as: Calculation and results: Using the corresponding panel data of 30 provincial regions, we can calculate the contribution rate of S&T in both stages, denoted θ * 1 as S&T contribution rate in wastes production stage, θ * 2 as wastes treatment capability and θ * 0 as S&T contribution rate in wastes production stage. All of required statistic data are collected from 2011 China Statistic Year Book, 2011 Chinese Environmental Statistic Year book and 2011 Cities Statistic Year Book in China. By used addictive two-stage DEA model, we can get the calculation results on Table 4. By using two-stage DEA model, we can get the S&T contribution rate to wastes' production and wastes' treatment. θ * 1 Expressed the effect of S&T to wastes' production, where the more this value the more influence on environmental pollution. θ * 0 Expressed the effect of S&T to wastes' treatments, where the more    Table 4, we can get the information as following: • Based on the value of θ * 1 , there are 25 provinces whose corresponding value larger than 0.6. Because S&T inputs can improve the efficiency of production and enlarge scale in enterprises, the productivity is enhances in multiple aspects. At the same time, emission of wastes is increased in the same process. The most serious provincial regions are Shanghai, Anhui, Shandong, Guangdong, Guizhou and NIngxia. Therefore, for these regions, governments should apply measures on strengthen the pollution treatments and energy saving capability in enterprises • Based on the value of θ * 0 , Shanghai has the highest value, i.e. 1 and other regions' values are less than 1. θ * 0 Means the positive effect on wastes' treatment. Therefore, the overall contribution of S&T to wastes' treatment is not high. There are five regions whose values are less than 0.6 where S&T has weak influence on wastes' treatment. To enhance the contribution of S&T to environmental purification, government should propose more S&T project and enlarge investment in regional environmental construction. Moreover, we should increase more S&T human resource and grants in the research filed of environmental science and ecological sciences

CONCLUSION
Based on the parallel DEA calculation results, there are 16 regions' efficiencies are less than 1. To optimize eco-environment and keep sustainable development mode in China, we should empower the wastes' treatments capability in the next few years. At the same time, we also should pay attention to the average level of efficient values that all of efficiency values are more than 0.9. The meaning is the gaps between different regions in eco-environmental optimization are not very huge. Therefore, it is feasible to optimize the overall eco-environment in China. Based on the calculation results of two-stage DEA model, S&T contribution to wastes' treatments in Shanghai is ranked on the top one among 30 provincial regions. Therefore, Shanghai should be the benchmark of other regions.
In the past 30 years, we didn't care too much about our eco-environment which produced some pollution and a lot of wastes. How to enhance the capability of deal with those wastes should be important measures to make our environment friendly. Now, Chinese government has already recognize the importance of protection on eco-environment and increased inputs to support the treatments of wastes. Governments should propose specific measures in different provincial regions based on their corresponding evaluation results. By referencing on the calculation results, government can get eco-environmental optimization levels in 30 regions and make corresponding measures to enhance optimization capability of eco-environment in China.

ACKNOWLEDGMENT
The main study of this study is supported and sponsored by National Natural Science Foundation of China (71071069), Young Foundation of Ministry of education, humanities and social science research projects (11YJC630100), project of Shandong Economic and Information Technology Committee (No. 2012EI107) and the Fundamental Research Funds for the Central Universities (11CX04031B).