Zhengsi Utt

Honglin Peng

Xiaowen Huang

Zhixiang

Junfei, Qingyuan, Yafei, Xiaohui, Yanli, Ke, Xue, Zhen, Zheng, Jinrui Dong

𝑎 𝑗

𝑏 𝑗

𝛽 𝑚

𝛿 𝑘

𝜃 𝑓

𝜙 𝑔

𝜑 𝑚

Keywords: Data envelopment analysis, Human beings--Effect of environment on, Linear programming, Industrial efficiency, Benchmarking

With the development of economy, environmental pollution has become increasingly serious, especially in developing countries such as China and India. To realize the sustainable development of environment and economy, the scientific evaluation of environmental efficiency is very important. This thesis investigates the environmental efficiency evaluation based on data envelopment analysis (DEA). Four environmental efficiency evaluation problems are studied. Firstly, an integrated Enhanced Russell measure model is proposed for evaluating the environmental efficiency with the presence of undesirable outputs in fuzzy circumstance. It is then applied to thermal power firms in China. Then, by considering undesirable outputs, a new closest target DEA model based on Range Adjusted Measure is established to measure the water environmental efficiency of Xiangjiang River Basin in China. In addition, a new two-stage DEA model with shared inputs is built to evaluate the total-factor energy efficiency and the overall environmental efficiency of China's industrial sector. Finally, the dynamic environmental efficiency evaluation of a parallel transportation network considering regional heterogeneity is considered. The Metafrontier Malmquist-Luenberger productivity index based on a network DEA model is built and then applied to analyze China's transportation sector.

All these DEA models are applied to real-life examples and used to measure their environmental efficiency and set the benchmark for their performance improvement.

v

Ré sumé

Avec le développement de l'économie, la pollution de l'environnement est devenue de plus en plus grave, en particulier dans les pays en voie de développement tels que la Chine et l'Inde. Pour réaliser le développement durable de l'environnement et de l'économie, l'évaluation scientifique de l'efficacité environnementale est très importante.

Cette thèse examine l'évaluation de l'efficacité environnementale basée sur l'analyse d'enveloppement de données (DEA). Quatre problèmes d'évaluation de l'efficacité environnementale sont étudiés. Tout d'abord, un modèle de mesure Russell renforcé est proposé pour évaluer l'efficacité environnementale des entreprises de production d'énergie thermique en Chine. Ensuite, compte tenu de la production indésirable, un nouveau modèle DEA plus proche d'une cible basé sur un intervalle de mesure ajusté est établi pour mesurer l'efficacité environnementale du bassin de la rivière Xiangjiang en Chine. De plus, un nouveau modèle DEA en deux étapes avec entrées partagées est construit pour évaluer l'efficacité énergétique du facteur total et l'efficacité environnementale globale du secteur industriel de la Chine. Enfin, le modèle d'évaluation de l'efficacité environnementale d'un réseau parallèle de transport prenant en compte l'hétérogénéité régionale est proposé pour analyser le secteur de transport en Chine.

Tous ces DEA modèles sont appliqués à des exemples réels et utilisés pour mesurer leur efficacité environnementale et donner une référence pour l'amélioration de leur performance.

Mots clés: DEA, Méthode, Homme --Effets de l'environnement, Programmation linéaire, Efficience (gestion), Référenciation vii

General introduction

Nowadays, the continuous exposure of environmental pollution has seriously restricted the social development of many countries, especially developing countries.

With the acceleration of urbanization process, environmental pollution has become more and more serious. In the past 40 years, China's economy has achieved rapid development, but the high-speed economic growth mainly depended on huge investment and high resource consumption at the cost of high pollution and low efficiency. However, this model of development leads to a contradiction between economic development and environmental protection. As a result, the deterioration of the environment is becoming more and more serious. After the long-term practice, people have realized the importance of environmental protection in the sustainable development of the economy of a country. Sustainable development cannot be realized without effective management of the environment. To achieve effective environmental management, we require scientific and objective environmental performance evaluation methods.

In view of the above-mentioned context, this thesis investigates several environmental performance evaluation problems based on data envelopment analysis and develops relevant evaluation methods that can be used in practice. The problems to be addressed in this thesis include: how to evaluate the environmental performance of systems with fuzzy numbers, how to measure the environmental performance in order to set the closest target for the environmental inefficient system using least effort to achieve environmental efficiency, how to measure the overall environmental efficiency and total factor energy efficiency of a complex two-stage system, and how to evaluate the dynamic change of environmental performance of a parallel transportation network with regional heterogeneity. Based on the theoretical investigation of these problems, effective environmental performance evaluation methods are developed and applied to some practical problems in this thesis. This thesis is organized in seven chapters, and the main contents of the seven chapters are given as follows:

The first chapter is the introduction. We first present the background (context) of this thesis and provide a literature review on Data Envelopment Analysis (DEA), the basic method for our environmental performance evaluation. The problems studied in this thesis are then introduced. Finally, we present the structure and outline the main viii contributions of this thesis.

The second chapter introduces the basic theory of DEA, including the basic concepts of data envelopment analysis (DEA), the basic DEA models and some basic concepts in environmental efficiency evaluation.

The third chapter is environmental efficiency evaluation for a single-stage system with fuzzy numbers and its application. In this chapter, an integrated Enhanced Russell measure model is proposed based on data envelopment analysis for evaluating the performance of decision making units in the presence of undesirable outputs in fuzzy circumstance. Then, the new model is applied to analyze the environmental efficiency and provide the benchmarks for the thermal power firms in China, which can guide the decision makers to make suitable future production plans for improving their performance.

The fourth chapter is environmental efficiency evaluation for a singlestage system considering the path for performance improvement and its application. By considering undesirable outputs, a new closest target DEA model based on Range Adjusted Measure (RAM) is established to measure the environmental performance of the system. The proposed model is used to measure the environmental efficiency of the regions in Xiangjiang River Basin in China, and the closest target is set for these inefficient regions so that they can make the least effort to achieve efficiency.

The fifth chapter is environmental efficiency evaluation of a two-stage system via total-factor energy efficiency and its application. With the rapid development of industry, the problems of growing energy consumption and environmental pollution in industry are drawing increasing attention of the government and scholars. In this chapter, we divide the industrial system into two stages, i.e., an energy utilization stage and a pollution treatment stage, for accurately evaluating the total-factor energy efficiency of the system as well as its overall environmental efficiency. We build a new two-stage data envelopment analysis model with shared inputs to analyze the China's industry that was commonly considered as a "black box" in traditional environmental efficiency methods. Based on the theoretical analysis of the model, some policy suggestions are given to this industry.

The sixth chapter is environmental efficiency evaluation of parallel transportation network considering regional heterogeneity and its application. In this chapter, we examine the China's transportation sector by dividing it into four main subsystems: railway, highway, waterway, and civil aviation, and further build a network data ix envelopment analysis model for performance measurement of the sector with considering undesirable output-CO2 emission. Moreover, considering the heterogeneity of transportation sectors in different areas of China, a new metafrontier Malmquist-Luenberger productivity index is proposed based on the network DEA model, which is used to investigate the productivity growth of 30 regions' transportation sectors during 2007-2013. Finally, some suggestions are given for guiding the development of China's transportation sector.

The seventh chapter concludes this thesis with prospective for future research. In this chapter, the main works of this thesis are first summarized, and the main contributions and possible improvements of this thesis are then outlined. Finally, some suggestions for future research directions are provided. Table 3.

••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••8 Figure 5.1 Two-stage structure system of China's industry•••••••••••••••••••••••••••••••••••••••••••••••••••••••••67 Figure 5.2 The industrial efficiencies of different areas in China••••••••••••••••••••••••••••••••••••••••79
•••••••••••••••••••••••••••••••••••••92
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•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••104
•••••••••••••••••••••••••••••••••••••••••••••••••••••••106
••••••••••••••••••••••••••••••••••••••107
•••••••••••••••••••••••••••••••••••••••• 107 xvii

List of Tables

1 Statistical description•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 34
••••••••••••••••••••••••35 Table 3.3 Ranking of the firms•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 38
Table 3.4 Proportion for firms to be efficient in the fuzzy circumstance when 𝛼 = 0.5

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•••••••••••••••••••• 54
, China••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 55
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 56
to 2014•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 57 Table 4.5 Water environmental efficiencies of seven cities in Xiangjiang River Basin•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••58
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••59
•••••••••••••••••••••••••••••••••••••••••••• 74
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••75 Table 5.3 Six administrative areas••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••78
••••••••••••79 Table 5.5 Benchmarks for China's industry••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••82 Table 6.1 Variables and descriptions••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••93 Table 6.2

CO2 emission factors by major carbonaceous fuel types in China

•••••••••••••100 Table 6.3 Transformation coefficient to standard coal••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••101
Table 6.4 Distribution of 30 administrative regions in three areas of China

••••••••••••••101
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Background for the evaluation of environmental efficiency

In recent years, the environmental problems, such as water pollution and air pollution, have seriously affected the sustainable development of economies of most countries, especially some developing countries, such as India and China. With the rapid industrialization, the environmental pollution is becoming more and more serious, causing direct damage to the ecosystems of these countries. Therefore, the dynamic balance between environment and economy has become an important social problem (Wu et al., 2014). Through the analysis of long-term practices, people have recognized that sustainable development of the economic and environment is the main way to solve this problem, which indicates the development should meet the needs of the present generation without compromising the ability of future generations. In order to achieve sustainable economic development, environmental protection has become a global consensus. In the year of 2015, 196 countries met in Paris for the United Nations Climate Change Conference and finally signed the "Paris Agreement" with the objective to alleviate environmental and climate change. The Paris Agreement aims at governing emission reductions from 2020 through commitments of countries to their nationally determined contributions. As an important member, China plays the critical CHAPTER 1. Introduction role in the global environmental improvement. Therefore, this thesis is mainly focused on the environmental issues in China.

Recently, China's economy has achieved rapid development. The GDP grows from 367.9 billion RMB in 1978 to 90.03 trillion RMB 2018. But the rapid economic growth mainly depends on high consumption of energy and resources at the cost of high pollution and low efficiency. In recent years, the contradiction between economic development and environmental protection has become increasingly prominent.

Meanwhile people are facing increasingly serious environmental deterioration problems (Wu et al., 2014;An et al., 2017;[START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF]. For example, heavy metal pollution in Xiangjiang River Basin of Hunan province, eutrophication pollution in Taihu Lake of Jiangsu province, and heavy winter haze of North China. With the increasing awareness of environmental protection, more attentions are paid to environmental protection [START_REF] Glucker | Public participation in environmental impact assessment: why, who and how?[END_REF]. The 13th Five-Year Plan clearly pointed out that China will increase the environmental supervision and protection to realize an overall improvement of the ecological environment (Xinhua News Agency, 2015). The report of the 19th National Congress of the Communist Party of China further clarified the basic strategy of "adhering to the harmonious coexistence of man and nature", and proposed to promote green development by focusing on solving environmental problems. Besides, this report proposed to strength and reform the ecological environment supervision system [START_REF] Xi | Secure a Decisive Victory in Building a Moderately Prosperous Society in All Respects and Strive for the Great Success of Socialism with Chinese Characteristics for a New Era[END_REF]. With the extensive research on environmental problems, people have realized the importance of environmental protection in the sustainable development of the economy of a country. The sustainable development cannot be realized without effective management of the environment. To achieve effective environmental management, we require scientific and objective environmental performance evaluation methods. (Wu et al., 2014;[START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF].

Environmental efficiency evaluation should provide a comprehensive evaluation of the performance of an organization in all aspects of resources consumption, economic output and environmental output. It should not only show tell us the environmental efficiency of the evaluated system on the macroscopic level, but also provides us with detailed benchmarking information for the design and implementation of environmental management policies [START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF]. Therefore, environmental efficiency evaluation is a key factor in solving environmental problems (Halkos and Tzeremes, 2013). The environmental efficiency evaluation has attracted much attention of scholars and has been deeply investigated and applied in real life (Sueyoshi et al., 2017). Among various environmental efficiency evaluation methods, data envelopment analysis (DEA) is one of the most popular methods. The book of "2016 Research Fronts" jointly published by the Science and Technology Strategy Consulting Institute of the Chinese Academy of Sciences, the Literature Information Center of the Chinese Academy of Sciences, and Clarivate Analytics (formerly the Intellectual Property and Technology Division of Thomson Reuters) stated that environmental and energy efficiency evaluation based on data envelopment analysis is one of the two key hotspots in the fields of economics, psychology and other social sciences. The book especially emphasized that the 35 core papers in the field of environmental and energy efficiency evaluation all adopt the data envelopment analysis method*. Data envelopment analysis was proposed in 1978 by [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF]. It is a nonparametric method for evaluating the performance of a set of homogeneous decision making units (DMUs) based on linear programming models. Besides, it can deal with the performance evaluation of multi-input and multi-output systems, and the obtained results can provide benchmarking information for performance improvement [START_REF] Boudreau | 50th Anniversary Article: Organizational behavior, strategy, performance, and design in management science[END_REF]. Recently, DEA has become one of the important research topics in management science. A large number of studies on the DEA methodological developments and applications have been conducted, such as [START_REF] Banker | Some models for estimating technical and scale inefficiencies in data envelopment analysis[END_REF], [START_REF] Andersen | A procedure for ranking efficient units in data envelopment analysis[END_REF] and [START_REF] Chen | Scale efficiency in two-stage network DEA[END_REF]. DEA has been extended and applied to the evaluation of environmental efficiency considering environmental factors (undesirable outputs), and has gradually become one of the best and most popular environmental efficiency evaluation methods (Wang et al., 2013;[START_REF] Wang | Potential gains from carbon emissions trading in China: A DEA based estimation on abatement cost savings[END_REF]Song and Guan, 2014). Thus, DEA is chosen as the basic methodology for the evaluation of environmental efficiency and further apply it to analyze the real environmental problems.

Literature review: DEA-based environmental efficiency evaluation

According to the theory of joint production, desirable outputs are always accompanied by undesirable outputs [START_REF] Färe | Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach[END_REF][START_REF] Chen | Eco-efficiency measurement and decomposition in the two-stage DEA analysis framework[END_REF]. Usually, the performance evaluation considering both economic factors (desirable outputs) and CHAPTER 1. Introduction environmental factors (undesirable outputs) is defined as environmental efficiency evaluation (see [START_REF] Fang | Choosing competitive industries in manufacturing of China under low-carbon economy: A three-stage DEA analysis[END_REF]Wu et al., 2014). Environmental factors, such as wastewater, carbon dioxide, sulfur dioxide, solid waste, etc. are usually undesirable outputs, so one key issue of environmental efficiency evaluation is how to deal with undesirable outputs. Due to the increased environmental concerns and government environmental policies, more and more attention has been paid to these undesirable outputs. Currently, there are two main methods for assessing environmental efficiency: stochastic frontier analysis (SFA) and data envelopment analysis (DEA) (Coelli et al., 2005). SFA is a parametric estimation method which uses the maximum likelihood estimation (MLE) to estimate the production function. This method uses a parametric modelling approach to measure a "frontier" value and thereby provides a measure to evaluate environmental efficiency through the frontier value. However, pre-determined production function form may not match the reality. Moreover, SFA will become much difficult when dealing with a multi-input and multi-output system. In contrast to SFA, DEA is a non-parametric programming technique for measuring the relative efficiency of a set of homogenous decision making units. It not only can deal with multiple-output multiple-input systems but also has the advantage of having no need to assume any particular functional forms relating to the inputs and outputs. Moreover, it has become one of the most popular methods for environmental efficiency evaluation. Usually, the real-life environmental systems are multi-input and multi-output systems that consider both desirable outputs and undesirable outputs, therefore, DEA is chosen as the basic method for measuring environmental efficiency in this thesis.

The research of environmental efficiency evaluation based on DEA has received much attention from researchers. Fä re et al. (1989) is one of the important theoretical foundations of environmental efficiency evaluation. After that, the related theoretical methods have been largely developed. According to the addressing ways of undesirable outputs, the environmental efficiency evaluation studies can be classified into two categories: direct approaches and indirect approaches. Direct approaches can be further divided into three categories. The first one is based on Fä re et al. (1989), which replaced strong disposability assumption of outputs by weakly disposable assumption. This work has been extensively developed [START_REF] Seiford | A response to comments on modeling undesirable factors in efficiency evaluation[END_REF][START_REF] Zhou | A study of carbon dioxide emissions performance of China's transport sector[END_REF][START_REF] Wang | Potential gains from carbon emissions trading in China: A DEA based estimation on abatement cost savings[END_REF]. The second one is based on slacks-based measure or Russell measure [START_REF] Zhou | Slacks-based efficiency measures for modeling environmental performance[END_REF]Bi et al., 2014;[START_REF] Chen | Environmental efficiency analysis of China's regional industry: a data envelopment analysis (DEA) based approach[END_REF][START_REF] Liu | Energy and environmental efficiency analysis of China's regional transportation sectors: a slack-based DEA approach[END_REF]. The third one is based 1.2 Literature review: DEA-based environmental efficiency evaluation on the direction distance function (DDF) (Chung et al., 1997;[START_REF] Boyd | Plant level productivity, efficiency, and environmental performance of the container glass industry[END_REF][START_REF] Picazo-Tadeo | Assessing ecoefficiency with directional distance functions[END_REF]Halkos and Tzeremes, 2013;Sueyoshsi and Goto, 2017). Indirect approaches can be further divided into two categories. The first one treats undesirable outputs as inputs in performance evaluation [START_REF] Liu | DEA models via goal programming[END_REF][START_REF] Dyckhoff | Measuring ecological efficiency with data envelopment analysis (DEA)[END_REF][START_REF] Yang | Evaluation of regional environmental efficiencies in China based on super-efficiency-DEA[END_REF]. This approach only needs the information on whether the data should be minimized or maximized, but it cannot reflect a real production process [START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]. The second one includes a non-linear monotonic decreasing transformation approach [START_REF] Scheel | Undesirable outputs in efficiency valuations[END_REF] and a linear monotonic decreasing transformation approach [START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]Wu et al., 2013).

Most of the above environmental efficiency works by DEA focused on singlestage system or considered the evaluated system as a "black box" without considering its internal structure. However, we cannot find the inefficiency in the internal production process of a system through this way, and thus it is hard to improve the system's performance. With the increasing competition and relation among economic entities, the systems become more and more complex, it is urgent to propose the environmental efficiency evaluation for a network system. In recent years, the network DEA method becomes an effective method to measure the performance of multi-stage systems, which provides new ideas and breakthroughs for the study of complex environmental efficiency evaluation problems.

As mentioned above, the previous studies about environmental efficiency did not consider the internal structure of the system, and treated the system as a "black box" which overlooked the transformations to which the inputs are subject within the considered system [START_REF] Ma | Data envelopment analysis model and method[END_REF][START_REF] Yang | Review of data envelopment analysis[END_REF]. This simple way has been widely applied to environmental management (Song and Wang, 2013;[START_REF] Lin | Do energy and environmental efficiency benefit from foreign trade? -The case of China's industrial sectors[END_REF][START_REF] Zhou | Slacks-based efficiency measures for modeling environmental performance[END_REF]Halkos and Tzeremes, 2013;[START_REF] Liu | Energy and environmental efficiency analysis of China's regional transportation sectors: a slack-based DEA approach[END_REF]. However, many evaluated systems cannot simply be considered as "black boxes", otherwise, it may lead to biased results on the evaluation [START_REF] Du | DEA-based Evaluation on City Innovation in China[END_REF]An et al., 2017;Fä re and Grosskopf, 2000;[START_REF] Kao | Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[END_REF]. [START_REF] Kao | Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[END_REF] found that although the performance of each subsystem of a decision-making unit is worse than that of the corresponding subsystem of another decision-making unit, it is possible that the performance of the former is greater than that of the latter in the case of ignoring the internal structure of the systems. [START_REF] Brockett | Implementation of DEA models using GAMS[END_REF] proposed that considering the intermediate production processes in the evaluation can identify all the sources that cause the inefficiency of the CHAPTER 1. Introduction whole system. In order to solve these problems, the network DEA method is proposed and widely used in environmental efficiency evaluation to consider the internal structure of the system. As the network DEA can measure the inefficiency of internal production process of the system, it has been widely concerned by scholars in recent years, and has become one of the research hotspots in environmental efficiency evaluation.

According to the types of network structure, the research on environmental efficiency evaluation based on network DEA can be classified into three categories.

The first category is the series network DEA environmental efficiency evaluation which evaluates the DMUs with two or more internal subsystems in series which are linked with intermediate measures. Most of the existing studies on series network focus on two-stage network system. The two-stage network system specifically includes the traditional two-stage system and the extended general two-stage system. The former refers to the two-stage network system in which the intermediate measures are both the whole outputs of the first stage and the whole inputs of the second stage [START_REF] Bai-Chen | Does generation form influence environmental efficiency performance? An analysis of China's power system[END_REF]Halkos et al., 2015), and the latter refers to a two-stage network system in which the intermediate measures are only partial or whole outputs of the first stage and partial or whole inputs of the second stage (Xie et al., 2012;Song et al., 2014;[START_REF] Bian | Efficiency evaluation of Chinese regional industrial systems with undesirable factors using a two-stage slacks-based measure approach[END_REF]Song et al., 2015;[START_REF] Wu | Two-stage network structures with undesirable intermediate outputs reused: A DEA based approach[END_REF][START_REF] Chen | Eco-efficiency measurement and decomposition in the two-stage DEA analysis framework[END_REF]Chu et al., 2016;[START_REF] Shi | Environmental efficiency analysis based on relational two-stage DEA model[END_REF]Wu et al., 2016a;[START_REF] Lozano | Technical and environmental efficiency of a two-stage production and abatement system[END_REF]Li et al., 2018;[START_REF] Zhou | A novel Data Envelopment Analysis model for evaluating industrial production and environmental management system[END_REF].The second category is the parallel network DEA environmental efficiency evaluation which evaluates the DMUs with two or more internal parallel subsystems. In the initial parallel network DEA environmental efficiency evaluation studies, each subsystem was operated independently. Fä re et al. (1997) first studied the performance of such network structure systems. Later, this structure was further extended and applied to environmental efficiency evaluation [START_REF] Bi | DEA Model for Parallel Production System with Environmental Constraint[END_REF]Gong et al., 2016). Now, the research on parallel network DEA environmental efficiency evaluation has been extended to nonindependent parallel systems [START_REF] Bian | Efficiency evaluation for regional urban water use and wastewater decontamination systems in China: A DEA approach[END_REF]Wu et al., 2016b;Liu et al., 2017;Li et al., 2018). The third category is the mixed network DEA environmental efficiency evaluation. The mixed network system which studies a kind of system with parallel and series sub-systems. Recently, the research on environmental efficiency evaluation based on mixed DEA is gradually increasing (Huang et al., 2014).

Research topics

Research topics

The above literature review shows that environmental efficiency evaluation has been widely studied by scholars, but there are still some open problems. For example, how to evaluate the environmental efficiency of systems with fuzzy numbers? How to measure the environmental efficiency in order to set the closest target for an environmental inefficient system using least effort to achieve environmental efficient?

How to measure the overall environmental efficiency and total factor energy efficiency of a complex two-stage system? and how to evaluate the dynamic change of environment efficiency of a parallel network system? Based on the theoretical investigation of these problems, effective environmental performance evaluation methods are developed and applied to some practical problems in this thesis. The main contents of this thesis are summarized as follows:

In chapter 3, an integrated Enhanced Russell measure model is proposed based on data envelopment analysis for evaluating the performance of decision making units in the presence of undesirable outputs under a fuzzy circumstance. In this chapter, a new model is applied to analyze the environmental efficiency and provide the benchmarks for thermal power firms in China, which can guide the decision makers of these firms to make suitable future production plans to improve their performance.

Considering the undesirable outputs, a new closest target DEA model based on

Range Adjusted Measure (RAM) is established to measure the environmental efficiency of a single-stage system. The proposed model is used to measure the water environmental efficiency of the regions in Xiangjiang River Basin in China. Besides, the closest targets are set for these inefficient regions so that they can make the least effort to achieve efficient.

With the rapid development of industry, the problems of growing energy consumption and environmental pollution in industry attracted increasing attention of the government and scholars. In chapter 5, we divide an industrial system into two stages, i.e., an energy utilization stage and a pollution treatment stage, for accurately evaluating the total-factor energy efficiency of the system as well as its overall environmental efficiency. We build a new two-stage data envelopment analysis model with shared inputs to analyze the China's industry that was commonly considered as a This thesis will be divided into two parts according to the structure of the systems evaluated. The first part is dedicated to environmental efficiency evaluation methods and applications of single-stage systems, which contains two chapters. The second part is dedicated to environmental efficiency evaluation methods and applications of network systems, which also contains two chapters.

The environmental efficiency evaluation methods for single-stage systems and their applications are presented in Chapter 3 and Chapter 4. Chapter 3 studies the environmental efficiency evaluation of single-stage systems considering fuzzy numbers, and the proposed model is applied to China's thermal power firms. Chapter 4 presents an environmental efficiency evaluation method for a single-stage system considering performance improvement path, and the proposed method is applied to Xiangjiang River Basin in China. Some environmental efficiency evaluation methods and their applications of network systems are described in Chapter 5 and Chapter 6. Chapter 5 investigates the environmental efficiency evaluation of a complex two-stage system in terms of total factor energy efficiency, and the proposed models are applied to China's industry sector.

Chapter 6 studies the environmental efficiency evaluation of a parallel network system, and the proposed models are applied to China's transportation sector.

Contributions

(1) Considering environmental factors, a Fuzzy Enhanced Russell measure model is firstly built based on the Enhanced Russell measure and fuzzy theory. α-cut method is used to calculate the upper and lower bound values of environmental efficiencies. Finally, 30 thermal power firms in China are analyzed by the proposed method.

(2) Many previous works on the environmental efficiency evaluation provide methods for determining the benchmarks for the evaluated systems. However, the benchmarks determined by these methods are usually the furthest target for each inefficient system to achieve efficient. In order to make the evaluated system use the least effort to achieve environmental efficient, we proposed a closest target DEA model based on Range Adjusted Measure (RAM) to measure the water environmental efficiency and set the benchmarks for Xiangjiang River Basin in China.

(3) Most previous studies on environmental and energy efficiency consider an evaluated system as a "black box" without considering its internal structure, which CHAPTER 1. Introduction often leads to less reliable results. In order to overcome this problem, a two-stage DEA model is proposed to measure regional industrial overall environmental efficiency, energy utilization efficiency, pollution treatment efficiency, and the total-factor energy efficiency in chapter 5. This chapter mainly introduces the relevant preliminaries, including the basic concepts of data envelopment analysis (DEA), the basic DEA models and some basic concepts in environmental efficiency evaluation.

Data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric programming method for efficiency evaluation of a set of entities called decision making units (DMUs) which convert multiple inputs to multiple outputs. It is a cross-research field of operational research, management science and mathematical economics. The seminal DEA model was proposed by [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF]. So far, it has been widely developed and applied in many areas, such as business firms, hospitals, banks, thermal power firms, and others.

Through DEA method, the relative efficiency of the evaluated DMU can be obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs.

Compared with other methods, DEA has an evident advantage in dealing with the efficiency assessment of multi-input multi-output DMU. DEA can identify the best practice DMUs which form an efficient production frontier. Furthermore, it can provide some valuable management implications and useful information for decision makers to improve the performance. For example, through horizontal comparison among DMUs, the efficiency performance of each decision-making unit can be measured, and the benchmarks can be found to guide the future development directions of the inefficient DMUs. The longitudinal comparison among DMUs can be used to derive the productivity level, the technological progress of each evaluated DMU. Besides, DEA can also be used for allocating resources or fixed-costs, measuring the returns to scale of DMU, and others.

More importantly, compared with another efficiency evaluation method, the Stochastic Frontier Analysis (SFA), DEA has evident advantages in dealing with multiinput and multi-output system while until recently SFA only allowed a single output, or multiple outputs with using a cost function if price data are available (Paradi et al., 2017).

Basic concepts (1) Decision making unit

In real-life production and service activities, we often meet such management problem that we should evaluate the performance of some homogenous departments during a period, in which each department is called a decision making unit (DMU). It can be seen that DMU refers to any entity that converts inputs into outputs, such as universities, enterprises, hospitals, banks, etc. For these DMUs, the inputs can be labors, capital, fixed cost, the outputs show the effectiveness of the activity. For example, the evaluation of the operational efficiency of similar air-conditioning production enterprises in a certain area, each enterprise is a DMU, the employees of the enterprise, the investment in fixed assets, etc. are input indicators, and the number of airconditioners and the quality of air-conditioning are output indicators.

When applying DEA for the efficiency evaluation of DMUs, we assume the DMUs are homogeneous, that is, all DMUs should have same external environment; all DMUs have the same input and output indicators; and all DMUs have the same production process. If the DMUs do not satisfy the homogeneity, it needs to be processed, please refer to related works such as Cook et al. (2013) and [START_REF] Imanirad | Partial input to output impacts in DEA: The case of DMU-specific impacts[END_REF].

(2) Performance evaluation

Basic concepts

13

The performance evaluation of a DMU with single-input and single-output is generally based on the ratio of output to input. For the performance evaluation of multiinput and multi-output DMU, it is defined as the ratio of the weighted value of the outputs to the weighted value of the inputs. It should be noted that, without loss of generality, performance in this thesis refers to the relative efficiency of the DMU, that is, the relative efficiency of the evaluated DMU is obtained by comparing with the other DMUs' multiple inputs and multiple outputs.

(3) Production possibility set Consider a set of n DMUs, with each, 𝐷𝑀𝑈 𝑗 (𝑗 = 1, … , 𝑛) , using m inputs𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ) 𝑇 to produce s outputs 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) 𝑇 , where T in the superscript indicates transpose. Meanwhile, 𝑋 𝑗 ≥ 0,𝑌 𝑗 ≥ 0,𝑗 = 1, … , 𝑛, that is, the value of each input and output is greater than or equal to 0, and at least the value of one input indicator and one output indicator is positive. Besides, 𝑥 𝑖𝑗 denotes the ith input of 𝐷𝑀𝑈 𝑗 , and 𝑦 𝑟𝑗 denotes the rth output of 𝐷𝑀𝑈 𝑗 .

The production possibility set (PPS) is then defined as a set of all feasible production points, that is:

𝑇 = {(𝑋, 𝑌)|𝑋 can produce 𝑌} (2.1)
Equivalently, technology T can be equivalently represented by its output sets 𝑃(𝑋) = {𝑌|(𝑋, 𝑌) ∈ 𝑇} or its input sets 𝑃(𝑌) = {𝑋|(𝑋, 𝑌) ∈ 𝑇}.

For the PPS, based on Wei (2004), the axioms are given as follows.

Axiom 1. For an observed production activity (𝑋 𝑗 , 𝑌 𝑗 )(𝑗 = 1, … , 𝑛), the input vector and output vector are 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 )and 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) respectively.

Then, this production activity is feasible. Based on the definition of Wei ( 2004), axiom 1 is called ordinary axiom, axiom 2 is called convex axiom, axiom 3 is called invalid axiom, axiom 4a is called cone axiom, and axiom 4b is called contraction axiom, axiom 4c is called expansion axiom. The axiom 3 means that using more input can always produce less output. The axiom 4a

indicates that when the input increases (or decreases) by a multiple, the produced output can also increase (or decrease) by the same multiple. The axiom 4b shows that when the input is reduced by a certain ratio, the output reduced by the same proportion can be produced. The axiom 4c indicates that when the input is increased by a certain multiple, the output increased by the same multiple can be produced.

Based on the above axioms 1, 2, 3 and 4a, the production possibility set under constant returns to scale (CRS) can be formulated as follows.

𝑇 𝐶𝑅𝑆 = { (𝑋, 𝑌): 𝑋 𝑖 ≥ ∑ 𝜆 𝑗 𝑥 𝑖𝑗 𝑛 𝑗=1 , 𝑖 = 1, … , 𝑚; 𝑌 𝑟 ≤ ∑ 𝜆 𝑗 𝑦 𝑟𝑗 𝑛 𝑗=1 , 𝑟 = 1, … , 𝑠 } (2.2)
Based on the axioms 1, 2 and 3, the production possibility set under variable returns to scale (VRS) can be expressed as

𝑇 𝑉𝑅𝑆 = {(𝑋, 𝑌): 𝑋 𝑖 ≥ ∑ 𝜆 𝑗 𝑥 𝑖𝑗 𝑛 𝑗=1 , 𝑖 = 1, … , 𝑚; 𝑌 𝑟 ≤ ∑ 𝜆 𝑗 𝑦 𝑟𝑗 𝑛 𝑗=1 , 𝑟 = 1, … , 𝑠; ∑ 𝜆 𝑗 𝑛 𝑗=1 = 1} (2.3)
Based on the axioms1, 2, 3, 4b, the production possibility set under non-increasing returns to scale (NRIS) can be formulated as follows.

𝑇 𝑁𝐼𝑅𝑆 = {(𝑋, 𝑌): 𝑋 𝑖 ≥ ∑ 𝜆 𝑗 𝑥 𝑖𝑗 𝑛 𝑗=1 , 𝑖 = 1, … , 𝑚; 𝑌 𝑟 ≤ ∑ 𝜆 𝑗 𝑦 𝑟𝑗 𝑛 𝑗=1 , 𝑟 = 1, … , 𝑠; ∑ 𝜆 𝑗 𝑛 𝑗=1 ≤ 1} (2.4)
Based on axioms 1, 2, 3 and 4c, the production possibility set under non-decreasing returns to scale (NDRS) can be shown as follows.

𝑇 𝑁𝐷𝑅𝑆 = {(𝑋, 𝑌): 𝑋 𝑖 ≥ ∑ 𝜆 𝑗 𝑥 𝑖𝑗 𝑛 𝑗=1 , 𝑖 = 1, … , 𝑚; 𝑌 𝑟 ≤ ∑ 𝜆 𝑗 𝑦 𝑟𝑗 𝑛 𝑗=1 , 𝑟 = 1, … , 𝑠; ∑ 𝜆 𝑗 𝑛 𝑗=1 ≥ 1} (2.5) (4

) Production frontier

The production frontier is a curved surface made of all efficient points in the PPS.

It represents the boundary at which production may be set to obtain the maximum output of existing inputs or to obtain minimum inputs from existing outputs. Therefore, the combination of input and output of the decision making unit (DMU) on the production frontier is optimal. According to Wei (2004), the production frontier is defined as:

Definition 2.1. Assuming 𝜔 ≥ 0,𝜇 ≥ 0,𝐿 = {(𝑋, 𝑌)|𝜔 𝑇 𝑋 -𝜇 𝑇 𝑌 = 0} , 𝑇 ⊂ {(𝑋, 𝑌)|𝜔 𝑇 𝑋 -𝜇 𝑇 𝑌 ≥ 0}
and 𝐿 ∩ 𝑇 ≠ ∅ , then the weakly efficient surface of production possibility set 𝑇 is 𝐿, and the corresponding weak production frontier is 𝐿 ∩ 𝑇. Especially, if 𝜔 ≥ 0,𝜇 ≥ 0, then 𝐿 is called the efficient surface of 𝑇, 𝐿 ∩ 𝑇 is the production frontier of production possibility set 𝑇. if the optimal value of model (2.8) is less than 1, the evaluated 𝐷𝑀𝑈 0 is inefficient.

Basic DEA models

According to the basic concepts in section 2.2, we know that CCR model is under

the assumption of constant returns to scale. [START_REF] Banker | Some models for estimating technical and scale inefficiencies in data envelopment analysis[END_REF] extended the DEA model under the assumption of variable returns to scale, which is abbreviated as BCC model. The traditional DEA model usually considers labor, capital as inputs and production yield, profit as outputs. These outputs that the DMU prefers to produce as much as possible in the production process are known as desirable outputs. However, according to the theory of joint production, desirable outputs are always accompanied by some outputs which are expected to be less in the process of production, such as carbon dioxide, sulfur dioxide, waste water, and solid waste. These outputs are defined as undesirable outputs. For example, when assessing the efficiency of paper mills, it is imperative to consider the paper products, as well as undesirable outputs such as wastewater discharge. Such comprehensive efficiency evaluation which consider both desirable outputs and undesirable outputs is called environmental efficiency evaluation.

Due to the existence of undesirable outputs in environmental efficiency evaluation, we cannot directly use the traditional DEA model to evaluate the environmental efficiency, so new processing method should be proposed. If undesirable outputs are considered in the DEA technology framework, the corresponding technology can be called the environmental DEA technology. Then, the efficiency obtained from the environmental DEA technology is defined by environmental efficiency (Zhou et al., 2008;Sueyoshi et al., 2017).

(

2) Strong and weak disposability

Strong disposability includes strong disposability of inputs and strong disposability of outputs.

Strong disposability of inputs: If (𝑋, 𝑌) ∈ 𝑇 and 𝑋 ′ ≥ 𝑋, then (𝑋 ′ , Y) ∈ 𝑇. This means if the inputs are not reduced, the original output can be produced.

Strong disposability of outputs: If (𝑋, 𝑌) ∈ 𝑇 and 𝑌 ′ ≤ 𝑌, then (X, 𝑌 ′ ) ∈ 𝑇. This means if the inputs do not change, it is feasible to produce all the reduced existing outputs in any directions (that is, some or all of the outputs are reduced).

Weak disposability includes weak disposability of inputs and weak disposability of outputs.

Weak disposability of inputs: if (𝑋, 𝑌) ∈ 𝑇 and 𝛽 ≥ 1, then (𝛽𝑋, 𝑌) ∈ 𝑇. This states if inputs 𝑋 can produce outputs, then it is possible to produce the outputs 𝑌 by increasing the inputs by a factor 𝛽.

Basic concepts of environmental efficiency evaluation

Weak disposability of outputs: If (𝑋, 𝑌) ∈ 𝑇 and 0 ≤ 𝜃 ≤ 1, then (𝑋, 𝜃𝑌) ∈ 𝑇.

This represents that if inputs 𝑋 can produce outputs 𝑌, then it is possible to produce the reduced outputs 𝜃𝑌 using the original input.

According to the above definitions, under the assumption strong disposability of inputs, the increase of inputs will not cause the decrease of outputs. While under the assumption of weak disposability of inputs, the increase of inputs may lead to the decrease of outputs.

(3) Environmental production possibility set a. Direct method

The first one is to treat the undesirable outputs under the weak disposability assumption and the desirable outputs under the strong disposability assumption. In this method, the PPS is usually assumed to satisfy the following two conditions:

CHAPTER 2. Basic DEA theory

If the production activity (𝑋, 𝑌, 𝑈) ∈ 𝑇 and 0 ≤ 𝜃 ≤ 1, then production activity (𝑋, 𝜃𝑌, 𝜃𝑈) ∈ 𝑇 , If the production activity (𝑋, 𝑌, 𝑈) ∈ 𝑇 and 𝑈 = 0, then = 0 ;

(2.12)

The second direct method is to deal with undesirable outputs based on Russell measure which is shown as follows.

𝐷 𝑇 (𝑋, 𝑌, 𝑈) = 𝐼𝑛𝑓{𝑓(𝜃 𝑖 , ∅ 𝑟 , 𝜙 𝑘 ): (𝜃 𝑖 𝑥 𝑖 , ∅ 𝑟 𝑦 𝑟 , 𝜙 𝑘 𝑢 𝑘 ) ∈ 𝑇} (2.13)

The third direct method is to treat undesirable outputs based on the slack variables:

𝐷 𝑇 (𝑋, 𝑌, 𝑈) = 𝐼𝑛𝑓{𝑓(𝑠 -, 𝑠 + , 𝑠 --): (𝑋 -𝑠 -, 𝑌 + 𝑠 + , 𝑈 -𝑠 --) ∈ 𝑇} (2.14)

The fourth direct method is to treat undesirable outputs based on the directional distance function (DDF) which measures the environment efficiency by simultaneously increasing desirable outputs and reducing undesirable outputs. The general form of DDF with undesirable outputs is defined as follows.

𝐷 𝑇 (𝑋, 𝑌, 𝑈, 𝑔) = 𝑠𝑢𝑝{𝛽: (𝑋 -𝛽𝑔 𝑋 , 𝑌 + 𝛽𝑔 𝑌 , 𝑈 -𝛽𝑔 𝑈 ) ∈ 𝑇} (2.15)

b. Indirect method

The first indirect method is to treat the undesirable outputs as inputs [START_REF] Liu | DEA models via goal programming[END_REF]. The main idea behind this method is that the efficient DMU always prefers more desirable outputs and less inputs. Because of its simplicity and clarity, this method is widely used in the environment efficiency evaluation [START_REF] Bian | Resource and environment efficiency analysis of provinces in China: A DEA approach based on Shannon's entropy[END_REF][START_REF] Shi | Chinese regional industrial energy efficiency evaluation based on a DEA model of fixing non-energy inputs[END_REF]. However, treating undesirable outputs as inputs fails to reflect the true production process.

The second indirect method is conducting data transformation to undesirable outputs first, and then evaluating the environmental efficiency by using the traditional DEA model based on the transformed data. For example, [START_REF] Scheel | Undesirable outputs in efficiency valuations[END_REF] guide the decision makers to make suitable future production plans for improving their performance.

Introduction

In recent years, with the rapid development of China's economy, China is facing huge energy consumption and serious environmental pollution problems. In order to reduce environmental pollution, the Chinese government has put forward the strategic goal of building a resource-conserving and environment-friendly society to achieve sustainable economic, energy and environmental development. For example, in 2014, China promulgated a new important environmental law, "Environmental Protection Law of People's Republic of China", which gives more punitive powers to environmental authorities and also defines geographical "red lines" where the area's ecology must require special protection (the NPC Standing Committee, 2014). Besides, the Chinese government has recognized the importance of environmental efficiency measurement and improvement and has taken a series of measures to deal with this issue, such as energy conservation assessment (ECA) and environmental impact assessment (EIA) (Hu, 2012). Among all kinds of energy types, electricity is the major resource of energy in China for many years. Furthermore, among various ways of electricity generation, China relies heavily on thermal power, hydropower and thermoelectricity. In particular, thermal power accounted for about 74.4% of all the electricity in 2016. Such a situation will be kept for a long time. As thermal power production usually produces a large amount of pollutions but with less treatment, it has become the major source resulting in the environmental problems of China. Thus, it is essential for us to measure the efficiency of thermal power firms so as to increase their productivity and reduce emissions.

Data envelopment analysis (DEA) is a non-parametric programming technique for evaluating the relative efficiency of a set of homogenous decision making units (DMUs) with multiple inputs and multiple outputs. It has been popularly applied in schools, hospitals, farms, banks and many other areas (Cook and Seiford, 2009;Cooper et al., 2004). Traditional DEA models aim at producing the maximum quantity of outputs for the given amount of inputs or consuming the minimum quantity of inputs for producing the given amount of outputs. Besides, all traditional DEA models are radial models, such as CCR, BCC and their extensions, which are either input-oriented or outputoriented [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF][START_REF] Banker | Some models for estimating technical and scale inefficiencies in data envelopment analysis[END_REF]. Comparing with these traditional DEA models, non-orientation modelling makes frontier efficiency studies more relevant to the production of thermal power firms because non-orientation ensures the analysis captures slacks on both input side and output side. Several non-orientation approaches have been built, such as the additive model, Russell measure (RM) model, slacks-based measure and so on. It should be noted that among these approaches, Russell measure (RM) model is a well-known non-orientation measure for evaluating DMUs' performance and has been applied to many areas, such as baseball batting performance, Taiwan's commercial banks [START_REF] Lozano | Russell non-radial ecoefficiency measure and scale elasticity of a sample of electric/electronic products[END_REF][START_REF] Levkoff | Boundary problems with the "Russell" graph measure of technical efficiency: a refinement[END_REF]Hsiao et al., 2011). Thus, in this chapter, we choose Russell measure as a basis for performance evaluation.

As we know, undesirable outputs, such as smoke pollution and waste, are usually produced with desirable outputs in the production processes of thermal power firms (Rivas and Magadan, 2010). These factors are expected to be as few as possible. Thus, the traditional DEA models are not applicable to measure the performance of the DMUs with undesirable outputs. Usually, the performance of DMUs with both desirable outputs and undesirable outputs is usually defined as environmental efficiency [START_REF] Fang | Choosing competitive industries in manufacturing of China under low-carbon economy: A three-stage DEA analysis[END_REF]Wu et al., 2014). So far, many DEA models have been proposed to deal with undesirable outputs and finally obtain the environmental efficiency (Fä re et al., 1989;[START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]Zhou et al., 2008).

Based on the above analysis, an approach by using the Russell measure considering the undesirable outputs is needed to measure the environmental efficiency of thermal power firm. However, according to our best knowledge, there are many theoretical works in Russell measure and undesirable outputs areas respectively but few works integrated them. Moreover, during our investigation on the thermal power firms, we found the undesirable output "solid waste" of the thermal power firm is so complex as it contains the garbage, refuse, sludge and other discarded materials including solid, liquid, semi-solid, or contained gaseous material that the data of undesirable output is difficult to be measured precisely. We can obtain a fuzzy description of the "solid waste". This requires us to further extend the above approach to be applicable to the fuzzy circumstance. But such kind of DEA work is not available in the previous works.

In this chapter, we will propose a new enhanced Russell measure model which can well CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers address the fuzzy numbers and undesirable outputs problems simultaneously, and apply the new approach to analyze the thermal power firms in Anhui province of China. Our model can provide improvements for DMUs in more directions and in more realistic situation, and thus it can be flexibly applicable to other similar cases.

3.2 Review of Russell Measure, Fuzzy DEA, and undesirable outputs

In the following subsections, four streams of literature relevant to this research are briefly summarized. They include Russell measure, Fuzzy DEA methods, undesirable outputs and environmental efficiency. Based on the literature review, the research gap is pointed out.

Russell measure

Russell measure was first introduced by Fä re and Lovell (1978). It was named as "Russell" because the scholar R.R. Russell subsequently contributed to its further development. Due to its non-radial property, it has a wide of applications. [START_REF] Lozano | Russell non-radial ecoefficiency measure and scale elasticity of a sample of electric/electronic products[END_REF] proposed a Russell non-radial eco-efficiency measure to compute eco-efficiency scale elasticity bounds. Hsiao et al. (2011) introduced the entropy concept to Russell measure DEA model for eliminating the equal-weight effect in order to increase evaluation accuracy. Although this original Russell measure accounts for all the inefficiencies of an evaluated DMU in both input side and output side, there are some evident disadvantages of this measure. One is that RM models are usually non-linear programming problems, which makes the computation complicated. Another one is that RM models cannot be well interpreted because they are weighted average of arithmetic and harmonic means [START_REF] Pastor | An enhanced DEA Russell graph efficiency measure[END_REF].

In order to avoid the mentioned difficulties, [START_REF] Pastor | An enhanced DEA Russell graph efficiency measure[END_REF] proposed a closely extended measure based on Russell measure which called Enhanced Russell measure (ERM). ERM can be interpreted as the ratio of the average efficiency of inputs and the average efficiency of outputs, which is a better interpretation of efficiency than Russell measure. Moreover, it can be decomposed into input component of average efficiency and an output one to analyze the performance of the evaluated DMUs. Besides, ERM has been studied by many other researchers because its advantage in calculation and interpretation. For example, Cooper et al. (2007) proposed an aggregate ERM that can be formed with all the desirable properties of an aggregate measure. [START_REF] Ashrafi | An enhamced Russell measure of efficiency in the presence of non-discretionary factores in data envelopment analysis[END_REF] built an Enhanced Russell measure model considering non-discretionary factors. [START_REF] Esmaeili | An enhanced Russell measure in DEA with interval data[END_REF] developed a new approach based upon the ERM for dealing with interval data in DEA.

Fuzzy DEA models

As we know, traditional DEA models assume that all the data for inputs and outputs are crisp, so they cannot deal with imprecise data. To solve this uncertain situation, fuzzy number theory is introduced in DEA area. The concept of fuzzy set was firstly proposed by [START_REF] Zadeh | Fuzzy sets[END_REF] to deal with imprecise estimates in uncertain circumstance. Recent years, numerous DEA models have been developed in the fuzzy environments. For example, Kao andLiu (2000a, 2000b) developed a procedure to measure the efficiencies of DMUs with fuzzy observations by applying 𝛼-cut approach. Leon et al. (2003) built several DEA models in fuzzy form by using some ranking methods based on the comparison of 𝛼-cut. [START_REF] Lertworasirikul | Fuzzy data envelopment analysis for supply chain modeling and analysis[END_REF] developed DEA models considering imprecise data represented by fuzzy sets. They indicated that fuzzy DEA models taking the form of fuzzy linear programming are usually solved with the aid of some methods that can rank the fuzzy sets. [START_REF] Wen | Fuzzy data envelopment analysis (DEA): Model and ranking method[END_REF] employed a fuzzy DEA model based on credibility measure and proposed a method for ranking all the DMUs. However, these previous fuzzy DEA models were extended from CCR or BCC models, which are radial models and do not account for all the slacks of the inputs and outputs simultaneously. In order to solve these deficiencies, Wang and Li (2010) proposed a fuzzy DEA model to deal with efficiency evaluation problem with imprecise data based on ERM model. Later, [START_REF] Wang | Full rank of fuzzy decision making units based on enhanced Russell measure[END_REF]

Undesirable outputs and Environmental efficiency

As we know, undesirable outputs are usually produced with desirable outputs in the production process, such as smoke pollution and waste (Perez-Calderon et al., 2011).

These factors are expected to be as few as possible. Now, research on undesirable CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers outputs has become a popular topic in DEA. According to our best knowledge, the literature in this area may be classified into two categories: direct approaches and indirect approaches. Direct approaches are mainly based on Fä re et al. (1989), which replaced strong disposability assumption of outputs by weakly disposability assumption. This work has been extensively developed (Fä re et al., 1993;[START_REF] Seiford | A response to comments on modeling undesirable factors in efficiency evaluation[END_REF]Fä re et al., 2005;[START_REF] Zhou | A non-radial DEA approach to measuring environmental performance[END_REF]Zhou et al., 2008;Tone, 2004). An important branch is employing directional distance function for addressing the undesirable outputs (Chung et al., 1997;Fä re et al., 2005). Indirect approaches are based on extended strong disposability assumption of output, which can be further divided into three categories.

The first one treats undesirable outputs as inputs for processing [START_REF] Liu | DEA models via goal programming[END_REF]Haulu and Veeman, 2001;[START_REF] Dyckhoff | Measuring ecological efficiency with data envelopment analysis (DEA)[END_REF][START_REF] Oggioni | Eco-efficiency of the world cement industry: a data envelopment analysis[END_REF]. This approach only needs the information on whether the data has to be minimized or maximized, but it cannot reflect a real production process [START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]. The second one includes a non-linear monotonic decreasing transformation approach [START_REF] Scheel | Undesirable outputs in efficiency valuations[END_REF] and a linear monotonic decreasing transformation approach [START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]. Some applications by using the second method can see [START_REF] Oggioni | Eco-efficiency of the world cement industry: a data envelopment analysis[END_REF], [START_REF] Grubesic | Evaluating the efficiency of the Essential Air Service program in the United States[END_REF] and Wu et al. (2013). The last one is slacks-based measure (SBM) approach, which deals with the undesirable outputs through the slacks of undesirable outputs (Tone, 2004).

Environmental efficiency refers to the efficiency of DMUs which consider both desirable outputs and undesirable outputs. A lot of environmental efficiency analysis by DEA approach has been taken. [START_REF] Korhonen | Eco-efficiency analysis of power plants: An extension of data envelopment analysis[END_REF] proposed two different approaches to measuring the environmental efficiency of 24 power plants in a European country: one approach is to measure technical efficiency and ecological efficiency (the relation of the desirable output to the undesirable outputs) separately, the other approach treat the undesirable outputs as inputs. Barba-Gutierrez et al. (2009) used DEA model to evaluate the eco-efficiency of different commonplace household electric appliances. Bi et al. (2012) proposed a slacks-based environmental efficiency index based on data envelopment analysis and were applied to analyze the industry sector of China. Huang et al. (2014) built a new DEA model, combining global benchmark technology, undesirable output, super efficiency and slacks-based measure, for measuring the dynamic change of regional environmental efficiency in China. Li Even though environmental efficiency has already extensively applied in many areas, it is rarely seen in the fuzzy circumstance, including the theoretical and practical works. In this chapter, we will consider a more complex but common circumstance in thermal power firms where the decision making units have fuzzy numbers and undesirable outputs simultaneously. Combining fuzzy numbers and undesirable output, a new approach is proposed in this chapter for addressing this environmental scenario based on Enhanced Russell measure. This chapter not only inherits the advantages of data envelopment analysis, but also extends DEA approach theoretically to solve a more real and complex problem. Assume that there are n DMUs in set N to be evaluated, each of which consumes the same inputs to produce the same outputs 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ) 𝑇 and 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) 𝑇 are inputs and outputs of 𝐷𝑀𝑈 𝑗 , respectively. 𝑋 𝑗 ≥ 𝟎 and 𝑌 𝑗 ≥ 𝟎 , at least one element in input vector and output vector is larger than 0.

Russell measure is a combination of the input and output measures of technical efficiency. For a given DMU, DMU 0 (𝑋 0 , 𝑌 0 ) , the technical efficiency of Russell measure can be obtained by the following model: Where 𝜆 𝑗 are intensity variables (also called structure variables). This model is under

the assumption of constant returns to scale (CRS). By adding the constraint ∑ 𝜆 𝑗 𝑛 𝑗=1

= 1 in the above model, we can deal with the variable returns to scale (VRS) case.

From model (3.1), we can find that 𝑅 𝑔 is a weighted average of arithmetic and harmonic means which is difficult to interpret and compute. Concerning these deficiencies, [START_REF] Pastor | An enhanced DEA Russell graph efficiency measure[END_REF] proposed the Enhanced Russell measure which is represented in the following model.

0 1 0 1 0 1 0 1 min . . , 1,... , , 1,..., , 1; 1; 0, 1,..., , 1,..., . m i i e s r r n ij j i i j n rj j r r j i r j m R s s t x x i m y y r s i m r s                        (3.2)
Similarly, the VRS version of ERM can be obtained by adding the constraint

∑ 𝜆 𝑗 𝑛 𝑗=1 = 1. The objective of model (3.
2) is minimizing the ratio of the average efficiency of inputs to the average inefficiency of outputs. When the optimal value of 𝑅 𝑒 is equal to 1, the DMU being evaluated is Koopmans-efficient (Koopmans, 1951).

The above non-linear programming problem can be transformed into a linear one by employing the method in [START_REF] Charnes | Programming with linear fractional functionals[END_REF]. Here, we omit the process of this transformation process. More details can be seen in [START_REF] Pastor | An enhanced DEA Russell graph efficiency measure[END_REF]. number. Among them, triangular fuzzy number is one of important and commonly used fuzzy numbers. Except for the triangular fuzzy number itself, the crisp number can also be treated as a degenerated interval fuzzy number with only one value in the domain.

Thus, we can see all the variables of the DMUs as triangular fuzzy numbers.

Suppose 𝑄 is triangular fuzzy number, 𝑄 𝐿 and 𝑄 𝑈 are the least and most desirable bound values, respectively, 𝑄 𝑀 is the center of fuzzy number, the triangular fuzzy number can be expressed by Q = (𝑄 𝐿 , 𝑄 𝑀 , 𝑄 𝑈 ) and the membership function is

    ,, ( ) , , 0 , , ,
L LM ML U MU Q UM LU qQ q Q Q QQ Qq q q Q Q QQ q Q Q                            (3.3)
Denote the cut   of the triangular fuzzy number 𝑄 by 𝑄 𝛼 which satisfies 𝑄 𝛼 = {𝑞|𝜇 𝑄 (𝑞) ≥ 𝛼}, where (0 ≤ 𝛼 ≤ 1). Then, 𝑄 𝛼 = [(𝑄) 𝛼 𝐿 , (𝑄) 𝛼 𝑈 ]. According to this, for any triangular fuzzy number, we can transform it into interval. Thus, the 𝛼 -cut of the efficiencies of the evaluated DMU can be obtained accordingly.

In addition, it has been mentioned that there are four methods mentioned in section 3.2 for dealing with undesirable outputs. In fact, each way has its own strengths and weaknesses. All of them can be used to address the undesirable outputs as long as they reflect the meaningful economic trade-offs among undesirable outputs, desirable outputs and inputs, that is, one cannot reduce undesirable outputs for free. Whether one should assume an extended strong disposability or a weak disposability in a DEA model will much depend on the nature of the applications that it handles [START_REF] Liu | DEA models with undesirable inputs and outputs[END_REF]. As the undesirable outputs in the thermal power firms can be increased without reducing the amount of total industrial output value, thus the strong disposability of undesirable output is selected. Based on the chapter 2, the approach of Zhu and [START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF] in extended strong disposability assumption group is used in the development of the new CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers model, that is, adding a big enough positive scalar w to the reciprocal additive transformation of the kth undesirable output 𝑢 𝑘𝑗 .

Suppose that there are n DMUs in set N to be evaluated. For 𝐷𝑀𝑈 𝑗 (j = 1,2, … , n) , it applies inputs 𝑥 𝑖𝑗 (𝑖 = 1, … , 𝑚) ≥ 0, to produce desirable outputs 𝑦 𝑟𝑗 (𝑟 = 1, … , 𝑠) ≥ 0 and undesirable outputs 𝑢 𝑘𝑗 (𝑘 = 1, … , g) ≥ 0. Denote 𝑥 ̃𝑖𝑗 , 𝑦 ̃𝑟𝑗 and 𝑢 ̃𝑘𝑗 as the fuzzy counterparts of 𝑥 𝑖𝑗 , 𝑦 𝑟𝑗 and 𝑢 𝑘𝑗 , respectively. Fuzzy ERM model for measuring the efficiency of 𝐷𝑀𝑈 0 with undesirable outputs is as follows:

1 1 1 0 1 0 1 0 1 1 min 1 ( ) . . ; 1,..., , ; 1,..., , ; 1,..., , 1, , , 1, , , ,, 0, 1,
..., .

m i i e g s r k r k n j ij i i j n j rj r r j n j kj k k j i rk k kj j m R sg s t x x i m y y r s u u k g i rk w k u jn                               (3.4)
The model is clearly a non-linear programming with a fractional structure objective function. The variables of this model are 𝜃 𝑖 , 𝜑 𝑟 , 𝜙 𝑘 , 𝜆 𝑗 , wherein 𝜆 𝑗 is intensity variable, m, s, g are the number of inputs, good outputs and undesirable outputs, respectively. 𝑢 ̅ ̃𝑘𝑗 = -𝑢 ̃𝑘𝑗 + 𝑤 , where w is big enough positive value. This is the second method in indirect approaches for addressing undesirable outputs.

If 𝑢 ̃𝑘𝑗 = [𝑢 𝑘𝑗 𝐿 , 𝑢 𝑘𝑗 𝑀 , 𝑢 𝑘𝑗 𝑈 ], then the transformed vector is 𝑢 ̅ ̃𝑘𝑗 = [-𝑢 𝑘𝑗 𝑈 + 𝑤, -𝑢 𝑘𝑗 𝑀 + 𝑤, -𝑢 𝑘𝑗 𝐿 + 𝑤] = [𝑢 ̅ 𝑘𝑗 𝐿 , 𝑢 ̅ 𝑘𝑗 𝑀 , 𝑢 ̅ 𝑘𝑗 𝑈 ].
As the transformed undesirable output 𝑢 ̅ ̃𝑘𝑗 can be smaller than zero at its minimum level, thus -𝑢 𝑘𝑗 + 𝑤 ≥ 0, that is, 𝑢 𝑘𝑗 cannot be larger than 𝑤. CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers

1 11 0 0 0 1 0 00 1 0 0 0 0 1 0 min ( ) .. ( ) ( ) ( ) , 1,..., , ( ) ( ) ( ) , 1,..., , ( ) ( ) ( ) , 1,..., , ,, , m i U i e g s rk rk n U L L j ij i i i j j n L U U j rj r r ro a j j n L U U j kj k k k j j r i b R m s t a c s g t x t x b x i m t y t y a y r s t u t u c u k g ar bi                                       , , , ,, 0, , 0 1.
0 0 0 1 0 min ( ) .. ( ) ( ) ( ) , 1,..., , ( ) ( ) ( ) , 1,..., , ( ) ( ) ( ) , 1,..., , ,, , m i L i e g s rk rk n L U U j ij i i i j j n U L L j rj r r ro a j j n U L L j kj k k k j j r i b R m s t a c s g t x t x b x i m t y t y a y r s t u t u c u k g ar bi                                       , , , ,, 0, , 0 1.
k L k j ck ck tj         (3.7)
The optimal values of model (3.6) and model (3.7) constitute the α-cut of the highest and lowest efficiency of 𝐷𝑀𝑈 0 . We treat our model as a parametric program related to the possible value of α-cut over the interval [0, 1]. Since the interval contains an infinite number of real values between 0 and 1, we cannot consider all the values. Instead, we discretize the interval by only considering a finite number of values= 𝑘 × 𝛥, 𝑘 = 0,1, … , 𝐾. ,where K is the largest integer equal to 1 Δ ⁄ , Δ is a step size, in this chapter, we set it 0.1. For each 𝛼, we can solve model (3.6) and (3.7) to obtain their corresponding objective values. In this way, we can obtain the lower bound efficiency and upper bound efficiency of the DMUs in each scenario. Then, the DMUs can be ranked through these interval efficiencies in different scenarios. Moreover, the possible rules of the efficiencies when 𝛼 is located in some intervals can be found to guide the decision maker to make more suitable policy when the real 𝛼 is unknown.

CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers

Application to the environmental efficiency evaluation of thermal power firms in China

In this section, we apply our approach to evaluate the environmental efficiencies of 30 thermal power firms in China in the year of 2010, which contain fuzzy number and undesirable output. According to the properties of this kind of firms, we select "production time" and "coal consumption" as inputs, "total industrial output value" as desirable output, and "solid waste" as undesirable output. The factor of "production time" chosen as an input is mainly because it can well reflect the workloads of workers and the cost of the firms' machines. This indicator was also used in Song et al. (2014) for evaluating the thermoelectric firms which is very similar with the thermal power firms. "Solid waste" contains the garbage, refuse, sludge and other discarded materials including solid, liquid, semi-solid, or contained gaseous material, from the thermal power firms. Because of the complexity of solid wastes, a fuzzy description of the solid waste is obtained. Except "Solid waste", the other indexes are precisely obtained. The units of these indexes are "hours", "tons", "10 thousand RMB" and "tons" respectively.

Denote "production time", "coal consumption", "total industrial output value" by 𝑥 1 ,𝑥 2 , 𝑦 respectively, and the lower, middle and upper level of "solid waste" by 𝑢 𝐿 , 𝑢 𝑀 , 𝑢 𝑈 respectively. The statistical descriptions of these data are shown in Table 3.1. It can be seen from Table 3.1 that "coal consumption" had the largest mean value (expectation) while "production time" had the lowest mean value (expectation). Besides, all the data of these indexes had a large of variance, which can be indicated by the standard deviation of these indexes. Among them, "production time" data had the largest concentration, which can be calculated by the ratio of standard deviation and mean. Moreover, the maximum and minimum values of each index had a large deviation.

Before applying our new model, we first transform the undesirable outputs into "desirable outputs" by 𝑢 ̅ ̃𝑘𝑗 = -𝑢 ̃𝑘𝑗 + 𝑤, and let w=17228652. By using model (3.6) and model (3.7), the upper and lower bounds of the 𝛼 -cut fuzzy efficiency of the DMUs under evaluated are obtained. Table 3.2 shows the upper and lower bounds of the fuzzy efficiency when 𝛼 is set 0 to 1 with a step 0.1 respectively. 0.8 0.9 1 L 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 L 0.9278 0.9278 0.9278 0.9279 0.9279 0.9279 0.9279 0.9280 0.9280 0.9280 0.9280 U 0.9282 0.9282 0.9282 0.9282 0.9281 0.9281 0.9281 0.9281 0.9281 0.9280 0.9280 L 0.8654 0.8657 0.8661 0.8665 0.8668 0.8672 0.8676 0.8679 0.8683 0.8687 0.8691 U 0.8727 0.8724 0.8720 0.8716 0.8713 0.8709 0.8705 0.8702 0.8698 0.8694 0.8691 L 0.4014 0.4014 0.4014 0.4014 0.4014 0.4015 0.4015 0.4015 0.4015 0.4015 0.4015 U 0.4016 0.4016 0.4016 0.4016 0.4016 0.4016 0.4016 0.4016 0.4015 0.4015 0.4015 L 0.9641 0.9641 0.9642 0.9642 0.9642 0.9643 0.9643 0.9643 0.9643 0.9644 0.9644 U 0.9647 0.9647 0.9647 0.9646 0.9646 0.9646 0.9645 0.9645 0.9645 0.9644 0.9644 L 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 L 0.7644 0.7646 0.7647 0.7649 0.7650 0.7652 0.7653 0.7655 0.7656 0.7658 0.7659 U 0.7674 0.7672 0.7671 0.7669 0.7668 0.7666 0.9721 0.7663 0.7662 0.7660 0.7659 L 0.7828 0.7829 0.7829 0.7829 0.7829 0.7830 0.7830 0.7830 0.7830 0.7831 0.7831 U 0.7833 0.7833 0.7833 0.7833 0.7832 0.7832 0.7832 0.7832 0.7831 0.7831 0.7831 L 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 0.7845 0.7842 0.7839 0.7836 0.7833 0.7830 0.7827 0.7824 0.7821 0.7818 0.7815 L 0.6680 0.6682 0.6684 0.6686 0.6688 0.6690 0.6692 0.6694 0.6696 0.6698 0.6700 U 0.6719 0.6717 0.6715 0.6713 0.7035 0.6710 0.6708 0.6706 0.6704 0.6702 0.6700 L 0.5172 0.5173 0.5173 0.5174 0.5174 0.5175 0.5176 0.5176 0.5177 0.5177 0.5178 U 0.5183 0.5183 0.5182 0.5182 0.5181 0.5180 0.5180 0.5179 0.5179 0.5178 0.5178 L 0.7458 0.7461 0.7464 0.7468 0.7471 0.7474 0.7477 0.7480 0.7484 0.7487 0.7490 U 0.7522 0.7519 0.7516 0.7512 0.7509 0.7506 0.7503 0.7500 0.7496 0.7493 0.7490 L 0.4638 0.4639 0.4639 0.4640 0.4640 0.4641 0.4642 0.4642 0.4643 0.4644 0.4644 U 0.4651 0.4650 0.4649 0.4649 0.4648 0.4647 0.4647 0.4646 0.4646 0.4645 0.4644 L 0.5601 0.5601 0.5602 0.5602 0.5602 0.5602 0.5603 0.5603 0.5603 0.5603 0.5604 U 0.5606 0.5606 0.5606 0.5605 0.5605 0.5605 0.5605 0.5604 0.5604 0.5604 0.5604 L 0.6313 0.6314 0.6315 0.6316 0.6317 0.6318 0.6319 0.6320 0.6320 0.6321 0.6322 U 0.6332 0.6331 0.6330 0.6329 0.6328 0.8951 0.6326 0.6325 0.6324 0.6323 0.6322 L 0.7147 0.7151 0.7154 0.7158 0.7162 0.7165 0.7169 0.7172 0.7176 0.7179 0.7183 U 0.7218 0.7215 0.7211 0.7208 0.7204 0.7201 0.7197 0.7193 0.7190 0.7186 0.7183 L 0.0000 0.0059 0.0117 0.0174 0.0230 0.0285 0.0339 0.0393 0.0445 0.0496 0.0547 U 0.1010 0.0967 0.0923 0.0878 0.0833 0.0787 0.0741 0.0694 0.0645 0.0597 0.0547 L 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 L 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 U 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Application to the environmental efficiency evaluation of thermal power firms in China 37

From Table 3.2, we can find that 6 of 30 thermal power firms were fully efficient whose upper and lower bound were all equal to 1 for any α, and the remaining 24 firms became inefficient when the value of α varies from 0 to 1. Moreover, when α increases, the upper bound efficiency of the evaluated DMU decreased and the lower bound increased. For example, for DMU5, when α varies from 0.1 to 0.9, the upper bound of the efficiency decreased from 0.9647 to 0.9644, while the lower bound efficiency increased from 0.9641 to 0.9644. There are two special cases, 𝛼 = 1 and 0, that should be mentioned. When α is equal to 1, there is only one value in the α -cut for the undesirable output of every DMU. In this case, the efficiency of the evaluated value is a crisp value. When 𝛼 =0, the efficiency scores of a specific DMU has the largest interval between the upper and lower bounds. For instance, the efficiency of 𝐷𝑀𝑈 12 was always 0.8828 when 𝛼 = 1, and the efficiency value varied between 0.8794 and 0.8883 when 𝛼 = 0.

Through the internal efficiencies in Table 3.2, we can rank the DMUs in each scenario by their geometric mean. For the sake of conciseness, we will not give the geometric average efficiency but just show the ranking of DMUs directly.

The first six DMUs were always efficient in all scenarios, they all rank No 1. A super efficiency method by [START_REF] Wang | Full rank of fuzzy decision making units based on enhanced Russell measure[END_REF] may be used to further rank these efficient DMUs. Then, DMU 5, 2, 12, 3, 10, 8 followed one by one after the above efficient DMUs, which had the same ranking in all scenarios. DMU 20,15,7,23,27,18,19,11,21,16,17,26 ranked differently in each scenario. Finally,DMU 25,22,24, 13, 4, 28 followed in the same order after the above DMUs in all scenarios.

It can be seen from Table 3.2 and Table 3.3 that DMU 13 and 24 had the worst performance among the enterprises, whose efficiencies were below 0.5, while all other enterprises' efficiencies were larger than 0.5. This means that DMU 13 and 24 had a large space for improvement in the future and they should take measures to solve the current inefficiencies. Through the results in Table 3.2, the average efficiencies of thermal power firms can be calculated. The average lower bound and upper bound efficiencies are around 0.73 to 0.74, which indicates that the average efficiencies of these firms are at a high level. This is probably because China (including Anhui province) has paid more attention to the environmental protection. Chinese government has introduced a series of laws for investigating and controlling the environment, such Moreover, our approach can provide benchmarks for the evaluated firms to improve their efficiencies. In order to illustrate this, we take the scenario α = 0.5 as an example. Denote the indexes of "Production time", "Coal consumption", " Based on the benchmarks in Table 3.4, we find that most of the improvements should be taken on the inputs. The total industrial output value and solid waste only need increase a small value at the current level. This indicates that if the firm wants to be environmental efficient, it should focus on its attention to its utilization of inputs. By these proportions of indexes, we can easily obtain the benchmarks (or targets) for evaluated DMUs when using the upper value of transformed "solid waste" under the best fuzzy circumstance. Similarly, through model (3.7), we can obtain the benchmarks (or targets) for evaluated DMUs when they obtain the lower value under the worst fuzzy circumstance. Because the limitation of contents, we omit this part to save space.

Conclusions

In this chapter, in order to measure the environmental efficiency of thermal power firms, we propose a fuzzy Enhanced Russell measure approach in the present of undesirable output. Firstly, the Fuzzy Enhanced Russell measure model is built based on the previous Enhanced Russell measure and fuzzy DEA models. Then, α-cut method is used to calculate the upper and lower bound environmental efficiencies. Finally, 30 thermal power firms in China are analyzed by our approach. Six efficient firms are determined, which coincides with the common sense about the situation of these firms.

The average environmental efficiency of 30 firms is good. We believe that with "the environmental law abiding guideline for thermal power firms" published by the Ministry of Environmental Protection of China in March 2013, these firms will have a better environmental efficiency because they are forced to enhance the pollution prevention and increase the environmental management level under this law.

Furthermore, the benchmarks for DMUs under a certain fuzzy circumstance are given.

It should be noted that 𝛼 -cut based method is chosen to solve the fuzzy programming problem in this chapter. Actually, there are several other methods, such as tolerance approach [START_REF] Sengupta | A fuzzy systems approach in data envelopment analysis[END_REF], possibility approach [START_REF] Lertworasirikul | Fuzzy BCC model for data envelopment analysis[END_REF], that can be used to address this problem. In the future, we will compare these methods in solving the problem. Moreover, how to apply our approach to more applications, such as real example with the ordinal data, is also an interesting research topic.

CHAPTER 4

Environmental efficiency evaluation of a single-stage system considering performance improvement path Contents [START_REF] Li | Heterogeneity analysis of the effects of technology progress on carbon intensity in China[END_REF]. While scientific evaluation of environmental efficiency can provide reasonable basis for enterprises or local governments to implement specific solutions for performance improvement.

However, due to the lack of professional environmental efficiency evaluation and scientific targets for efficiency improvement, Xiangjiang River Basin is still facing water resources shortage, water and atmospheric pollution and heavy metal pollution.

Therefore, it is urgent to measure the water environmental efficiency and set the benchmarks for Xiangjiang River Basin. Environmental efficiency can comprehensively reflect the ecological situation because it considers both the economic factors and environmental factors in the efficiency evaluation [START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF][START_REF] Fang | Choosing competitive industries in manufacturing of China under low-carbon economy: A three-stage DEA analysis[END_REF]. In this chapter, data envelopment analysis (DEA) approach with the closest target is applied to measure the environmental efficiency and set the closest targets for Xiangjiang River Basin.

DEA, as a non-parametric programming technique, has become more and more popular in evaluating the performance of a set of homogenous decision making units (DMUs) (An et al., 2016;[START_REF] Li | Heterogeneity analysis of the effects of technology progress on carbon intensity in China[END_REF]. So far, it has been widely applied in evaluating the environmental efficiency or ecological efficiency (Fä re et al., 1989;Tone, 2004;[START_REF] Leleu | Shadow pricing of undesirable outputs in nonparametric analysis[END_REF][START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF]. [START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF] reviewed the DEA models for environmental efficiency when considering a system as a "black box". In that review, environmental efficiency evaluation methods are classified into three categories according to their ways for addressing the undesirable outputs. In fact, several other methods should be added now. One is slacks-based measure (SBM) approach by Tone (2004) which deals with the undesirable outputs through the slacks of undesirable outputs. This method can simultaneously measure the inefficiencies in the inputs and outputs while the traditional method only can radial measure the efficiency improvement. Among the previous methods, an important and popular method is on weakly disposability assumption which is based on Fä re et al. (1989) where undesirable outputs are treated as their original forms. Several works have been developed in this direction [START_REF] Leleu | Shadow pricing of undesirable outputs in nonparametric analysis[END_REF][START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF][START_REF] Miao | Efficient allocation of CO2 emissions in China: a zero sum gains data envelopment model[END_REF]. Another important category of approaches treat pollution as a free disposable input [START_REF] Hailu | Non-parametric productivity analysis with References 151[END_REF]An et al., 2017). Each method has its own strengths and weaknesses. All of them can be used to address the undesirable outputs as long as they reflect the meaningful economic trade-offs among undesirable outputs, desirable outputs and inputs, that is, one cannot reduce undesirable outputs for free [START_REF] Liu | DEA models with undesirable inputs and outputs[END_REF]. Whether one should assume a strong disposability or a weakly disposability in a DEA model is mainly depend on the nature of the applications that it handles.

However, the previous studies almost set the "furthest" target for a DMU to reach efficient while measuring the environmental efficiency. Thus, the benchmark (target) may be not easily acceptable by the DMU. Recently, some developments focus on finding the "closest" target so that the DMU under evaluation can achieve efficient with the "least" effort. The idea behind the closest target is that the closer target suggests directions of improvement for the inputs and outputs of the inefficient unit that will lead the DMU to be efficient with least effort. There are two ways for finding the closest target. One is minimizing the selected distance. [START_REF] Frei | Projections onto efficient frontiers: theoretical and computational extensions to DEA[END_REF]

1 1 0 0 1 1 (1 ) / (1+ ) m s i r i r i r s s Min m x s y        (Tone, 2001).
Compared with the SBM model, the RAM model is not only a non-radial model that can simultaneously measure the inefficiency of inputs and outputs, but also can deal with also non-positive data in the input and output indicators. Thus, RAM is more suitable for the general environmental efficiency evaluation problem.

∂(𝑇) = {(𝑋, 𝑌) ∈ 𝑃|𝑋 ′ ≤ 𝑋, 𝑌 ′ ≥ 𝑌 ⟹ (𝑋 ′ , 𝑌 ′ ) = (𝑋, 𝑌)} (4.2) or 𝜕(𝑇) = {(𝑋, 𝑌)| -𝑣𝑋 + 𝑤𝑌 = 0, -𝑣𝑋 𝑗 + 𝑤𝑌 𝑗 ≤ 0, 𝑗 = 1, … , 𝑛, 𝑣 > 0 𝑚 , 𝑤 > 0 𝑚 } (4.3)
in the multiplier form with input and output weights (Ruiz et al., 2014).

Denote the set of extreme efficient points in the PPS by 𝐸. The following theorem from [START_REF] Aparicio | Closest targets and minimum distance to the Pareto-efficient frontier in DEA[END_REF] provides a useful characterization of 𝜕(𝑇), which will be used in the formulation of the closest target setting model:

Theorem 4.1 𝜕(𝑇) = { (𝑋, 𝑌) ∈ ℝ + 𝑚+𝑠 | | 𝑋 = ∑ 𝜆 𝑗 𝑋 𝑗 𝑗∈𝐸 , 𝑌 = ∑ 𝜆 𝑗 𝑌 𝑗 𝑗∈𝐸 , -𝑣𝑋 𝑗 + 𝑤𝑌 𝑗 + 𝑑 𝑗 = 0, 𝑗 ∈ 𝐸 𝑣 > 1 𝑚 , 𝑤 > 1 𝑠 𝑑 𝑗 ≤ 𝑀𝑏 𝑗 , 𝑗 ∈ 𝐸 𝜆 𝑗 ≤ 𝑀(1 -𝑏 𝑗 ), 𝑗 ∈ 𝐸 𝑑 𝑗 , 𝜆 𝑗 ≥ 0, 𝑏 𝑗 ∈ {0,1}, 𝑗 ∈ 𝐸 }
where M is a big positive quantity.

Proof. The proof is similar with [START_REF] Aparicio | Closest targets and minimum distance to the Pareto-efficient frontier in DEA[END_REF]. We omit it here.

Theorem 4.1 shows the points on a Pareto-efficient face of the technology, which are dominating the evaluated 𝐷𝑀𝑈 0 (𝑋 𝑜 , 𝑌 𝑜 ), can be expressed as a combination of extreme efficient units lying on the same efficient face of the production possibility set. More importantly, the set of infeasible points in which the minimum distance to the Pareto-efficient frontier is attained can be represented by a set of linear constraints.

Then, by applying it to the closest target model, we can find the closest target for inefficient DMU 𝑜 , such as Aparicio et al.'s (2007) mADD model.

Closest target RAM model considering undesirable outputs

Assume that n DMUs will be evaluated. Each of them 𝐷𝑀𝑈 𝑗 (𝑗 = 1, … , 𝑛)uses m inputs to produce s desirable outputs while generating q undesirable outputs. The notations are given as follows. 𝑥 𝑖𝑗 (𝑖 = 1, . . , 𝑚) is the ith input of 𝐷𝑀𝑈 𝑗 , 𝑦 𝑟𝑗 (𝑟 = 1, . . , 𝑠)is the rth desirable output of 𝐷𝑀𝑈 𝑗 and 𝑧 𝑝𝑗 (𝑝 = 1, . . , 𝑞) is the pth undesirable output of 𝐷𝑀𝑈 𝑗 . Based on the notations, the related definition of production possibility set is given.

Definition 4.2. The production possibility set considering undesirable outputs is defined as follows. where 𝜆 𝑗 stands for unknown variables (often referred to as "structural" or "intensity" variables) for connecting the input and output vectors by a convex combination. This production possibility set is under the constant variables to scale, by adding ∑ 𝜆 𝑗 𝑛 𝑗=1 = 1, the production possibility set will become under the variable returns to scale. In Definition 4.2, undesirable outputs are treated as inputs, which is similar to the way in [START_REF] Liu | DEA models via goal programming[END_REF]. The efficient DMUs always wish to minimize desirable inputs and undesirable outputs, and to maximize desirable outputs and undesirable inputs. As [START_REF] Liu | DEA models with undesirable inputs and outputs[END_REF] pointed out that if one only wishes to investigate operational efficiency from this point of view, there is no need to distinguish between inputs and outputs, but only minimum and maximum.

Based on the RAM model, we firstly construct the RAM model considering undesirable outputs, and then measure the environmental efficiency of the evaluated 𝐷𝑀𝑈 0 . The model is expressed as follows.

s s j n i m r s                                             ; 1,...,
q m s p i r e i p r i p i s ss m p s s R R R                   (4.5)
When the optimal value of model ( 4 in multiplier form with input and output weights.

Different from the model (4.4), based on the set H, we build the following closest target model for measuring the environmental efficiency of the evaluated 𝐷𝑀𝑈, i.e., 𝐷𝑀𝑈 0 , and meanwhile set the closest target for it to be efficient.

Closest target RAM model considering undesirable outputs

51 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 ( ) . . , 1,..., , , 1,..., , , 1,..., , 0, , 1 ( q m s p i r i p r i p i j ij i i jH j rj r r jH j pj p p jH q m s i ij p ij r rj j i p r i s s s Max m p s R R s R s t x s x i m y s y r s z s z p q v x z w y d j H v m q s                                                     0 0 0 1,..., ) 1 1,..., ( ) 1 1,..., , ( ) , , (1 ), , {0,1}, 0, 0, , , , 0, 1,
..., ; 1,..., ; 1,..., .

i p p r i j j j j j j j i r p i m R p q m q s R w r s m q s R d Mb j H M b j H b d j H s s s i m r s p q                              , , , , , (4.8)
where 𝑠 𝑖0 -, 𝑠 𝑟0 + and 𝑠 𝑝0 --are the slacks of the ith input, the rth desirable output and the pth undesirable output of 𝐷𝑀𝑈 𝑜 . M is a big enough positive quantity. The first three constraints are used to calculate the slacks to the linear combination of extreme efficient units and dominate 𝐷𝑀𝑈 𝑜 . The fourth to seventh constraints are the constraints corresponding to the multiplier formulation of RAM DEA model, but it only considered the extreme efficient DMUs in H, which can ensure that we consider all the possible points in 𝑇 𝑒𝑛𝑣 lie on or below these the hyperplanes. The eighth to tenth constraints are the key conditions that determine which DMU is active as a peer for the evaluation of 𝐷𝑀𝑈 𝑜 . If 𝜆 𝑗 > 0, then 𝑏 𝑗 = 0, 𝑑 𝑗 = 0. Thus, if 𝐷𝑀𝑈 𝑗 participates actively as a peer then it necessarily belongs to the hyperplane

1 1 1 0 q ms i ij p ij r rj j i p r v x z w y d             . If
𝜆 𝑗 = 0,then 𝑑 𝑗 ≥ 0, which indicates 𝐷𝑀𝑈 𝑗 is not a peer for evaluating 𝐷𝑀𝑈 0 .

Considering the constraints of the model (4.4) and model (4.8), the following theorem can be easily derived. We state Theorem 4.2 without proof. ) is an optimal solution of the closest target model (4.8). Then, the closest target for the evaluated 𝐷𝑀𝑈 𝑜 can be expressed as:

(𝑥 ̂𝑖0 = 𝑥 𝑖0 -𝑠 𝑖0 - * , 𝑦 ̂𝑟0 = 𝑦 𝑟0 + 𝑠 𝑖0 + * , 𝑧p 0 = 𝑧 𝑝0 -𝑠 𝑝0 -- * ) (4.9)

The environmental efficiency for the evaluated 𝐷𝑀𝑈 𝑜 based on the closest target can be obtained by computing the following formula. -- * ≥ 0, the optimal slacks in model (4.8) must be equal to zero too. Thus, the 𝐷𝑀𝑈 0 must be environmental efficient.

* * * 0 0 0 1 1 1 1 1 1 ( ) q m s p i r env i p r i p i s s s m p s R R s R                    (

Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China

In this section, we apply the proposed model to evaluate the environmental efficiency of water system in Xiangjiang River Basin in China. The results show that the water environmental efficiency obtained from model (4.8) is higher than the It can be clearly seen that the average water environmental efficiency was very high during this period. Compared with the classical water environment efficiency, we find that the water environment efficiency was more stable and the difference between cities was much smaller. The results showed that the closest target of each inefficient city was stable and more easily achieved.

Since the benchmarking analysis of the 15 monitoring areas of each year was similar, we only analyze the closest targets of the areas in 2014 to illustrate the proposed model.

The benchmarks in Table 4.6 provided the closest targets for the 15 monitoring areas to balance the development of economic growth with water environmental protection so as to achieve water environmental efficient. The areas marked in bold were water environmental efficient in 2014, that is the Trunk area of Changsha, and the Leishui area of Chenzhou. Except these areas, the other areas were water environment inefficient that needed to reduce inputs (labour, capital stock and energy consumption)

or increase GDP and dissolved oxygen or reduce total phosphorus in order to be efficient. Taking Lianshui area of Loudi as an example, in order to achieve efficient, we should reduce the labor force of 406.68 units and the energy consumption of 374.551 units, besides, the dissolved oxygen should be increased by 0.140 units and the total phosphorus should be decreased by 0.043 units, while maintaining the gross domestic product (GDP) and capital stock. It is noted that through the proposed method, we can not only measure the water environmental efficiency of each area but also provide the closest target for each inefficient area. Therefore, the proposed method has a strong appeal for guiding local government to formulate relevant economic and environmental policies. For example, if the environmental efficiency of an area performs badly, the government should issue policies to stimulate companies to use high-tech to reduce pollution, or shut down heavily polluted enterprises to reduce environmental pollution. system considering performance improvement path

Conclusions

The previous studies almost set the "furthest" target for a DMU to reach the environmental efficient while measuring the environmental efficiency. In this chapter, in order to make the evaluated DMU to achieve environmental efficiency with least effort, we construct a closest target environmental efficiency evaluation method based on RAM. Besides, the proposed method is applied to investigate the water environmental efficiency of Xiangjiang River Basin in China.

The results show that the average water environmental efficiency of the water system in Xiangjiang River Basin remained at a higher level from 2008-2014. This indicates that Hunan Province had made certain achievements in building a harmonious society with coordinated development of economy and environment. Compared with the classical environmental efficiency method, the water environmental efficiency obtained by the proposed method was higher than the classical method. Moreover, the proposed method can provide the closest target for the inefficient DMU to achieve efficient.

In addition, we find that most water environmental efficient areas are economically developed cities, such as Changsha and Zhuzhou. Therefore, the other inefficient areas can learn from these efficient areas and formulate corresponding policies according to their economic level and environmental conditions to improve the environmental efficiency.

CHAPTER 5

Environmental efficiency evaluation of a two-stage system via total-factor energy efficiency degradation caused by waste gas emissions, such as the heavy haze environmental problem in most of China's provinces (Wang et al., 2014). In order to realize sustainable development, China has to consider how to reduce energy consumption and pollutant emissions while maintaining rapid economic growth. China's 12th Five-Year Plan announced several new energy and CO 2 emission targets to be reached by 2015, reducing China's energy usage by 16%, SO 2 emissions and Chemical Oxygen Demand (COD) by 8%, and CO 2 emissions per unit of GDP by 17%. Targets for each China's provinces have also been announced. One of the critical tools to reduce final energy consumption, improve industrial competitiveness, and reduce pollutant emission is to measure and improve energy and environmental efficiency [START_REF] Oikonomou | Energy saving and energy efficiency concepts for policy making[END_REF].

In order to realize the goals of China's 12th Five-Year Plan, it is necessary to analyze the implementation situation of China's 11th Five-Year Plan, so the policymakers can take better measures to improve performance based on the analysis of previous energy and environmental efficiencies.

The literature mainly contains two methods for evaluating energy and environmental efficiency. One is the parametric method stochastic frontier approach (SFA) and the other is non-parametric method data envelopment analysis (DEA). SFA is a parametric estimation method making use of maximum likelihood estimation (MLE). This method uses a parametric modelling approach to measure a "frontier" value and thereby provide a measure to evaluate energy efficiency through the frontier value. [START_REF] Boyd | A method for measuring the efficiency gap between average and best practice energy use: the Energy Star industrial energy performance indicator[END_REF] inputs but also has the advantage of having no need to assume any particular functional forms relating to input and output [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF][START_REF] Yang | Supply chain DEA: production possibility set and performance evaluation method[END_REF][START_REF] Johnson | Nonparametric measurement of productivity and efficiency in education[END_REF]. A great number and variety of DEA applications and research projects have led to many new developments related to DEA efficiency. As a result, DEA is a capable method to evaluate energy efficiency and environmental efficiency.

Recently, a growing number of studies have employed conventional DEA models (Hu and Wang, 2006), non-radial DEA models [START_REF] Fukuyama | A directional slacks-based measure of technical efficiency[END_REF][START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF][START_REF] Zhang | Environmental energy efficiency of China's regional economies: A non-oriented slacks-based measure analysis[END_REF], range-adjusted measure-based DEA (RAM-DEA) models (Wang et al., 2013), and directional distance function (DDF) models (Wang et al., 2013;[START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF] to evaluate energy and environmental efficiency. It is well accepted that the conventional energy efficiency index is actually the partial-factor energy productivity (partial-factor energy efficiency) in which energy is the single input, while non-energy inputs (e.g., labor and capital stock) are neglected and undesirable outputs are not considered. Patterson (1996) gave a detailed discussion of this concept.

However, all real-life industrial economic production activities are joint-production processes where both energy resources (e.g., coal, oil, natural gas) and other resources (e.g., labor, capital) are used simultaneously to produce desirable outputs (e.g., GDP)

and undesirable outputs such as the emission of pollutants (e.g., solid waste, SO 2 , waste water). Therefore, when applied to real-life examples, the methods which only use partial-factor energy productivity to evaluate energy consumption may obtain implausible results (Han et al., 2007;Hu and Wang, 2006). Therefore, it is necessary to take into account total-factor inputs instead of a single energy input while also considering undesirable outputs so as to more exactly evaluate the energy and environmental efficiency. This issue can be well addressed by DEA technique because DEA is applicable to multiple inputs and multiple outputs problems. Based on this idea, some total-factor energy efficiency (TFEE) approaches have been proposed recently.

Hu and Wang (2006) applied the Range-Adjusted Measure (RAM)-based nonparametric approach to evaluate the regional energy and environmental efficiency of China over the period 2006-2010. In their efficiency evaluation models, the energy and non-energy inputs, as well as the desirable and undesirable outputs, are considered to characterize the energy consumption and economic production of several Chinese regions.

Most of the above-mentioned studies investigated the sector or regional totalfactor energy efficiency, while rare work has focused on the industrial total-factor energy efficiency and industrial environmental efficiency in China. Industry plays a vital role in the development of the economy in China, as evidenced by the fact that the gross industrial output value (GIOV) accounted for about 38.5% of China's gross domestic product (GDP) in 2012. More importantly, the industrial sector is an energy intensive sector which accounted for 70% of total final energy consumption in 2012 (NBSC, 2013(NBSC, , 2014)). Industrial pollution is also the main source of Chinese pollution.

Thus, it is urgent and meaningful to study the industrial total-factor energy efficiency and industrial environmental efficiency in China. In addition, the industrial system not only creates economic outputs, but also produces industrial pollution, such as industrial solid waste, industrial waste water, and industrial waste gas. Therefore, the environmental efficiency evaluation of the industrial system can not only evaluate the operation of the industrial system, but also obtain specific measures to improve the environmental efficiency so as to realize the sustainable development of the economy and the environment. However, almost all previously published works considered the industrial system as a "black box" when they measured the environmental efficiency of industrial system, which probably has resulted in ignorance of some deficiencies in the system. In this chapter, we divide the process of energy consumption and utilization in China's industry into two stages: the industrial energy utilization stage and the industrial pollution treatment stage. In the energy utilization stage, the main work is to produce the industrial products, while in industrial pollution treatment stage, the main work is to dispose of the pollution produced in the first stage. Accordingly, the provincial industrial overall environmental efficiency is decomposed into two parts, industrial energy utilization efficiency and industrial pollution treatment efficiency.

Through analyzing the two-stage structure of China's industry's energy consumption process, we can effectively investigate the inefficiencies of the internal structure of the system and provide valuable managerial insights when assessing the dual impacts of operating and business strategies for China's industrial sector.

So far, many published works have studied two-stage structure systems. Hampf (2014) proposed a model that described a two-stage process to measure the environmental efficiency and applied the model to an analysis of US power plants. Based on these two reviews, we briefly overview the works on two-stage systems as follows. i) The standard two-stage DEA approach proposed by [START_REF] Brockett | Implementation of DEA models using GAMS[END_REF] and [START_REF] Seiford | Profitability and marketability of the top 55 U.S. commercial banks[END_REF]. ii) The network DEA approach proposed by Fä re and Grosskopf (1996). iii) The relational two-stage DEA approach proposed by [START_REF] Kao | Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[END_REF] and [START_REF] Chen | Additive efficiency decomposition in two-stage DEA[END_REF], which assumes a multiplicative or additive relationship between overall efficiency and divisional efficiencies. iv) The game-theoretic two-stage DEA approach proposed by [START_REF] Liang | DEA models for two-stage processes: Game approach and efficiency decomposition[END_REF], which considers the two stages as two players in a game. Because we want to obtain benchmarks of the evaluated DMUs while measuring their environmental efficiencies, we chose the network DEA approach. Based on this approach, a new twostage DEA model is built to firstly obtain the overall environmental efficiency and the benchmark for each province's industry. Then, according to the benchmarks, we can further obtain the industrial total factor energy efficiency by the ratio of the excepted energy consumption and the actual energy consumption.

CHAPTER 5. Environmental efficiency evaluation of a two-stage 66 system via total-factor energy efficiency

Modeling of environmental efficiency evaluation of the two-stage system of China's industry

Currently, most studies on environmental efficiency have considered the evaluated system as a single stage without considering its internal structure. As a result, there is no clear evidence of the transformations to which the inputs are subject within the considered units [START_REF] Castelli | A classification of DEA models when References the internal structure of the Decision Making Units is considered[END_REF]. In contrast to the single-stage DEA model, twostage DEA models show the performance of the individual stages and thus are more informative for decision-makers. For our study of the industrial environmental efficiency evaluation in China, we divide the industrial production process into two sub-processes: the energy utilization process and the pollution treatment process. The former sub-process focuses on using energy and non-energy inputs to produce the desirable outputs and undesirable outputs, while the latter sub-process focuses on the recycling and disposing of the pollution and wastes which are produced in the former.

In keeping with previous works for measuring energy and environmental efficiency and the characteristics of China's industry, for the first stage we select the indices of industrial labor force (ILF), industrial capital (IC), and industrial energy consumption (IEC) as the inputs, and choose the indices of gross industrial output value (GIOV), industrial solid wastes generated (ISWG), industrial waste water discharged (IWWD), and industrial waste gas emitted (IWGE) as the outputs (Wu et al., 2014;[START_REF] Shi | Chinese regional industrial energy efficiency evaluation based on a DEA model of fixing non-energy inputs[END_REF]. Here, we employ "the net value of fixed assets" to reflect the "capital" which is the same as in the previous work of [START_REF] Wang | China's regional industrial energy efficiency and carbon emissions abatement costs[END_REF]. It is clear that other than GIOV, all outputs are undesirable outputs. In addition, we consider industrial capital (IC) and industrial labor force (ILF) as non-energy inputs and the industrial energy consumption (IEC) as the energy input in the first stage. For the second stage, we select industrial labor force (ILF), industrial capital (IC), investment in industrial pollution treatment (IIPT), and the undesirable outputs from the first stage as its inputs, and product output value by disposing of and utilizing solid waste, waste water, and waste gas (POVW) as its outputs. The structure can be seen in Figure 5.1. It is evident that in the industrial system, industrial labor force and industrial capital are used in both the energy utilization stage and the pollution treatment stage.

For example, some labors work in both stages by repairing equipment such as lights and machines. Thus, these resources are shared inputs for both sub-processes. In regard to shared inputs, so far there are several approaches, such as weighted restrictions [START_REF] Beasley | Determining teaching and research efficiencies[END_REF]Cook et al., 2000) and an additive objective function (Cook and Hababou, 2001). Notably, these works did not consider the internal structure of the processes. In dealing with shared inputs in the network production, [START_REF] Yu | Efficiency and effectiveness in railway performance using a multi-activity network DEA model[END_REF] evaluated the railway performances in a multi-activity network framework with shared inputs. [START_REF] Zha | Two-stage cooperation model with input freely distributed among the stages[END_REF] developed an approach to measure the performance of a two-stage production process in series, where the shared inputs could be freely allocated among different stages.

As we have mentioned, the industrial energy consumption in China can be divided into an energy utilization process and a pollution treatment process, in which the

x z d u i y x x m M z z k K d d s S u u f F u u f F                                   1 1 1 1 ) , 1,..., ( ) (1 ) (1 ) , 1,..., ( ) , 1,...
i i g G x x m M y y h H jn                                                                                       ,                 
(5.1)

In this formula, 𝛼 𝑗 (0 < 𝛼 𝑗 < 1) is the portion of shared inputs used by the first stage of 𝐷𝑀𝑈 𝑗 , while 1 -𝛼 𝑗 is the portion of shared inputs consumed by the second stage of 𝐷𝑀𝑈 𝑗 . This system is expressed in terms of the unknown parameters 𝜌 𝑗 , 𝜇 𝑗 .

∑ 𝜌 𝑗 𝑢 𝑓 𝑗 𝑛 𝑗=1

= 𝑢 𝑓 represents the weak disposability assumption about the undesirable outputs. ∑ (𝜌 𝑗 + 𝜇 𝑗 ) = 1 𝑛 𝑗=1 models our requirement of the variable returns to scale assumption. It should be noted that the production possibility set uses the same intensity variables 𝜌 𝑗 , 𝜇 𝑗 in the two stages. That is because we want the two sub-processes of the industry to cooperate to achieve the overall environmental efficiency of the system, with the two stages working under the control of a centralized decision-maker. Thus, the two stages jointly determine one optimal plan to maximize the overall environmental efficiency of the system. This way of addressing the intensity vector in PPS can be also found in [START_REF] Maghbouli | Two-stage network structures with undesirable outputs: A DEA based approach[END_REF]. Based on this production possibility CHAPTER 5. Environmental efficiency evaluation of a two-stage 70 system via total-factor energy efficiency set, we can build the following centralized model, which integrates the two stages under the control of a centralized decision-maker, for measuring the overall environmental efficiency of the two-stage system. ( ,,,1,,,,, .

0 1 1 1 1 1 1 00 1 0 1 0 1 1 1 1 min 2 .. Stage 1 constraints: ( ) , 1,..., ( ) , 1,..., , 1,..., M K F F G M m k f f g m m k f f g m n j j j j m m m j n j j j k k k j n jj s s j e M K F F G M st x x m M z z k K d d s                                                                        0 1 0 1 0 1 00 1 0 1 , 1,...,
n jj f f f j n jj f f f j n j j j g g g j n j j j j m m m j n j j j h h j j S u u f F u u f F i i g G x x m M y y h H                                         1 )1 1,..., ; 0, 1,..., 0 ,
n j j j j j j j m k f g m LW UP j n j n for all m k f g m                   (5.2)
In this formula, we treat the two stages as equally important, and the constraints 0 ≤ 𝛽 𝑚 , 𝛿 𝑘 , 𝜃 𝑓 , 𝜙 𝑔 , 𝜑 𝑚 ≤ 1 are the limitation for improvement. Constraint 𝐿𝑊 𝑗 ≤ 𝛼 𝑗 ≤ 𝑈𝑃 𝑗 is used to avoid extreme and unrealistic values being chosen. The optimal value 𝑒 0 * is defined as the overall environmental efficiency of 𝐷𝑀𝑈 0 . When 𝑒 0 * is 1, the whole system is environmental efficient; otherwise, it is environmental inefficient. The overall environmental efficiency can be decomposed into two terms: the first term

10 1 1 1 1 M K F m k f m k f e M K F                   
is the efficiency of the first stage, i.e., 1

F G M f g m f g m e F G M                   
is the efficiency of the second stage, i.e., pollution treatment efficiency. If the optimal value of the first term 𝑒 10 * = 1, the first stage is efficient; If the optimal value of the second term 𝑒 20 * = 1, the second stage is efficient. It can be easily known that the system is overall environmental efficient if and only if the two stages are both efficient.

This model is a non-linear programming model. Let 𝜌 𝑗 𝛼 𝑗 = 𝑎 𝑗 , 𝜇 𝑗 𝛼 𝑗 = 𝑏 𝑗 , we can transform the model as follows: From Table 5.1, it can be observed that the mean values of labor force, capital, and industrial energy consumption increase year by year, which means that the industrial investments of each province increased these years. The standard deviations of all the nine variables are high, which implies that there may be uneven economic and social development across different provinces.

0 0 1 1 1 1 1 1 0 0 0 0 0 1, 0 1 1 1 1 1 min 2 .. Stage 1 constraints: ( ) ( ) , 1,..., ( ) , 1,..., M K F F G M m k f f g m m k f f g m n j j j m m m m j j n j j j k k k j n jj s j e M K F F G M st a b x a b x x m M z z k K d                                                                    0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1, 0 1 , 1,...,
s n jj f f f j n jj f f f j n j j j g g g j n j j j j j m m m m j j n j j j h h j d s S u u f F u u f F i i g G a b x a b x x m M yy                                              1 0 0 0 , 1,...,

Results analysis

Through our models (5.3) and (5.4) in Section 5.3, we can obtain the overall environmental efficiency, the efficiency of two stages, and the total factor energy efficiency of the industrial system in each Chinese province when setting the lower bound and upper bounds of 𝛼 𝑗 to 3% and 97% respectively. The results are shown in Firstly, we focus on the total factor energy efficiencies of China's industrial sector.

It can be seen from Table 5.2 that average total factor energy efficiency of industry increased from 0.674 in 2006 to 0.850 in 2010. Guangdong and Hainan province were energy efficient during this period. In addition to these total factor energy efficient regions, Beijing city and Jiangsu province had high total factor energy efficiencies. This indicates that the performance in terms of energy utilization in these regions was relatively good. Analyzing these regions, we find that Guangdong, Beijing, Jiangsu are well-developed regions. Maybe the good local economy encouraged these regions to introduce more new high technology and incorporate advanced machinery in production, with the result that the energy was used more effectively. In the future, the low-energy-efficiency regions could investigate the techniques in these high-energyefficiency regions and learn from others' experience to improve their own performance in energy utilization.

Returning to Table 5.2, we can also see that the overall environmental efficiency as well as the efficiency of stage 1 and the efficiency of stage 2 improved significantly from 2006 to 2010 for the most provinces. It should be noted that using our approach, the three kinds of efficiencies of any region in were larger than the second stage efficiencies in the same year for these six areas. This indicates that the main inefficiencies of the industrial system were caused by the second stage, i.e., the pollution treatment stage. In 2010, however, these two stages'

efficiencies were nearly at the same level which indicated that the work of pollution treatment had made great progress in those years.

To sum up, four kinds of efficiencies of the six areas all had an increasing trend.

North China, East China, and South Central China had relatively better performances than the other areas. This phenomenon indicates that the efficiency in China has a regional character. Compared with the areas of Northeast, Southwest, and Northwest China, the areas of North China, East China, and South Central China are more

Benchmarking analysis

Through our models, we can also obtain benchmarks for these industries to become overall environmental efficient. In other words, we can set the targets of inputs and outputs so that achieving those goals would make the industry overall efficient.

Because our model is a two-stage input-oriented model, if the evaluated DMU intends to achieve efficiency, the DMU can reduce its two sub-processes' inputs and undesirable outputs simultaneously. For ease of illustration, we take only the year 2010 as an example. The benchmarks of provinces are shown in Table 5.5.

CHAPTER 5. Environmental efficiency evaluation of a two-stage 82 system via total-factor energy efficiency analyzing the change proportion of each variable, we can find that the main cause of inefficiencies in China's industry are the industrial solid wastes generated and the industrial waste water discharged. Thus, the government policy makers should take more and better measures to control these pollutants.

Conclusions

Efficiency improvement is one of the most cost-effective ways to achieve the goals of energy saving and environment protection. Most of the previous analysis approaches for energy efficiency and environmental efficiency consider the evaluated system as a black box system without considering the internal structure, which often results in less reliable and more imprecise results. In order to overcome this problem, this chapter proposes a two-stage DEA model to measure regional industrial overall environmental efficiency, energy utilization efficiency, pollution treatment efficiency, and the totalfactor energy efficiency. We apply this model to the statistics for 30 Chinese provinces Applied well, these will allow industries to realize comprehensive utilization of all kinds of energy.

Secondly, the best way to improve overall environmental efficiency in the studied regions and areas is to enhance the industrial pollution treatment. Compared with the first stage industrial energy utilization efficiency, the second stage industrial pollution treatment efficiency is lower. Furthermore, according to our results, we found most of the inefficiency of the second stage came from the poor treatment of the solid waste and waste water. Thus, the government should take more measures to control these pollutants to improve the overall environmental efficiency of industry, which will simultaneously improve the industrial energy and environmental efficiency.

Chapter 6

Environmental efficiency evaluation of a parallel network system considering regional heterogeneity Contents Thus, lowering energy consumption and carbon emissions of the transportation sector in these three different areas is crucial for long-term sustainable development of transportation, resources, and environment. In order to establish a green transportation sector, when we evaluate the evolution of the performance of the transportation sector, we should consider green factors so as to find its inefficiency and its efficiency changes in terms of both productivity growth and emission reduction.

Many single indicators, such as transportation intensity effect (TIE), and energy use per turnover (EUT), are used to evaluate the performance of transportation [START_REF] Wang | Using LMDI method to analyze transport sector CO2 emissions in China[END_REF][START_REF] Zhou | A study of carbon dioxide emissions performance of China's transport sector[END_REF] without taking into consideration other factors involved in the transportation process. To deal with this problem, data envelopment analysis (DEA) has been employed to evaluate the transportation performance by considering more factors, which is more appropriate than any single-factor indicators. DEA as a non-parametric approach can well evaluate a system with multiple inputs and multiple outputs and does not need a functional form assumption of the production [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF], so it has been widely used for measuring the performance of transportation (Wu et al., 2016;Viton 1997;[START_REF] Adler | Measuring the environmental efficiency of the global aviation fleet[END_REF].

So far, many DEA research works have focused on the transportation sector. These works can be classified into two categories: one is the static performance evaluation which measures the efficiency of a transportation system in a year or a period; and the other is the dynamic performance evaluation, which usually uses the Malmquist productivity index and its extensions to investigate the efficiency changes or productivity growth over multiple periods. In the first category, the research usually applied DEA models, such as conventional DEA models, slacks-based measure models, and network DEA models, to evaluate the performance of transportation in a year or a period without analyzing the technical process and efficiency changes involved in the development of the transportation sector [START_REF] Adler | Measuring the environmental efficiency of the global aviation fleet[END_REF][START_REF] Zhou | A study of carbon dioxide emissions performance of China's transport sector[END_REF]Song et al., 2015). [START_REF] Zhou | A study of carbon dioxide emissions performance of China's transport sector[END_REF] proposed a new DEA approach named the directional economic-environmental distance function (DEED) approach to compute the relative efficiency of aircraft-engine combinations which accounted for the production of both desirable and undesirable CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity outputs such as noise and air pollutant emissions. Song, Hao, and Zhu (2015) used an undesirable-output-oriented data envelopment analysis (DEA) model with slacks-based measure (SBM) to evaluate the changes in the environmental efficiency of the transportation sector in 30 Chinese administrative regions between 2003 and 2012.

Since ignoring the internal structure of a system probably overestimates the system's efficiency, recently, some scholars have built or applied network DEA models to recognize the internal inefficiency of transportation sectors. [START_REF] Wanke | Physical infrastructure and shipment consolidation efficiency drivers in Brazilian ports: A two-stage network-DEA approach[END_REF] In the second category, the performance of transportation sectors was dynamically analyzed using the Malmquist productivity index or its extended forms, which can measure the productivity growth and the growth's determinants in the transportation sector over multiple periods. Besides this, the index is capable of reflecting progress or regress in efficiency along with progress or regress of the frontier technology over time under the multiple inputs and multiple outputs framework. The Malmquist productivity index was first introduced by [START_REF] Malmquist | Index numbers and indifference surfaces[END_REF][START_REF] Caves | The economic theory of index numbers and the measurement of input, output, and productivity[END_REF] Malmquist index to a sample of 28 airports covering about 96%, 99%, and 99% respectively of the total number of passengers, movement, and cargo. [START_REF] Zhang | Dynamic total factor carbon emissions performance changes in the Chinese transportation industry[END_REF] measured the dynamic changes in carbon emission performance within regional transportation sectors by incorporating regional heterogeneity and arithmetic measure into the non-radial Malmquist carbon emissions index.

Based on this literature review, we can see that most works treat the transportation sector as a "black box", considering only the initial inputs and final outputs. Few works investigate the internal structure by using network DEA models, but the main limitation of these works is that they do not analyze the performance dynamically, thus information about productivity growth and its decompositions is missed even though it is very important for guiding local government investments (see more details in Chen and Yu, 2014; Wang and Feng, 2015). In this chapter, we will build a new framework for measuring the performance evolution of transportation sectors taking the internal structure into consideration. According to the means of transport, we classify the whole transportation sector into four parallel subsystems: railway transportation, highway transportation, waterway transportation, and civil aviation transportation. So far, few papers have considered the transportation efficiency evaluation of this network structure. Moreover, considering the heterogeneity of Chinese provincial transportation sectors, we classify them into three regions according to their location: Eastern China, Central China, and Western China. To consider green factors in the performance 90 CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity evaluation, we firstly build a new parallel DEA model for measuring the environmental efficiency of transportation sectors considering the undesirable output carbon dioxide.

Then, a new metafrontier Malmquist-Luenberger productivity index (MMLPI) based on our network DEA model is derived to investigate the productivity growth.

6.2 Environmental efficiency evaluation of a parallel transportation network system considering regional heterogeneity

In this section, we first look at the conventional DEA model and then develop a new network DEA model for a transportation sector. Further, we define the metafrontier Malmquist-Luenberger productivity index for the transportation sector. Since the transportation sector (system) in China is mainly composed of four subsystems: railway transportation, highway transportation, waterway transportation, and civil aviation transportation, we formulate the system using a parallel network DEA model.

Network DEA model

At the beginning, we assume each administrative region's transportation sector is a "black box", ignoring the internal structure, so conventional DEA model can be applied to measure the performance of transportation. Using the traditional denotations in DEA, we assume that there is a set of n DMUs (which are provincial transportation sectors here), and each 𝐷𝑀𝑈 𝑗 (𝑗 = 1,2, … , 𝑛) produces b different outputs using m different inputs which are denoted as 𝑦 𝑟𝑗 (𝑟 = 1,2, … , 𝑏) and 𝑥 𝑖𝑗 (𝑖 = 1,2, … , 𝑚) , respectively. [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] presented the output-oriented CCR model for measuring the efficiency of 𝐷𝑀𝑈 0 as follows. (By convention, "𝐷𝑀𝑈 0 " is used to denote the DMU currently under consideration.) 6.2 Environmental efficiency evaluation of a parallel transportation network system considering regional heterogeneity 91

where 𝑢 𝑟 , 𝜔 𝑖 are the prices and multipliers associated with the rth output and the ith input respectively. When 𝜙 is equal to 1, the 𝐷𝑀𝑈 0 is efficient, otherwise, the 𝐷𝑀𝑈 0 is inefficient. The dual problem of model ( 6

                         (6.2)
It can be seen that model (6.2) seeks the maximal increase of outputs for a DMU by using its inputs. Thus, the reciprocal of the optimal values of models (6.1) and (6.2), 1 𝜙 ⁄ , defines an output distance (also called efficiency) to the production frontier formed by the best-performing (efficient) DMUs, and is widely used for Malmquist productivity index measurement [START_REF] Pastor | A global Malmquist productivity index[END_REF][START_REF] Oh | A metafrontier approach for measuring Malmquist productivity index[END_REF].Since ignoring the internal structure of a system will result in the overestimation of the performance, we should delve further into the transportation sector. According to the means of transport, we divide the transportation sector into four main subsystems: railway transportation, highway transportation, waterway transportation, and civil aviation transportation. Following previous works [START_REF] Chang | Environmental efficiency analysis of transportation system in China: A non-radial DEA approach[END_REF]Halkos and Tzeremes, 2009;Lv et al., 2012;Song et al., 2016) for analyzing the transportation sector, we select energy consumption and capital stock as the inputs of the four subsystems. Because these inputs for the overall transportation system are difficultly distributed to each subsystem of each province, according to the same analysis in Chen (2017), we also consider the variables as shared inputs since they are variables for the local transportation government for general purposes, and also, their exact data for each subsystem in Chinese provinces are not available from statistical yearbooks. As there are no statistics in China about the capital stock of each transportation industry, the amount of fixed capital investment is used to represent capital stock, as other authors have done (e.g., [START_REF] Lee | Energy consumption and GDP in developing countries: a cointegrated panel analysis[END_REF][START_REF] Bian | Resource and environment efficiency analysis of provinces in China: A DEA approach based on Shannon's entropy[END_REF][START_REF] Chang | Environmental efficiency analysis of transportation system in China: A non-radial DEA approach[END_REF]. We choose the number of employees in railway, highway, waterway, civil aviation, the emissions of carbon dioxide and the gross product as outputs. Among them, the number of CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity employees in railway, highway, waterway, civil aviation can be obtained from the statistical year books so that it is defined as the individual inputs of these subsystems, while the values of the gross product and the emissions of carbon dioxide of the whole transportation system are available but the detail value in each subsystem are not known as the values cannot be easily split into each subsystem. For example, the transportation tasks for generating the gross products of transportation are usually attributed to the integration of several or all the transportation subsystems not just an individual subsystem, thus the values cannot be easily decomposed into each subsystem. Therefore, analogous to [START_REF] Chen | DEA model with shared resources and efficiency decomposition[END_REF], the emissions of carbon dioxide and the gross product are considered as the shared undesirable output and shared desirable output of these four subsystems. For these shared outputs, we only know their total values of the whole system but do not know that of each subsystem. Different from these shared outputs measures, the passenger volume and freight volume transported by each transportation subsystem are the individual outputs whose values can be obtained from the statistical yearbook. The corresponding structure for the transportation sector is given in Figure 6.1 as follows. To evaluate the performance of the above structure system, we must deal with the shared inputs and shared outputs. So far, there have been several approaches proposed for solving shared inputs, such as weighted restrictions [START_REF] Beasley | Determining teaching and research efficiencies[END_REF]Cook et al., 2000) and additive objective functions (Cook and Hababou, 2001). Note that these works neither specified the sharing proportions of shared inputs nor considered the inner structure of the system. Recently, some researchers have dealt with shared inputs in the network system. [START_REF] Yu | Efficiency and effectiveness in railway performance using a multi-activity network DEA model[END_REF] evaluated railway performances in a multiactivity network framework with shared inputs. [START_REF] Zha | Two-stage cooperation model with input freely distributed among the stages[END_REF] developed an approach to measure the performance of a two-stage production process in series, where CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity the shared inputs could be freely allocated among different stages. [START_REF] Chen | DEA model with shared resources and efficiency decomposition[END_REF] used a multiple DEA model to evaluate the performance of a two-stage network process with non-splittable shared inputs to both stages. Yu et al. (2015) estimated the production efficiency, service efficiency, and operational efficiency of multimode transit firms with shared technicians and ticket agents by using a dynamic network DEA model. Similarly, shared outputs could be addressed although such works are rare. Jahanshahloo et al. (2004) measured the efficiency of thirty-nine branches of a commercial Iranian bank with shared inputs and shared outputs. Recently, Kao (2016) built a network DEA model to reanalyze these bank branches. However, all these previous works did not consider shared undesirable outputs and shared inputs simultaneously in the measurement of the total factor productivity, thus they cannot be applied to measure the transportation sector as modeled in Figure 6.1. In this section, we proposed a new network DEA model for measuring the transportation sector with the structure in Figure 6.1, which has not only shared inputs, shared desirable outputs, and shared undesirable outputs, but also individual inputs and individual outputs. The model is as follows:

0 0 0 1 1 1 0 0 1 1 1 =1 1 1 1 =1 1 1 1 ( ) 1, ( ( )) ( ( )) 0,
,

q m d k p i i l l h h i l p h f b r r g g r g q f q b m d k p p r rj g gj i ij l lj h hj r p g i l p h f b p p r rj g g gj r g min x x v z s.t. y y y y x x v z j PPS y y                                                1 1 1 1 1 1 g 0, 1,.., , , 1, 1,..., , 1, 1,..., , 1, 1,..., , , , , , , , , 0, 1, 2,
..., ; 1,.

m d k p p p i i ij l lj h h hj i l h q p i p q p h p q p g p p p p i r h l i h g x x v z p q j PPS im hk gf v i m r                                       .., ; 1,..., ; 1,..., ; 1,..., ; 1,..., . b h k l d g f p q     (6.3)
In model (6.3), 𝜔 𝑖 , 𝑣 ℎ and𝜗 𝑙 denote the multipliers corresponding to shared input, individual input and shared undesirable output, respectively. 𝜇 𝑟 and 𝜉 𝑔 are the 6.2 Environmental efficiency evaluation of a parallel transportation network system considering regional heterogeneity 95 multipliers of individual desirable output and shared desirable output, respectively. This model can be seen as an extension of Chen et al. ( 2010) for the network system shown in Fig. 6.1 which considering the parallel network, undesirable output, shared input and shared output. The second constraint in this model requires the aggregate output to be less than or equal to the aggregate input which implies the efficiency of the whole system no more than 1, and the second constraint implies the efficiency of the

𝑆𝑢𝑏𝐷𝑀𝑈 𝑝 (𝑝 = 1, … , 𝑞) no more than 1. The constraints ∑ 𝛼 𝑖 𝑝 𝑞 𝑝=1 = 1 , ∑ 𝛽 ℎ 𝑝 𝑞 𝑝=1 = 1and ∑ 𝛾 𝑔 𝑝 𝑞 𝑝=1 = 1represent
0 0 0 1 1 1 0 11 1 1 1 1 =1 1 1 1 1 ( ) s.t. 1, 0, ; q m d k p i i l l h h i l p h f b r r g gj rg fq b m d k p r rj g gj i ij l lj h hj r g i l p h f bm p p p r rj g gj i ij l r g i min x x v z yy y y x x v z j PPS y y w x                                                   11 1 1 1 0, , 1,..., ; , 1,..., , , 1,..., , , 1,..., , , , , , , , , 0, 1, 2,
..., ; 1,..., ; 1,..., ;

dk pp lj h hj lh q p ii p q p hh p q p gg p p p p i r h l g i h g x u z j PPS p q w i m u v h k gf v w u i m r b h k l                           1,..., ; 1,..., ; 1,..., . d g f p q    (6.4)
By solving model (6.4), the output distance 1 𝜙 ⁄ (or environmental efficiency) of 𝐷𝑀𝑈 0 under the technology set 𝑃𝑃𝑆 can be obtained for computing productivity index.

Metafrontier Malmquist-Luenberger productivity index

96 CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity It is well known that the ratio of the efficiencies of a DMU in two different periods can be viewed as a measure of performance change. Because using different periods as the base period may yield inconsistent results, researchers such as [START_REF] Kao | Malmquist productivity index based on common-weights DEA: The case of Taiwan forests after reorganization[END_REF]Fä re et al. (1994) have suggested using the geometric mean of the performance changes calculated from the two base periods as the Malmquist Productivity Index (MPI). Since this seminal work of Fä re et al. (1994), MPI has been used in many empirical studies.

However, this productivity index did not consider the undesirable outputs and the heterogeneity among the DMUs, that is, it assumed all DMUs operate under the same production technology and produced all good outputs. In fact, a DMU under a given production technology cannot be directly compared with those operating under different technologies. This is because DMUs in one specific technology group have different production possibilities from those in other groups. Within China's transportation sector, there is much more high-speed railway in Eastern China than that in Western China. Thus, the productivity analysis with the conventional MPI approach may not be directly applicable to China's transportation sector for measuring performance changes. [START_REF] Oh | A metafrontier approach for measuring Malmquist productivity index[END_REF] ( , , , , , , , , , )

                         1 1 1 1 1 1 1 1 1 1 1 1 1
, , , , ) / ( , , , , ) ( , , , , ) / ( , , , , ) (i) The within-group efficiency change is .

EC  = 1 1 1 1 1 1 ( , , , , ) ( , , , , ) t t
BPC provides a measure of technical change within a group from time t to time t+1, which reflects the within-group technical change [START_REF] Pastor | A global Malmquist productivity index[END_REF]. 𝐵𝑃𝐶 > 1 (𝐵𝑃𝐶 < 1)represents the technical progress (regress) of the transportation sector.

(iii) The technology gap change  represents the increase of the productivity of the transportation sector from time t to time t+1.

1 t t TGR TGC TGR   1 1 1 1 1 1 1 1 1 1 ( , , ,
6.3 Application to the environmental efficiency evaluation of China's transportation sector considering regional heterogeneity

In this section, we will present the transportation database and descriptive statistics in Section 6.3.1. In Section 6.3.2 we will evaluate the performance of transportation and discuss the main features of the China's transportation in each region.

Data and variables

The data used in this study comes from the National Bureau of Statistics of the People's Republic of China. It includes databases from the China Statistical Yearbook for Regional Economy 2008-2014, China Statistical Yearbook 2008-2014, China Energy Statistical Yearbook 2008-2014, China City Statistical Yearbook 2008-2014, and Yearbook of China Transportation and Communications 2008-2014. Since much data is unavailable for Tibet, only the 30 regions which are shown in Table 6.4 were used in this analysis.

Based on Figure 6.1, we explain the input and output selection in detail as follows.

With respect to inputs, the individual inputs of the four subsystems are the number of employed persons in each of the four modes of transportation. Energy consumption and capital stock of the transportation sector are the shared inputs. In this chapter, the total fixed assets in the transportation sector are used for estimating the capital stock.

Regarding the outputs, the gross product, CO2 emission, the number of passengers and amount of freight are selected. Among them, the gross product made by the transportation sector is the desirable output, and CO2 emission of the transportation sector is the undesirable output. We assume that these two outputs are shared outputs since they can be split out in the subsystems exactly and the real values of them for each subsystem are not available from the statistical yearbooks, which is similar to the assumption on banks in the work of [START_REF] Chen | DEA model with shared resources and efficiency decomposition[END_REF]. In addition, the individual desirable outputs for the four subsystems are the number of passengers and amount of freight for each of the four subsystems. Except for the data of energy consumption by the transportation sector and CO2 emissions of the transportation sector, all the other data can be obtained from the China City Statistical Yearbook, China Statistical Yearbook, and some reports of the transportation sector. considering regional heterogeneity

The data for provincial CO2 emissions from the transportation sector and the data for provincial energy consumption by the transportation sector are not available for China. Following [START_REF] Chang | Environmental efficiency analysis of transportation system in China: A non-radial DEA approach[END_REF] Besides, the energy consumption of transportation in the form of standard coal cannot be obtained from statistics directly, so we use the consumption of types of fuels to estimate the total energy consumption of transportation. The transformation coefficient of each fuel to the standard coal is given in Table 6.3. There are significant differences among the different regions of China. By adopting geographical closeness as the criteria to decide the groups and using Chinese regional classifications, the regions were classified into three areas: Eastern China, Western China, and Central China. The classification of the 30 administrative regions (i.e., provinces, autonomous regions, and municipalities) is shown in Table 6.4.

Results Analysis

(1) Average Metafrontier Malmquist-Luenberger index and its decompositions Through our approach, the MMLPI and its decomposition across the different areas' transportation sectors during 2007-2013 are calculated. To assess changes in China's transportation sector performance incorporating regional heterogeneity, the average MMLPI and the parts in its decomposition during the period 2007 to 2013 are calculated for each region.

102 CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity strongly stimulating infrastructure development and the steel industry for purposes of economic recovery. Note that higher EC does not mean the higher performance but means high-efficiency improvement during these years. These results clearly point out which regions can be used as benchmarks within the same group because their experience may benefit other regions to improve performance or to avoid transportation sector setbacks. Analogously, BPC and TGC can help sector managers determine the effect of innovation and technology leading in the productivity increase of each region's transportation sector. To save space, this paper does not give further details about these indexes.

(2) Metafrontier Malmquist-Luenberger index and its decompositions for each area

In order to analyze the transportation development trends of regions from a larger scale viewpoint, we use the group classification of the 30 regions in Table 6.4 and determine the MMLPI and its decompositions for Eastern China, Central China, Western China, and all of China.

As Figure 6.3 shows, the MMLPI of China's transportation sector presents a positive trend over the 2007-2013 period. The MMLPI increased by 0.0744 units on CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity average from 2007 to 2013, which means the productivity of China's transportation sector increased 7.44%. Western China and Central China showed the highest transportation productivity growth value over the period, with 0.1576 and 0.1104, respectively, while Eastern China showed an average decrease of 0.0350. In the longitudinal aspect, the average MMLPI changed greatly in 2007-2008 and 2008-2009 in China and then maintained a stable level with minor changes thereafter. 6.6, we can find the increase of China's transportation MMLPI mainly came from BPC and TGC, but different areas performed differently. The average efficiency change (EC) measure of transportation performance from The TGC represents the change in technology gap, measuring the gap between the global production possibility frontier and the intertemporal production frontier. As observed in Table 6.6, the average TGC of China's transportation performance was 1.0520, which means that that the gap between the global frontier and intertemporal frontier was reduced. This suggests that the average Chinese region had a technical leadership effect during the sample period. Firstly, adjust the energy structure of the transportation industry and encourage the use of new energy transportation vehicles. It can be seen from Table 6.2 that the corresponding carbon dioxide emission coefficients of crude oil, diesel oil, fuel oil, gasoline, etc. are very high, while the emission factors of natural gas and electric energy are very low. Therefore, in order to reduce the undesirable output-carbon dioxide emissions in the transportation industry to increase MMLPI, the Chinese government should optimize the energy structure of the transportation sector.

Secondly, rational planning and strengthening cooperation between regions. It can be seen from the analysis results of 6.3.3 that the development of China's transportation sector is regional. Among them, the catch-up effect (EC) is the largest in the eastern China, the innovation effect (BPC) is the largest in the western China, and the technology leading effect (TGC) is the largest in the central China. Therefore, cooperation and exchanges between regions should be strengthened to gradually narrow the gap in the regional transportation sector. In this chapter, we conclude the works of this thesis and give some directions for further study.

Conclusions

In recent years, environmental problems have seriously blocked sustainable development of many countries, especially in developing countries. The contradiction between environment protection and economic development is becoming more and more obvious. In order to realize the sustainable development of environment and economy, China has formulated a series of development plans, environmental protection policies and so on. Among them, scientific environmental efficiency evaluation is particularly important, which is a comprehensive assessment of the economic outputs and environmental outputs. It not only provides a macroscopic understanding of the environmental efficiency of the system, but also provides detailed benchmarking information for the environmental efficiency improvement. Therefore, environmental efficiency evaluation is one of important keys to solve environmental issues. So far, this topic has attracted extensive attention from scholars. Among the related research, data envelopment analysis (DEA) is one of the most popular methods.

Based on the DEA method, the main works of this paper are summarized as follows:

(1) This thesis studies the environmental efficiency evaluation of a single-stage system considering fuzzy numbers and its application. Even though environmental efficiency has already extensively applied in many areas, it is rarely seen in the fuzzy circumstance. In this thesis, we propose an enhanced Russell measure DEA model to analyze the environmental performance of thermal power firms with fuzzy undesirable outputs. The result shows that six of the 30 thermal power firms are efficient, and the inefficient thermal power firms should focus on the consumption of inputs to improve environmental performance.

(2) We study environmental efficiency evaluation of a single-stage system considering the performance improvement path and its application to Xiangjiang River.

Since the target (benchmark) set by the previous environmental performance studies is usually the furthest one for a DMU to be efficient, it may be hardly accepted by the (3) This thesis studies the environmental efficiency evaluation of a two-stage system. With the rapid development of the industry, the problems of energy consumption and environmental pollution have attracted more and more attention from government and scholars, while improving the industrial environmental efficiency and identifying the key factors affecting efficiency are of great significance for achieving coordinated development of industry and environmental protection. However, almost all previous works considered the internal structure as a "black box" when they measured the environmental efficiency of industrial system, which probably resulted in ignorance of some deficiencies in the system. To solve this problem, we divide the process of China's industry into two stages: the industrial energy utilization stage and the industrial pollution treatment stage. Accordingly, the industrial overall environmental efficiency is decomposed into two parts, i.e., industrial energy utilization efficiency and industrial pollution treatment efficiency. The results show that all the four kinds of efficiencies of the six areas had an increasing trend. North China, East China, and South Central China had relatively better performance than the other areas.

This indicates that the efficiency in China has the regional characteristics. Compared

Perspectives

Several environmental efficiency evaluation models have been proposed and studied for the environmental efficiency evaluation for the single-stage system and the network system. However, there are still some future directions that can further extend our works.

(1) The first direction is to consider the stochastic data in the environmental efficiency evaluation. In addition to the existence of fuzzy numbers in the environmental efficiency evaluation of the single-stage system in Chapter 3, the multi-développement économique durable, la protection de l'environnement est devenue un consensus mondial. En tant que membre important, la Chine joue un rôle essentiel dans l'amé lioration de l'environnement mondial. Par consé quent, cette thè se se concentre principalement sur les problè mes environnementaux en Chine.

Aprè s la recherche intensive sur les problè mes environnementaux, nous ré alisons progressivement que la ré alisation du dé veloppement durable ne peut ê tre ré alisé e sans une gestion efficace de l'environnement, laquelle dépend d'une évaluation scientifique et objective de l'efficacité environnementale (Wu et al., 2014;[START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF].

L'é valuation de l'efficacité environnementale est une é valuation complè te des performances d'une organisation dans tous les aspects de la consommation de ressources, des ré sultats é conomiques et des ré sultats environnementaux. Elle ne peut pas seulement montrer l'efficacité environnementale d'un système évalué au niveau macroscopique, mais doit fournit é galement des informations de ré fé rence dé taillé es pour l'élaboration et la mise en oeuvre de politiques de gestion environnementale [START_REF] Song | Environmental efficiency evaluation based on data envelopment analysis: A review[END_REF]. Par consé quent, l'é valuation de l'efficacité environnementale est un facteur clé dans la ré solution des problè mes environnementaux (Halkos et Tzeremes, 2013).

1.2 Revue de la litté rature: é valuation de l'efficacité environnementale basé e sur la DEA L'évaluation de l'efficacité environnementale a attiré une attention soutenue de la part des chercheurs et a é té profondé ment exploré e et appliqué e dans la vie ré elle (Sueyoshi et al., 2017). Parmi les diffé rentes mé thodes d'é valuation de l'efficacité environnementale, l'analyse par enveloppement de donné es (DEA) est l'une des mé thodes les plus populaires. La recherche d'évaluation de l'efficacité environnementale basée sur la DEA a retenu l'attention des chercheurs [START_REF] Färe | Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach[END_REF][START_REF] Seiford | A response to comments on modeling undesirable factors in efficiency evaluation[END_REF][START_REF] Kao | Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[END_REF]Halkos and Tzeremes, 2013;Sueyoshsi and Goto, 2017). Selon les mé thodes utilisé es pour traiter les extrants indé sirables, les études d'évaluation de l'efficacité environnementale peuvent être classées en deux caté gories: approches directes (Fä re et al., 1989;[START_REF] Seiford | A response to comments on modeling undesirable factors in efficiency evaluation[END_REF][START_REF] Zhou | A study of carbon dioxide emissions performance of China's transport sector[END_REF][START_REF] Wang | Potential gains from carbon emissions trading in China: A DEA based estimation on abatement cost savings[END_REF] et approches indirectes [START_REF] Liu | DEA models via goal programming[END_REF]Wu et al., 2013;[START_REF] Yang | Evaluation of regional environmental efficiencies in China based on super-efficiency-DEA[END_REF].

La plupart des travaux sur l'efficacité environnementale ré alisé s par la DEA é taient axé s sur un systè me à une é tape ou considé raient un systè me é valué comme une « boî te noire» sans tenir compte de sa structure interne. Cependant, nous ne pouvons pas 7.2 Perspectives 117 trouver l'inefficacité dans le processus de production interne d'un système de cette manière et il est donc difficile d'améliorer les performances du système. Avec la concurrence croissante et les relations entre les entité s é conomiques, les systè mes deviennent de plus en plus complexes, il est important de proposer des mé thodes pour l'é valuation de l'efficacité environnementale d'un systè me de ré seau. Au cours des derniè res anné es, la mé thode DEA en ré seau est devenue une mé thode efficace pour mesurer la performance de systè mes multi-é tapes. Elle fournit de nouvelles idé es et de nouvelles percées pour l'étude de problèmes complexes d'évaluation de l'efficacité environnementale. (Song and Wang, 2013;[START_REF] Lin | Do energy and environmental efficiency benefit from foreign trade? -The case of China's industrial sectors[END_REF]An et al., 2017;[START_REF] Kao | Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[END_REF]. En particulier, si 𝜔 ≥ 0,𝜇 ≥ 0, alors L est appelée la surface efficace de T, 𝐿 ∩ 𝑇 est la frontière de production de l'ensemble de possibilités de production T. Il a é té nommé « Russell» parce que le spé cialiste R.R. Russell a par la suite contribué à son dé veloppement ulté rieur. En raison de sa proprié té non radiale, il a de nombreuses applications [START_REF] Lozano | Russell non-radial ecoefficiency measure and scale elasticity of a sample of electric/electronic products[END_REF]Hsiao et al., 2011).

Modè

(2) Fuzzy DEA models , 1993;[START_REF] Seiford | A response to comments on modeling undesirable factors in efficiency evaluation[END_REF]Fä re et al., 2005;[START_REF] Zhou | A non-radial DEA approach to measuring environmental performance[END_REF]Zhou et al., 2008;Tone, 2004). Les approches indirectes sont basé es sur une hypothè se de ré sultats forte et jetable [START_REF] Liu | DEA models via goal programming[END_REF][START_REF] Dyckhoff | Measuring ecological efficiency with data envelopment analysis (DEA)[END_REF][START_REF] Seiford | Modeling undesirable factors in efficiency evaluation[END_REF]Tone, 2004). L'efficacité environnementale désigne l'efficacité des UDM qui tiennent compte à la fois des ré sultats souhaitables et des ré sultats indé sirables. Jusqu'à pré sent, de nombreuses analyses d'efficacité environnementale par approche DEA ont é té effectué es [START_REF] Korhonen | Eco-efficiency analysis of power plants: An extension of data envelopment analysis[END_REF]Bi et al., 2012;Huang et al., 2014). La DEA, en tant que technique de programmation non paramé trique, est de plus en plus utilisé e pour é valuer les performances d'un ensemble d'unité s de prise de dé cision homogè nes [START_REF] Li | Heterogeneity analysis of the effects of technology progress on carbon intensity in China[END_REF]. Jusqu'à pré sent, il a é té largement appliqué dans l'é valuation de l'efficacité environnementale ou de l'efficacité é cologique (Fä re et al., 1989;[START_REF] Leleu | Shadow pricing of undesirable outputs in nonparametric analysis[END_REF]

..., , ,, ,, ,, ,, 0, 1,
..., ; 1,..., ; 1,..., . En raison des avantages de la mé thode DEA, la DEA est choisie comme mé thode de base pour é valuer l'efficacité é nergé tique et l'efficacité environnementale.

Ré cemment, un nombre croissant d'é tudes ont utilisé des modè les DEA conventionnels (Hu and Wang, 2006), des modè les DEA non radiaux [START_REF] Fukuyama | A directional slacks-based measure of technical efficiency[END_REF][START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF][START_REF] Zhang | Environmental energy efficiency of China's regional economies: A non-oriented slacks-based measure analysis[END_REF], mesure ajusté e en fonction de la plage. modè les basé s sur la DEA (RAM-DEA) (Wang et al., 2013) et modè les de fonction de distance directionnelle (DDF) (Wang et al., 2013;[START_REF] Zhou | Energy and CO2 emission performance in electricity generation: a non-radial directional distance function approach[END_REF]

0 0 0 1 1 1 0 0 1 1 1 =1 1 1 1 =1 1 1 1 ( ) 1, ( ( )) ( ( )
                         1 1 1 1 1 1 1 1 1 1 1 1 1
, , , , ) / ( , , , , ) ( , , , , ) / ( , , , , ) Ecole Doctorale "Sciences pour l'Ingénieur"

Thèse réalisée en partenariat entre :

  Figure 1.1 The organization of this thesis•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••8

Figure 6 . 1

 61 Figure 6.1 The network structure of China's transportation sector••••••••••••••••••••••••••••••••••••••92

Figure 6 . 2

 62 Figure 6.2 Metafrontier in a Malmquist-Luenberger productivity index framework for Transportation sector••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 97

Figure 6 . 3

 63 Figure 6.3 Metafrontier Malmquist-Luenberger index change of China and its three areas•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••104

Figure 6 . 4

 64 Figure 6.4 Efficiency change of China and its three areas•••••••••••••••••••••••••••••••••••••••••••••••••••••••••106

Figure 6 .

 6 Figure 6.5 Best-practice gap change of China and its three areas••••••••••••••••••••••••••••••••••••••••107

Figure 6 . 6

 66 Figure 6.6 Technology gap change of China and its three areas•••••••••••••••••••••••••••••••••••••••••• 107

  for the evaluation of environmental efficiency ................................ 1 1.2 Literature review: DEA-based environmental efficiency evaluation ................... 3 1.3 Research topics ..................................................................................................... 7 1.4 Structure and Contributions of the thesis ............................................................. 8 1.4.1 Structure ....................................................................................................................8 1.4.2 Contributions ..............................................................................................................9

1. 2

 2 Literature review: DEA-based environmental efficiency evaluation 3

  " in traditional environmental efficiency methods. Based on the theoretical analysis of the model, some policy suggestions are given.In chapter 6, we examine China's transportation sector by dividing it into four main parallel subsystems: railway, highway, waterway, and civil aviation, and further build a network DEA model for performance measurement of China's transportation sector with consideration of undesirable output-CO2 emission. Moreover, considering regional heterogeneity of transportation sectors in different areas of China, a new metafrontier Malmquist-Luenberger productivity index is proposed based on the network DEA model, which is used to investigate the productivity growth of 30 regions' transportation sectors during 2007-2013. Finally, some suggestions are given for guiding the development of China's transportation sector. 1.4 Structure and Contributions of the thesis 1.4.1 Structure This thesis is focused on environmental efficiency evaluation by data envelopment analysis and its applications. According to different systems studied, this thesis is organized as in figure 1.1.

Figure 1 . 1

 11 Figure 1.1 The organization of this thesis

( 4 )

 4 Only few studies used a network DEA model to study the internal structure of China's transportation system previously. However, these studies lack a dynamic performance evaluation of the system. In chapter 6, China's transportation sector is divided into four parallel subsystems, and a new network DEA model is proposed to measure its environmental efficiency. Moreover, a metafrontier Malmquist-Luenberger productivity index is used to investigate the green productivity growth of provincial transportation sectors by considering the heterogeneity of transportation sectors in different regions of China. envelopment analysis ................................................................................. 11 2.2 Basic concepts .................................................................................................... 12 2.3 Basic DEA models ............................................................................................. 15 2.4 Basic concepts of environmental efficiency evaluation ..................................... 17

Axiom 2 .

 2 For any two production activities in PPS, i.e., (𝑋, 𝑌) ∈ 𝑇 , (𝑋 ̂, 𝑌 ̂) ∈ 𝑇, and any 𝛼 ∈ [0,1], then we have 𝛼(𝑋, 𝑌)+ (1 -𝛼)(𝑋 ̂, 𝑌 ̂) = (𝛼𝑋 + (1 -𝛼)𝑋 ̂, 𝛼𝑌 + (1 -𝛼)𝑌 ̂) ∈ 𝑇.Axiom 3. For any real production activity in PPS, i.e., (𝑋, 𝑌) ∈ 𝑇 , if a production activity (𝑋 ̂, 𝑌 ̂) satisifies 𝑋 ̂≥ 𝑋 and 𝑌 ̂≤ 𝑌, then we have (𝑋 ̂, 𝑌 ̂) ∈ 𝑇.Axiom 4a. For any real production activity in PPS, i.e., (𝑋, 𝑌) ∈ 𝑇 , we have 𝛼(𝑋, 𝑌) = (𝛼𝑋, 𝛼𝑌) ∈ 𝑇 for any 𝛼 ∈ [0, +∞).

CHAPTER 2 .

 2 Basic DEA theory Axiom 4b. For any real production activity in PPS, i.e., (𝑋, 𝑌) ∈ 𝑇 , we have 𝛼(𝑋, 𝑌) = (𝛼𝑋, 𝛼𝑌) ∈ 𝑇 any 𝛼 ∈ [0, 1]. Axiom 4c. If any real production activity in PPS, i.e., (𝑋, 𝑌) ∈ 𝑇 , we have 𝛼(𝑋, 𝑌) = (𝛼𝑋, 𝛼𝑌) ∈ 𝑇 for any 𝛼 ∈ [1, +∞).

  extended it to super efficiency form for fully ranking DMUs. Hsiao et al. (2011) proposed a fuzzy superefficiency slack-based measure DEA model (Fuzzy Super SBM) and a fuzzy slackbased measure DEA model (Fuzzy SBM DEA) to analyze the operational performance of parameters with fuzzy-numbered.

3. 2

 2 Review of Russell Measure, Fuzzy DEA, and undesirable outputs and Shi (2014) applied an improved super-SBM model to measure the environmental efficiency of Chinese industrial sectors.

3. 3

 3 Modelling of a single-stage system with undesirable outputs and fuzzy numbers 3.3.1 Russell DEA model and enhanced Russell DEA model Fä re and Lovell (1978) introduced a non-radial model, which is called the Russell measure model. In order to address the complicated calculation of Russell measure, Pastor et al. (1999) extended the Russell measure model and proposed a new measure called the Enhanced Russell measure.

3. 3

 3 Modelling of a single-stage system with undesirable outputs and fuzzy numbers 29 3.3.2 Fuzzy enhanced Russell DEA model considering undesirable outputs Fuzzy set theory has been proposed as a popular way to quantify imprecise and vague data in DEA models. The main types of fuzzy numbers are triangular fuzzy number, trapezoidal fuzzy number, rectangular fuzzy number and irregular fuzzy

  So, the proportion of kth undesirable output in model (3.4) cannot exceed than 𝑤 𝑢 ̅ ̃𝑘𝑗 ⁄ . For ease of illustration, denote 𝑤 𝑢 ̅ ̃𝑘𝑗 ⁄ by ℓ ̃. Then, through the Charnes-Cooper transformation, the nonlinear model (3.4) can be converted into a linear programming formulation. Firstly, denote β = ( , 𝑏 𝑖 = 𝛽𝜃 𝑖 , 𝑎 𝑟 = 𝛽𝜑 𝑟 , 𝑐 𝑘 = 𝛽𝜙 𝑘 , 𝑡 𝑗 = 𝛽𝜆 𝑗 , model (3.4) is transformed into the following linear program:

  use the respective αcut of 𝑥 𝑖𝑗 , 𝑦 𝑟𝑗 and 𝑢 ̅ 𝑘𝑗 to calculate the efficiency of the DMU under evaluated. Firstly, we obtain the fuzzy number of 𝑥 𝑖𝑗 , (𝑥 𝑖𝑗 ) 𝛼 = {𝑥 𝑖𝑗 |𝜇 𝑥 ̃𝑖𝑗 (𝑥 𝑖𝑗 ) ≥ 𝛼} = [(𝑥 𝑖𝑗 ) can obtain (𝑦 𝑟𝑗 ) 𝛼 and (𝑢 ̅ 𝑘𝑗 ) 𝛼 . By setting various values of 𝛼 ∈ [0,1], the membership function of 𝑅 ̃𝑒 is obtained correspondingly. When evaluating 𝐷𝑀𝑈 0 , we can use the smallest input values (𝑥 𝑖0 ) 𝛼 𝐿 and the largest output values (𝑦 𝑟0 ) 𝛼 𝑈 , (𝑢 ̅ 𝑘0 ) 𝛼 𝑈 of 𝐷𝑀𝑈 0 , while use the largest input values (𝑥 𝑖𝑗 ) 𝛼 𝑈 and the smallest output values (𝑦 𝑟𝑗 ) 𝛼 𝐿 , (𝑢 ̅ 𝑘𝑗 ) 𝛼 𝐿 of 𝐷𝑀𝑈 𝑗 (𝑗 = 1, … , 𝑛, 𝑗 ≠ 0) in the evaluation to get the upper bound of 𝐷𝑀𝑈 0 's efficiency (𝑅 𝑒 ) 𝛼 𝑈 . In this situation, ℓ ̃ is set the value of 𝑤 (𝑢 ̅ 𝑘0 ) 𝛼 𝑈 ⁄ , denote ℓ ̃ 𝛼 𝑈 . The model is as follow:

  use the largest input values (𝑥 𝑖0 ) 𝛼 𝑈 and the smallest output values (𝑦 𝑟0 ) 𝛼 𝐿 , (𝑢 ̅ 𝑘0 ) 𝛼 𝐿 of 𝐷𝑀𝑈 0 , and use the smallest input values (𝑥 𝑖𝑗 ) 𝛼 𝐿 and the largest output values (𝑦 𝑟𝑗 ) 𝛼 𝑈 , (𝑢 ̅ 𝑘𝑗 ) 𝛼 𝑈 of 𝐷𝑀𝑈 𝑗 (𝑗 = 1, … , 𝑛, 𝑗 ≠ 0) in the evaluation to get the lower bound of 𝐷𝑀𝑈 0 's efficiency (𝑅 𝑒 ) 𝛼 𝐿 . In this situation, ℓ ̃ is set the value of 𝑤 (𝑢 ̅ 𝑘0 ) 𝛼 𝐿 ⁄ , denote ℓ ̃ 𝛼 𝐿 . The corresponding model is shown as below:

CHAPTER 3 .

 3 Environmental efficiency evaluation of a single-stage system with fuzzy numbers as the Environmental Impact Assessment Law of the People's Republic of China, Electricity Law of the People's Republic of China, Circular Economy Promotion Law of the People's Republic of China. Also, many thermal power firms in Anhui province have opened training classes to improve their workers' consciousness of controlling the pollutions in the production. All these measures promoted these firms to have a good average environmental efficiency.

3. 4

 4 Application to the environmental efficiency evaluation of thermal power firms in China 41

Definition 4. 1 .(

 1 Denote (𝑋 𝑗 , 𝑌 𝑗 )(𝑗 = 1, … , 𝑛) by the production activities of all DMUs, the production possibility set 𝑇 is 11 4.1, we can character the efficient frontier of the PPS, 𝜕(𝑇), which consists of the non-dominated points of 𝑇, as CHAPTER 4. Environmental efficiency evaluation of a single-stage 48 system considering performance improvement path

  𝑇 𝑒𝑛𝑣 = {(𝑥, 𝑦, 𝑧)|𝑥 ≥ ∑ 𝑥 𝑖𝑗 𝜆 𝑗

  .4) is equal to one, DMU 0 is classical environmental efficient, otherwise, it is classical environmental inefficient. It is clear that classical environmental efficiency of a DMU calculated from model (4.4) is based on the furthest targets (maximum input and output slacks) for the DMU to be efficient. Denote the set of all extreme classical environmental efficient points by Set H. By Definition 4.2, we can similarly character the efficient frontier ∂(T env ) of the PPS, which consists of the non-dominated points, as 𝜕(𝑇 𝑒𝑛𝑣 ) = {(𝑋, 𝑌, 𝑍) ∈ 𝑃|𝑋 ′ ≤ 𝑋, 𝑌 ′ ≥ 𝑌, 𝑍 ′ ≤ 𝑍 ⟹ (𝑋 ′ , 𝑌 ′ , 𝑍 ′ ) = (𝑋, 𝑌, 𝑍)} (4.6) Or 𝜕(𝑇 𝑒𝑛𝑣 ) = {(𝑋, 𝑌, 𝑍)| -𝑣𝑋 + 𝑤𝑌 -𝜋𝑍 = 0, -𝑣𝑋 𝑗 + 𝑤𝑌 𝑗 -𝜋𝑍 𝑗 ≤ 0, 𝑗 = 1, … , 𝑛, 𝑣 > 0 𝑚 , 𝑤 > 0 𝑚 , 𝜋 > 0 𝑚 } (4.7)

-

  4.10) Without the specific illustration, the environmental efficiency in the later part of this chapter are all refer to the environmental efficiency based on the closest target model, model (4.8), and the classical environmental inefficient refers to the efficiency based on the model (4.4). It should be noted that 𝐷𝑀𝑈 𝑜 is environmental efficient if and only if all slacks 𝑠 𝑖0 - * , 𝑠 𝑟0 + * and 𝑠 𝑝0 -- * in model (4.8) are zero, that is 𝜌 𝑒𝑛𝑣 = 1. Based on the model (4.4) and model (4.8), we have the following theorem. Theorem 4.3. If the evaluated 𝐷𝑀𝑈 0 is classical environmental efficient, the 𝐷𝑀𝑈 0 must be environmental efficient.Proof. According to the definition of classical environmental efficient, an optimal slack vector (𝑠 𝑖0 - * , 𝑠 𝑟0 + * , 𝑠 𝑝0 -- * ) in model (4.4) for a classical environmental efficient 𝐷𝑀𝑈 0 must be zero. From the constraints of model (4.4) and (4.8), we can find slacks (= 0) for the classical environmental efficient 𝐷𝑀𝑈 0 in model (4.4) must be a feasible solution of model (4.8). As the constraints 𝑠 𝑖0

4. 4

 4 Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China 53 classical water environmental efficiency obtained from model (4.4) and the target set by the closest target model is easily realized. 4.4.1 Data and variables Based on the research purpose and the validity of the data, we investigate the water environmental efficiency of 15 monitoring areas in seven cities of Xiangjiang River basin in China from 2008-2014. In this chapter, labor force, capital stock, and energy consumption of each monitoring area are selected as input variables. The indexes of water pollution generally include dissolved oxygen, total phosphorus, ammonia nitrogen, PH, permanganate and other indicators. As DEA requires the number of decision making units to be more than twice of the number of indicators, and there is also a strong correlation between the above indexes. In order to achieve the distinction and validity of the assessment results, dissolved oxygen (DO) and total phosphorus (TP) are selected as water pollution indexes. Since the environmental factors are usually undesirable, here, we use the reciprocal of dissolved oxygen (DO) denoted by DO' as the undesirable output. Besides, gross domestic product (GDP) of each area is selected as desirable output. All the data are collected from the "China Statistical Yearbook", "Hunan Statistical Yearbook", and "Water Quality Monitoring Station" covering the years of 2009-2015. The descriptive statistics of inputs and outputs are shown in

4. 4

 4 Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China 59

Contents 5 . 1

 51 Introduction ........................................................................................................ 61 5.2 Modeling of environmental efficiency evaluation of the two-stage system of China's industry ....................................................................................................... 66 5.3 Application to the environmental efficiency evaluation of China's industry .... 73 5.3.1 Data and variables .................................................................................................. 73 5.3.2 Results analysis ...................................................................................................... 74 5.3.3 Benchmarking analysis ........................................................................................... 81 5.4 Conclusions ........................................................................................................ 83With the rapid development of China's industry, the problems of growing energy consumption and environmental pollution are drawing increasing attention from government managers and scholars. In this chapter, we divide the industrial system into two stages, i.e., an energy utilization stage and a pollution treatment stage, for accurately evaluating the total-factor energy efficiency as well as the overall environmental efficiency. Based on the two-stage structure of the industrial system, we build a new two-stage data envelopment analysis (DEA) model with shared inputs and apply this model to China's industry.5.1 IntroductionChina has achieved tremendous success in economic development during the past several decades, meanwhile, the government is coping with current internal challenges of energy shortage and environmental degradation. The degradation includes, for example, a shortage of water resources in the western area and desertification in the northwest of the country. China is also facing an urgent problem of environmental CHAPTER 5. Environmental efficiency evaluation of a two-stage 62 system via total-factor energy efficiency

  [START_REF] Boyd | The evolution of the Energy Star: energy performance indicator for benchmarking industrial plant manufacturing energy use[END_REF] used SFA method in the American Energy Star Program to calculate an energy performance indicator.[START_REF] Lin | Exploring energy efficiency in China׳ s iron and steel industry: A stochastic frontier approach[END_REF] used the excessive energy-input SFA to analyze the total factor energy efficiency and the corresponding energy conservation potential of China's iron and steel industry.However, pre-determined production functions may not match the reality, and SFA faces challenges when dealing with a multi-output problem. In contrast to SFA, DEA is a non-parametric programming technique for measuring the relative efficiency of a set of homogenous decision making units (DMUs). It was first proposed by[START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] and not only can deal with multiple outputs and multiple

  Cook et al. (2010) reviewed related DEA publications on two-stage systems, i.e., twostage DEA models, where the outputs from the first stage are intermediate measures and taken as the inputs for the second stage. Halkos et al. (2014) reviewed the DEA works for an extensive two-stage systems which allow "exogenous" inputs as intermediate measures.

5. 2 Figure 5 . 1

 251 Figure 5.1 Two-stage structure system of China's industry

  undesirable outputs in the energy utilization process are part of the inputs of the pollution treatment process. Assume there are n DMUs, each of which represents the industry of an administrative region of China (𝐷𝑀𝑈 𝑗 , j = 1, … , n). Denote the shared inputs by 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑀𝑗 ) and energy inputs by 𝑍 𝑗 = (𝑧 1𝑗 , … , 𝑧 𝐾𝑗 ) in the first stage. The desirable outputs of the first stage are denoted by 𝐷 𝑗 = (𝑑 1𝑗 , … , 𝑑 𝑆𝑗 ), and the undesirable outputs of the first stage by 𝑈 𝑗 = (𝑢 1𝑗 , … , 𝑢 𝐹𝑗 ) which are also the inputs of the second stage, the new inputs of the second stage by 𝐼 𝑗 = (𝑖 1𝑗 , … , 𝑖 G𝑗 ) and the outputs of the second stage by 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝐻𝑗

  index is defined as the ratio of the expected energy consumption to the actual energy consumption in a multi-factor production progress. Based on this, we can derive the TFEE index of 𝐷𝑀𝑈 0 by the proposed model in this chapter as follows: to the environmental efficiency evaluation of China's industry In this section, we will use the proposed two-stage DEA model to evaluate the industrial energy efficiency, industrial overall environmental efficiency, industrial energy utilization efficiency, and industrial pollution treatment efficiency of 30 provinces in China. The corresponding strategy and policy implications are discussed in order to propose guidelines for the improvement of the industrial performance of different provinces.5.3.1 Data and variablesThis study uses the data of 30 provinces in China to estimate their energy and environmental efficiencies during the 11th Five-Year plan period(2006)(2007)(2008)(2009)(2010). It should be noted that after the year of 2011, indicators of statistical system, method of survey and related technologies were revised by the Ministry of Environmental Protection, so the data in these years are not included for our analysis. As mentioned in Section 5.2, the input and output variables employed in this study include industrial labor force (ILF), industrial capital (IC), industrial energy consumption (IEC), investment on industrial pollution treatment (IIPT), gross industrial output value (GIOV), industrial solid wastes generated (ISWG), industrial waste water discharged (IWWD), industrial waste gas emitted (IWGE), and product output value by disposing of and utilizing solid waste, waste water, and waste gas (POVW). The dimension of these variables are in Ten thousand employees, Billion RMB, Ten thousand tons of standard coal, Billion RMB, Million tons, Tons, Million tons, Million RMB, and Billion RMB, respectively. The data are collected from the China Statistical Yearbook, China Energy Statistical Yearbook, and China Statistical Yearbook on Environment for each of the years 2007-2011. Because many data of Tibet are not available in the statistics, Tibet is not considered in our analysis. Descriptive statistical analysis on these variables are shown in

Figure 5 . 2

 52 Figure 5.2 The industrial efficiencies of different areas in China To analyze the differences among the four kinds of efficiencies in the six areas, we average all the values of the same kind of efficiency during the period. The results are shown in Table 5.4.

From

  Figure 5.2 (b), we can also see that the overall environmental efficiencies of the six areas all had an increasing trend during those years. In addition, the overall environmental efficiencies of North China, East China, and South Central China were higher than other areas on average. North China, Southwest China, and Northwest China had a significant decline in 2009, which may have been caused by the global economic crisis in 2008. Different from these three areas, East China maintained steadily growth during 2006-2010, which showed that their industry had strong ability to resist economic difficulties. This is consistent with the real situation of industry in East China and reflects the validity of our approach. Looking at the two stages' efficiencies shown in (c) and (d) of Figure 5.2, we find that they had the same situation as the overall environmental efficiencies. Besides, most of the first stage efficiencies

5. 3

 3 Application to the environmental efficiency evaluation of China's industry 81 attractive for skilled laborers and qualified enterprises. Many skilled laborers in Northwest China migrate to other regions seeking employment in places such as Beijing in North China, Shanghai in East China, and Guangzhou in South Central China. Moreover, the natural resources in the Northeast and Southwest were limited, which can be seen from the China Energy Statistical Yearbook 2007-2011. With the development of China's domestic transportation system, the disadvantages of location for Northeast and Southwest areas becomes weaker since they can get resources more easily. Based on these results, we suggest that the Chinese government should pay attention to the differences among areas to balance the development of China's industry.

  for the years 2006-2010. In addition, we group the 30 provinces into six areas(North China, Northeast China, East China, South Central China, Southwest China, and Northwest China) to analyze the efficiencies of larger scale areas. The results indicate that China's industrial performance was greatly improved during the study period but the six areas had a notable degree of distinct differences. According to these results, we give the following policy recommendations for improving industrial performance, especially overall environmental efficiency and total factor energy efficiency. Firstly, fully utilize the industrial energy resources such as coal and crude oil. In terms of the average industrial energy efficiency in areas, North China performs the best while Northeast China performs the worst. These relatively low efficiency areas can be improved by (a) introducing new technology to reduce industrial energy intensity CHAPTER 5. Environmental efficiency evaluation of a two-stage 84 system via total-factor energy efficiency (i.e., industrial energy consumption for per unit gross industrial output value); and (b) retiring backward technology and equipment, adopting new high-technology equipment with lower pollution, and saving electricity to achieve continuous and efficient progress.

6. 1

 1 IntroductionAs an important part of human social and economic activities, transportation is to realize the physical location movement of people and goods by organizing various resources such as tools, staff, funds, etc. According to the means of transport, transportation services are mainly carried railway transportation, highway transportation, waterway transportation, civil aviation transportation and pipeline transportation. As pipeline transportation is only suitable for liquid transportation, and its application range is limited. We will not study it in this chapter. In 2016, the number of civil aviation airports reached 218 and the passenger volume reached 1016.357 million journeys; the railway mileage (i.e. distance traveled on railway lines) had reached about 124 thousand kilometers, which ranked the second place in the world, as did the electrified railway mileage. Besides, the operational mileage (i.e. total length of railway lines) of high-speed rail reached 22 thousand kilometers, which ranked first over the world, and the scale under construction exceeded 10,000 kilometers.Meanwhile, the number of high-speed railways under construction exceeds 10000 km; the total national highway mileage is 4.6963 million km, with an increase of 119000 km over the previous year; and the length of navigation of inland waterways nationwide is 127,100 km, with an increase of 100 km over the previous year. National ports have 30,388 berths for production and 2,317 berths of 10, 000 tonnage or above(MTPRC, 2017). Although China's transportation sector has developed rapidly, this progress has been accompanied by problems. a) In China, the transportation sector accounted for 8% of total energy consumption and 10% of total carbon emission in 2013, according to China Statistical Yearbook 2015. b) The overall scale of China's transportation infrastructure is large now, but the construction mainly leans towards Eastern China, and the disparity between Eastern China, Central China, and Western China is enlarging.

  employed output-oriented DEA models with different returns to scale assumptions to study the carbon emissions performance of China's transport sector from 2003 to 2009; the results indicated that the number of efficient regions decreased starting in 2004, bottomed out in 2006, and improved slightly afterwards. Chang et al. (2013) measured the carbon emissions and potential reductions of these in the regional transport sector in 2009 by using the SBM-DEA model; the results showed that the transportation sector in most provinces of China were not ecoefficient.[START_REF] Zhou | Measuring energy efficiency performance of China's transport sector: A data envelopment analysis approach[END_REF] presented an application of DEA approach with consideration of undesirable outputs to analyze energy efficiency and potential energy savings for the Chinese transport industry during2003 -2009[START_REF] Adler | Measuring the environmental efficiency of the global aviation fleet[END_REF]

  analyzed the efficiency in Brazilian ports by using a two-stage network-DEA approach to simultaneously optimize physical infrastructure and shipment consolidation efficiency levels through considering shipment frequency per year as the critical intermediate output. Tavassoli et al. (2014) developed a two-stage network SBM model with shared inputs to assess the performance of 11 domestic airlines in Iran by introducing linking activities between components. In that paper, the first stage evaluated airline technical efficiency and the second stage measured the service effectiveness. Lu et al. (2012) examined the production efficiency and marketing efficiency of 30 US airline companies by a two-stage DEA model. In addition, they conducted a regression analysis of the effect of corporate governance mechanisms on airlines performance. Yu et al. (2015) proposed a multi-activity network data envelopment analysis model to assess the performance in terms of individual activities, individual processes, individual periods, and overall operation. Wu et al. (2016) divided the transportation into passenger transportation and freight transportation, and then used a parallel network DEA model for measuring the energy and environmental efficiency of Chinese provincial transportation sectors in 2012. Liu et al. (2017) analyzed the land transportation sector of China (including railway transportation and road transportation) during 2009-2012 by using a parallel slack-based measure data envelopment analysis model.

  extended it by applying the ratio of two distances. After Fä re and[START_REF] Färe | Malmquist productivity indexes and Fisher ideal indexes[END_REF] introduced the non-parametric technique DEA to the Malmquist productivity index measurement, the index began to receive much attention from scholars. Nicola et al. (2013) measured the productivity of 20 Italian airport management companies during 2006-2008 using a DEA Malmquist index that included a quality component. Scotti and Volta (2015) used a Biennial Malmquist-Luenberger (BML) index to measure the productivity of European airlines during 2000-2010. They compared the BML index with the traditional index and found the environment-sensitive productivity growth was lower than that given by the traditional index. Zhang et al. (2015) employed a non-radial Malmquist carbon dioxide (CO2) emission performance index (NMCPI) to analyze the changes in the total-factor CO2 emission performance of the regional transportation sector in China for the period 2002 to 2010. Gitto and Mancuso (2012) evaluated the productivity evolution, from 2000 through 2006, of Italian airports by applying the

  ..., , 1, 2,..., .

Figure 6 . 1 j

 61 Figure 6.1 The network structure of China's transportation sector

  proposed a metafrontier Malmquist-Luenberger productivity index (MMLPI) which introduces a metaproduction function to the nonparametric analysis of productivity growth in order to compare productivity changes and the decomposed components for economic agents under different technologies. Based on Oh and Lee (2010), a new metafrontier Malmquist-Luenberger productivity index (MMLPI) which considers the undesirable output is proposed. For analyze the productivity, in the context of China's transportation sector divided into three regions (Eastern China, Central China, and Western China), we illustrate the MMLPI as follows.

Figure 6 . 2

 62 Figure 6.2 Metafrontier in a Malmquist-Luenberger productivity index framework for Transportation sector

  The three areas are characterized as follows: (1) the Eastern area is well developed in transportation and it has larger gross domestic products (GDP) than the other two areas; (2) the Central area is an underdeveloped area in transportation but has achieved rapid development in recent years; and (3) the Western area has the largest land area with comparatively low population density and is the least developed area in terms of the transportation density. The administrative regions in the same area are similar (homogenous) but in the different areas are largely different (heterogeneous).

  The average MMLPI of the Central China decreased in 2008-2009 while that of Eastern and Western China increased in 2008-2009.

Figure 6 . 3

 63 Figure 6.3 Metafrontier Malmquist-Luenberger index change of China and its three areas

  2007 to 2013 under the MMLPI framework was 1.0833, which indicates that the transportation sector moved toward the technology frontier over the study period, which can be regarded as a catching-up effect. Considering the three geographic areas, the average efficiency change of Eastern China fluctuated largely from 2007 to 2010, then remained at a similar level around 1 from 2010 to 2013. Central China and Western China performances had the same trend as Eastern China. This phenomenon can be clearly seen in Figure 6.4, and was probably caused by the global financial crisis which occurred in 2008. China began the "4 Trillion Plan" in the second half of 2008 to stimulate the development of the economy, including infrastructure development, energy saving, and emission reduction. In particular, investments in the highway system and high-speed railways accounted for more than half of the total capital. Thus, the MMLPI saw a large increase in 2008-2009. After 2009, however, the effect became weak and the average efficiency changes were approximately 1 which means there was almost no change in the efficiency.

Figure 6 . 5

 65 Figure 6.5 Best-practice gap change of China and its three areas

Figure 6 . 6

 66 Figure 6.6 Technology gap change of China and its three areas

  ...................................................................................................... 111 7.2 Perspectives ...................................................................................................... 113

  DMUs. In order to make the evaluated DMU achieve the environmental efficient with the least effort (cost), this paper proposes a closest target DEA model based on range adjusted measure to evaluate the water environmental efficiency of 15 monitoring areas in seven cities in Xiangjiang River basin of China. The results show that the average closest target environmental efficiencies of Xiangjiang River basin in 2008-2014 are steady around 0.93. Comparing the efficiencies of the 15 areas, we find the Trunk area of Changsha, the Mishui area of Hengyang, the Trunk area of Hengyang, and the Chuling area of Hengyang perform well, and the efficiencies are all higher than 0.99. The results indicate that Hunan Province has made some achievements in the control of water quality pollution in Xiangjiang River.

  with the areas of Northeast, Southwest, and Northwest China, the areas of North China, East China, and South Central China are more attractive for skilled laborers and qualified enterprises. Many skilled laborers in Northwest China migrate to other places such as Beijing in North China, Shanghai in East China, and Guangzhou in South Central China for seeking better job opportunity. Besides, through the China Energy Statistical Yearbook 2007-2011, the natural resources in the Northeast and Southwest were relatively fewer. Therefore, the Chinese government should pay attention to the differences among areas so as to balance the development of Chinese industry. (4) This thesis studies the environmental efficiency evaluation of a parallel network system considering heterogeneity, and further applies to China's transportation sector. Firstly, based on the parallel network structure, we establish a parallel network DEA model considering undesirable output. Second, according to the difference of transportation development in different areas of China, we use the Metafrontier Malmquist-Luenberger productivity index (MMLPI) based on the proposed DEA model to dynamically analyze the environmental efficiency of China's transportation sector. Finally, we analyze the transportation sector of 30 administrative regions in China from 2007 to 2013 based on the network DEA model and MMLPI. we found that Eastern China had the largest within-group efficiency change, Western China had the largest best-practice gap change, and Central China had the largest technology leadership change. By calculating these three factors for driving productivity growth, each region can find its weakness directly and arrange its resources for its transportation sector accordingly.

1. 3

 3 Sujets de recherche La litté rature cité e ci-dessus montre que l'évaluation de l'efficacité environnementale a é té largement prise en compte par les spé cialistes, mais il reste quelques lacunes à combler. Par exemple, comment é valuer l'efficacité environnementale des systè mes flous avec des nombres flous? Comment mesurer l'efficacité environnementale afin de définir l'objectif le plus proche pour un système inefficace en matière d'environnement en utilisant le moins d'effort possible l'efficacité énergétique de facteur totale d'un système complexe à deux étages? Et comment évaluer l'évolution dynamique de l'efficacité environnementale d'un système de réseau parallèle? Cette thèse vise à étudier ces problèmes théoriques et à appliquer les résultats théoriques à des problèmes environnementaux dans la vie réelle. 1.4 Structure de la thè se Cette thè se porte sur l'é valuation de l'efficacité environnementale par l'analyse d'enveloppement de donné es et ses applications. Cette thè se sera divisé e en deux parties selon la structure du systè me é valué . La premiè re partie concerne les mé thodes d'é valuation de l'efficacité environnementale pour les systè mes à une é tape et leurs applications, qui comprend deux chapitres. La deuxiè me partie concerne les mé thodes d'é valuation de l'efficacité environnementale pour les systè mes en ré seau et leurs applications, qui contient deux chapitres. T en exposant indique une transposition. Pendant ce temps, 𝑋 𝑗 ≥ 0,𝑌 𝑗 ≥ 0,𝑗 = 1, … , 𝑛, c'est-à-dire que la valeur de chaque entrée et sortie est supérieure ou égale à sur 0, et au moins la valeur d'un indicateur d'entrée et d'un indicateur de sortie est positive. De plus, 𝑥 𝑖𝑗 indique la ième entrée de 𝐷𝑀𝑈 𝑗 , et 𝑦 𝑟𝑗 indique la ième sortie de 𝐷𝑀𝑈 𝑗 . L'ensemble de possibilité s de production est ensuite dé fini comme un ensemble de tous les points de production ré alisables, à savoir: 𝑇 = {(𝑋, 𝑌)|𝑋 peuvent produire 𝑌} (A.2.1) De maniè re é quivalente, la technologie T peut ê tre repré senté e de maniè re é quivalente par ses ensembles de sortie 𝑃(𝑋) = {𝑌|(𝑋, 𝑌) ∈ 𝑇} ou ses ensembles d'entré e 𝑃(𝑌) = {𝑋|(𝑋, 𝑌) ∈ 𝑇}. (4) Frontiè re de production La frontiè re de production est une surface incurvé e constitué e de tous les points efficaces du PPS. Il repré sente la limite à laquelle la production peut ê tre dé finie pour obtenir le rendement maximal des intrants existants ou pour obtenir les intrants minimums des produits existants. Selon Wei (2004), la frontiè re de production En supposant que 𝜔 ≥ 0,𝜇 ≥ 0,𝐿 = {(𝑋, 𝑌)|𝜔 𝑇 𝑋 -𝜇 𝑇 𝑌 = 0},𝑇 ⊂ {(𝑋, 𝑌)|𝜔 𝑇 𝑋 -𝜇 𝑇 𝑌 ≥ 0} et 𝐿 ∩ 𝑇 ≠ ∅, le jeu de possibilité s de production faiblement efficace dé fini sur T est L, et la frontiè re de production faible correspondante est 𝐿 ∩ 𝑇.

  est clairement une programmation non liné aire avec une fonction d'objectif à structure fractionnaire. Par la transformation de Charnes-Cooper, le modè le non liné aire (A.3.1) peut ê tre converti en une formulation de programmation liné aire.

  du modè le (A.3.2), nous pouvons utiliser la mé thode α-cut pour calculer les efficacité s environnementales des bornes supé rieure et infé rieure des 𝐷𝑀𝑈 0 . 3.4 Application à l'é valuation de l'efficacité environnementale des entreprises thermiques Dans cette section, nous appliquons notre approche pour évaluer l'efficacité environnementale de 30 entreprises d'énergie thermique en Chine en 2010, laquelle contient un nombre flou et une production indé sirable. Sur la base du modè le proposé , les limites supé rieures et infé rieures de l'efficacité floue coupé e en α des DMU sous-é valué es sont obtenues. Nous pouvons constater que 6 des 30 entreprises d'énergie thermique étaient pleinement efficaces et que leurs bornes supé rieure et infé rieure é taient toutes é gales à 1 pour tout α et que les 24 entreprises restantes devenaient inefficaces lorsque la valeur de α variait de 0 à 1. De plus, lorsque α augmente, l'efficacité de la borne supé rieure de la DMU é valué e diminue et celle de la borne infé rieure augmente. De plus, notre approche peut fournir des points de repè re aux entreprises é valué es pour amé liorer leur efficacité . Nous trouvons que la plupart des amé liorations devraient ê tre prises sur les intrants. La valeur totale de la production industrielle et les déchets solides n'ont besoin que d'augmenter une petite valeur au niveau actuel. Cela indique que si l'entreprise veut ê tre é cologiquement efficace, elle doit se concentrer sur l'utilisation d'intrants. A.4 Évaluation de l'efficacité environnementale d'un systè me à une seule é tape tenant compte de l'amé lioration des performances 127 A.4 Évaluation de l'efficacité environnementale d'un systè me à une seule é tape tenant compte de l'amé lioration de performances 4.1 Introduction La riviè re Xiangjiang, la plus grande riviè re de la province du Hunan en Chine, est la « riviè re mè re» de la province du Hunan. Le bassin de la riviè re Xiangjiang est la ré gion la plus densé ment peuplé e avec le plus haut niveau d'urbanisation et l'é conomie la plus dé veloppé e de la province du Hunan. Cependant, la population nombreuse et le dé veloppement é conomique rapide ont entraî né la plus grande pression sur les ressources et l'environnement. Toutefois, en raison du manque d'é valuation de l'efficacité environnementale par les professionnels et d'objectifs scientifiques d'amé lioration de l'efficacité , le bassin de la riviè re Xiangjiang est toujours confronté à une pé nurie de ressources en eau, à la pollution de l'eau et de la pollution atmosphé rique et aux mé taux lourds. Par consé quent, il est urgent de mesurer l'efficacité environnementale de l'eau et de dé finir les critè res de ré fé rence pour le bassin de la riviè re Xiangjiang. Dans ce chapitre, une approche d'analyse d'enveloppement de donné es (DEA) avec la cible la plus proche est appliqué e pour mesurer l'efficacité environnementale et dé finir les cibles les plus proches pour le bassin de la riviè re Xiangjiang.

  𝑗 * ) est un solution optimale du modèle cible le plus proche (A.4.1). Ensuite, la cible la plus proche pour le 𝐷𝑀𝑈 𝑜 évalué peut être exprimée par:(𝑥 ̂𝑖0 = 𝑥 𝑖0 -𝑠 𝑖0 - * , 𝑦 ̂𝑟0 = 𝑦 𝑟0 + 𝑠 𝑖0 + * , 𝑧̂𝑝 0 = 𝑧 𝑝0 -𝑠 𝑝0 -- * ) (A.4.2) L'efficacité environnementale pour la 𝐷𝑀𝑈 𝑜 évaluée basée sur la cible la plus proche peut être obtenue en calculant la formule suivante. à l'é valuation de l'efficacité environnementale de l'eau du bassin de la riviè re Xiangjiang Nous appliquons le modè le proposé pour é valuer l'efficacité environnementale du systè me d'alimentation en eau dans le bassin de la riviè re Xiangjiang en Chine. Les ré sultats montrent que l'efficacité environnementale moyenne de l'eau est trè s é levé e pendant cette pé riode. Comparé à l'efficacité classique de l'environnement aquatique, nous constatons que l'efficacité de l'environnement aquatique est plus stable et que la diffé rence entre les villes est beaucoup plus petite. Les ré sultats montrent que la cible la plus proche de chaque ville inefficace est stable et plus facilement atteinte. En outre, nous constatons que la plupart des zones é conomiquement rationnelles en eau sont des villes dé veloppé es sur le plan é conomique, telles que Changsha et Zhuzhou. Par consé quent, les autres zones inefficaces peuvent apprendre de ces zones efficaces et formuler les politiques correspondantes en fonction de leur niveau é conomique et des conditions environnementales afin d'amé liorer l'efficacité environnementale. A.5 Evaluation de l'efficacité environnementale d'un systè me à deux é tapes via l'efficacité é nergé tique de facteur total 131 A.5 Evaluation de l'efficacité environnementale d'un systè me à deux é tapes via l'efficacité é nergé tique de facteur total 5.1 Introduction Alors que la Chine connaî t un succè s considé rable en matiè re de dé veloppement é conomique au cours des derniè res dé cennies, le gouvernement fait face aux dé fis internes actuels de la pénurie d'énergie et de la dégradation de l'environnement. Afin de ré aliser les objectifs du douziè me plan quinquennal chinois, il est né cessaire d'analyser la situation de mise en oeuvre du onzième plan quinquennal chinois pour la pé riode 2006-2010 afin analyse des rendements é nergé tiques et environnementaux anté rieurs.

  pour é valuer l'efficacité é nergé tique et environnementale, bien que rarement axé sur l'efficacité é nergé tique industrielle totale et l'efficacité environnementale industrielle en Chine. L'industrie joue un rôle essentiel dans le développement de l'économie en Chine, comme en té moigne le fait que la valeur de la production industrielle brute repré sentait environ 38,5% du produit inté rieur brut (GDP) de la Chine en 2012. Plus important encore, le secteur industriel est un secteur à forte intensité é nergé tique qui repré sentait 70% de la consommation totale d'é nergie finale en 2012 (NBSC, 2013, 2014). La pollution industrielle est é galement la principale source de pollution en Chine. Il est donc urgent et utile d'étudier l'efficacité énergétique industrielle totale et industrielle en Chine.Au meilleur de nos connaissances, presque tous les ouvrages publié s anté rieurement considé raient le systè me industriel comme une « boî te noire» lorsqu'ils mesuraient l'efficacité environnementale du systè me industriel, ce qui a probablement conduit à la mé connaissance de certaines dé faillances du systè me. Dans ce chapitre, nous divisons le processus de consommation et d'utilisation de l'énergie dans l'industrie chinoise en deux phases: la phase d'utilisation industrielle de l'énergie et la phase de traitement de la pollution industrielle. En analysant la structure en deux é tapes du processus de consommation d'énergie de l'industrie chinoise, nous pouvons étudier efficacement les inefficacité s de la structure interne du systè me et fournir des indications pré cieuses pour la gestion lors de l'évaluation du double impact des straté gies opé rationnelles et commerciales du secteur industriel chinois.5.2 Modélisation de l'évaluation de l'efficacité environnementale du système industriel chinoisPour notre é tude de l'é valuation de l'efficacité environnementale industrielle en Chine, nous divisons le processus de production industrielle en deux sous-processus: le processus d'utilisation de l'é nergie et le processus de traitement de la pollution. Le premier sous-processus est axé sur l'utilisation d'intrants é nergé tiques et non é nergé tiques pour produire les extrants souhaitables et indé sirables, tandis que le dernier sous-processus est axé sur le recyclage et l'é limination de la pollution et des dé chets produits dans le premier. La structure est visible à la figure 5.1.

Figure 5 . 1

 51 Figure 5.1 Système de structure en deux étapes de l'industrie chinoise Supposons qu'il y a n DMU, chacun repr é sentant l'industrie d'une r é gion administrative de la Chine (𝐷𝑀𝑈 𝑗 , 𝑗 = 1, … , 𝑛). Indiquez les entrées partagées par 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑀𝑗 ) et les entrées d'énergie par 𝑍 𝑗 = (𝑧 1𝑗 , … , 𝑧 𝐾𝑗 ) au premier stade. Les sorties souhaitables du premier é tage sont noté es 𝐷 𝑗 = (𝑑 1𝑗 , … , 𝑑 𝑆𝑗 ) et les sorties indé sirables du premier é tage par 𝑈 𝑗 = (𝑢 1𝑗 , … , 𝑢 𝐹𝑗 ), qui sont é galement les entré es du deuxiè me é tage. Notons les nouvelles entrées du deuxième étage par 𝐼 𝑗 = (𝑖 1𝑗 , … , 𝑖 G𝑗 )

Figure 6 . 1

 61 Figure 6.1 La structure du ré seau du secteur des transports en Chine

  plus, compte tenu de l'hétérogénéité des secteurs des transports dans différentes régions de la Chine, un nouvel indice de productivité métafrontier Malmquist-, basé sur le modèle de réseau DEA. L'indice de productivité du métafrontier Malmquist-Luenberger (MMLPI) est décomposé en trois mesures individuelles: le changement d'efficacité au sein du groupe (l'effet de rattrapage), le changement de meilleure pratique (l'effet d'innovation) et le changement de leadership technologique) comme suit.( , , , , , , , , , )

  𝑇𝐸 𝑡 , 𝐵𝑃𝐺 𝑡 , et 𝑇𝐺𝑅 𝑡 sont respectivement le niveau d'efficacité technique d'un DMU (comme un secteur de transport provincial) dans le groupe R, le fossé des meilleures pratiques en matière d'observation au sein du groupe R et le fossé technologique des observations pour le DMU du groupe R par rapport à la technologie globale, le tout à l'heure t (Battese et al. 2004; Oh et Lee 2010). 6.3 Application à l'évaluation de l'efficacité environnementale du secteur des transports (1) Indice Metafrontier Malmquist-Luenberger moyen et ses dé compositions Parmi les 30 ré gions, seules 6 ré gions ont affiché une tendance à la baisse du MMLPI. Shangdong a enregistré la plus forte augmentation du MMLPI moyen, tandis que Hainan a enregistré la plus forte baisse. En ce qui concerne l'indice CE, six ré gions sont plus é loigné es des frontiè res, une ré gion est resté e inchangé e et les autres ré gions ont enregistré une augmentation de la CE moyenne. Notez qu'une CE plus é levé e ne signifie pas une performance supé rieure, mais une amé lioration à haut rendement au cours de ces anné es. Ces ré sultats indiquent clairement quelles ré gions peuvent ê tre utilisé es comme ré fé rences dans le mê me groupe, car leur expé rience peut ê tre bénéfique à d'autres régions pour améliorer leurs performances ou éviter les revers du secteur des transports. De maniè re analogue, BPC et TGC peuvent aider les A.6 Evaluation de l'efficacité environnementale d'un ré seau parallè le prenant en compte l'hé té rogé né ité ré gionale 139 gestionnaires de secteur à déterminer l'effet de l'innovation et de la technologie en vue d'accroître la productivité du secteur des transports de chaque région. (2) Indice Metafrontier Malmquist-Luenberger et ses dé compositions pour chaque zone Afin d'analyser les tendances du dé veloppement des transports des ré gions d'un point de vue plus large, les ré gions ont é té classé es en trois zones: la Chine orientale, la Chine occidentale et la Chine centrale. Les ré sultats montrent que la Chine occidentale et la Chine centrale ont affiché la plus forte croissance en termes de croissance de la productivité des transports au cours de la pé riode, avec 0,1576 et 0,1104, respectivement, tandis que l'est de la Chine a enregistré une baisse moyenne de 0,0350. Afin d'enquêter sur les sources de ces changements dans les performances du secteur des transports en Chine, le MMLPI est dé composé en trois mesures distinctes: le changement d'efficacité au sein du groupe, le changement de meilleure pratique (BPC) et le changement de dé ficit technologique (TGC). Nous pouvons constater que l'augmentation du MMLPI des transports en Chine provient principalement de BPC et de TGC, mais les ré sultats ont é té diffé rents selon les ré gions. , compte tenu de la production indésirable, un nouveau modèle DEA plus proche d'un cible basé sur un intervalle de mesure ajusté est établi pour mesurer l'efficacité environnementale du bassin de la rivière Xiangjiang en Chine. De plus, un nouveau modèle DEA en deux étapes avec entrées partagées est construit pour évaluer l'efficacité énergétique du facteur total et l'efficacité environnementale globale du secteur industriel de la Chine. Enfin, le modèle d'évaluation de l'efficacité environnementale d'un réseau parallèle prenant en compte l'hétérogénéité est proposé pour analyser le secteur de transport en Chine. Tous ces modèles sont appliqués à des exemples réels et utilisés pour mesurer

Table 3 .

 3 2 The lower and upper bounds of the environmental efficiency•

Table 4 .

 4 1 Descriptive statistics of inputs and outputs during 2008-2014•

Table 4 .

 4 2 Classical water environmental efficiencies of 15 monitoring areas in Hunan

Table 4 .

 4 3 Average classical water environmental efficiencies of seven cities in Xiangjiang River Basin•

Table 4 .

 4 4 Water environmental efficiencies of the 15 monitoring areas from 2008

Table 4 .

 4 6 Benchmarking analysis of the 15 monitoring areas in 2014

Table 5 .

 5 1 Descriptive statistical analysis of inputs and outputs•

Table 5 .

 5 2 Four kinds of efficiencies of industry in 30 regions of China from 2006-2010

Table 5 .

 5 4 Average efficiency of six administrative areas during 2006-2010•

Table 6 .

 6 5 The average metafrontier Malmquist-Luenberger index and its decompositions for each region 2007-2013•

Table 6 .

 6 6 Changes in MMPI and its decompositions of China's transportation sector 2007-2013•

  𝑢 𝑟 and 𝑤 𝑖 are the weights of the rth output and ith input, respectively. The first constraint means the ratio of weighted outputs to weighted inputs does not exceed 1 for each DMU. The objective is to seek a set of most favorable weights to maximize the If the optimal value of model (2.8) is 1, the evaluated 𝐷𝑀𝑈 0 is efficient;

					CHAPTER 2. Basic DEA theory
	𝑤 𝑖 ≥ 0, 𝑖 = 1, … , 𝑚.
	ratio of 𝐷𝑀𝑈 0 . Model (2.6) is a fractional linear programming. By applying the
	Charnes-Cooper transformation, let 𝑡 =	∑ 𝑠 𝑟=1 ∑ 𝑖=1 𝑚	𝑢 𝑟 𝑦 𝑟0 𝑤 𝑖 𝑥 𝑖0	, 𝜇 = 𝑡𝑢, 𝜔 = 𝑡𝑤, model (2.6) can be
	converted into model (2.7) as follows.
		𝑠
	max ∑ 𝜇 𝑟 𝑦 𝑟0
		𝑟=1
		𝑠			𝑚
	𝑠. 𝑡.	∑ 𝜇 𝑟 𝑦 𝑟𝑗	-∑ 𝜔 𝑖 𝑥 𝑖𝑗	≤ 0,
		𝑟=1			𝑖=1
		𝑚
		∑ 𝜔 𝑖 𝑥 𝑖0	= 1,
		𝑖=1
		𝜇 𝑟 ≥ 0, 𝑟 = 1, … , 𝑠,	(2.7)
	𝜔 min 𝜃
		𝑛
	𝑠. 𝑡. ∑ 𝜆 𝑗 𝑥 𝑖𝑗	≤ 𝜃𝑥 𝑖0 , 𝑖 = 1, … , 𝑚,
		𝑗=1
	max	∑ 𝑢 𝑟 𝑦 𝑟0 𝑠 𝑟=1 ∑ 𝑤 𝑖 𝑥 𝑖0 𝑛 𝑚 𝑖=1 ∑ 𝜆 𝑗 𝑦 𝑟𝑗 ≥ 𝑦 𝑟0 , 𝑟 = 1, … , 𝑠,
	𝑠. 𝑡.	∑ 𝑢 𝑟 𝑦 𝑟𝑗 𝑠 𝑗=1 𝑟=1 ∑ 𝑤 𝑖 𝑥 𝑖𝑗 𝑚 𝑖=1 𝜆	≤ 1, 𝑗 = 1, … , 𝑛
	𝑢 𝑟 ≥ 0, 𝑟 = 1, … , 𝑠,	(2.6)

In this section, two basic DEA models, i.e., CCR model and BCC model, are introduced. The former was proposed by

[START_REF] Charnes | Measuring the efficiency of decision making units[END_REF]

, is the earliest DEA model. According to the initials of the three authors, the model was named CCR model.

Assuming that there are n evaluated DMUs, each DMU uses the same inputs to produce the same outputs. 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ) 𝑇 and 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) 𝑇 are the input vector and output vector of 𝐷𝑀𝑈 𝑗 , respectively, where T in the superscript indicates transpose. The efficiency of each DMU is the ratio of the weighted outputs to the weighted inputs, the evaluated DMU is denoted as 𝐷𝑀𝑈 0 . The multiplier CCR model can be formulated as follows.

where 𝑖 ≥ 0, 𝑖 = 1, … , 𝑚. Definition 2.2. If the optimal value of model (2.7) is 1, the evaluated 𝐷𝑀𝑈 0 is efficient; if the optimal value of model (2.7) is less than 1, the evaluated 𝐷𝑀𝑈 0 is inefficient.

By duality, model (2.7) is equivalent to model (2.8), which is the envelopment form of CCR model. 𝑗 ≥ 0, 𝑗 = 1, … . , 𝑛.

(2.8) Definition 2.3.

(1) Environmental efficiency CHAPTER 2. Basic DEA theory

  The multiplier BCC model can be formulated as follows.

	min 𝜃
	𝑛
	𝑠. 𝑡. ∑ 𝜆 𝑗 𝑥 𝑖𝑗	≤ 𝜃𝑥 𝑖0 , 𝑖 = 1, … , 𝑚,
	𝑗=1
	𝑛
	∑ 𝜆 𝑗 𝑦 𝑟𝑗	≥ 𝑦 𝑟0 , 𝑟 = 1, … , 𝑠,
	𝑗=1
	𝑛
	∑ 𝜆 𝑗	= 1,
	𝑗=1
	𝜆 𝑗 ≥ 0, 𝑗 = 1, … . , 𝑛.	(2.9)
	Similarly, by duality, the envelopment form of BCC model is as follows.
	𝑠
	max ∑ 𝜇 𝑟 𝑦 𝑟0 -𝜇 0
	𝑟=1
	𝑠		𝑚
	𝑠. 𝑡. ∑ 𝜇 𝑟 𝑦 𝑟𝑗	-∑ 𝜔 𝑖 𝑥 𝑖𝑗	-𝜇 0 ≤ 0,
	𝑟=1		𝑖=1
	𝑚
	∑ 𝜔 𝑖 𝑥 𝑖0	= 1,
	𝑖=1
	𝜇 𝑟 ≥ 0, 𝑟 = 1, … , 𝑠,	(2.10)
	𝜔 𝑖 ≥ 0, 𝑖 = 1, … , 𝑚
	2.4 Basic concepts of environmental efficiency evaluation

DEA based methods for dealing with undesirable outputs

	Assume that both desirable and undesirable outputs are produced in the production
	process, denote 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ), 𝑈 𝑗 = (𝑢 1𝑗 , … , 𝑢 𝑏𝑗 ), 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) as inputs,
	undesirable outputs and desirable outputs of DMU 𝑗 (𝑗 = 1, … , 𝑛), respectively. The
	related production possibility set are expressed as follows.
	𝑇 = {(𝑋, 𝑌, 𝑈): 𝑋 can produce (𝑌, 𝑈)}	(2.11)
	Based on the definitions of weak disposability and strong disposability, for
	systems that considering environmental factors, if (𝑋, 𝑌, 𝑈) ∈ 𝑇, 𝑌 ′ ≤ 𝑌, 𝑈 ′ ≥ 𝑈 and
	(𝑋, 𝑌 ′ , 𝑈′) ∈ 𝑇, then the outputs are strongly disposable. If (𝑋, 𝑌, 𝑈) ∈ 𝑇, 𝜇 ∈ [0,1] and
	(𝑋, 𝜇𝑌, 𝜇𝑈) ∈ 𝑇, then the outputs are weakly disposable.
	(4) How to deal with undesirable outputs in the DEA model is crucial to assess the
	environmental efficiency of DMUs. After that, the model can take into account both
	desirable outputs (such as economic indicators) and undesirable outputs (such as
	pollution indicators). Since Fä re et al. (1989) proposed the first DEA model to deal with
	undesirable outputs with the weak disposability, the environmental efficiency
	evaluation considering the undesirable outputs were largely extended. According to the
	existing DEA-related literature, the methods for dealing with undesirable outputs can
	be classified into two categories: direct method and indirect method.

CHAPTER 3 Environmental efficiency evaluation of a single-stage system with fuzzy numbers Contents 3

  .1 Introduction ........................................................................................................ 22 3.2 Review of Russell Measure, Fuzzy DEA, and undesirable outputs ................... 24 3.2.1 Russell measure ..................................................................................................... 24 3.2.2 Fuzzy DEA models ................................................................................................. 25 3.2.3 Undesirable outputs and Environmental efficiency ................................................ 25 3.3 Modelling of a single-stage system with undesirable outputs and fuzzy numbers .................................................................................................................................. 27 3.3.1 Russell DEA model and enhanced Russell DEA model......................................... 27

	3.3.2 Fuzzy enhanced Russell DEA model considering undesirable outputs ................. 29
	3.4 Application to the environmental efficiency evaluation of thermal power firms
	in China .................................................................................................................... 34
	3.5 Conclusions ........................................................................................................ 40
	Thermal power has accounted for the major part of the electricity generation over
	recent several decades in China. It plays an important role in supporting China's
	and Seiford economic development while it also brings great pressure to the environment protection
	and Zhu (2002) suggested the linear monotonic decreasing transformation approach to because of a large amount of pollution generated during its production. In order to solve
	transform undesirable output into a new variable like desirable output variable, that is, or alleviate the environmental problem caused by thermal power firms, efficiency 𝑓(𝑈) = -𝑈 + 𝛽. Golany and Roll (1989) and Lovell et al. (1995) used the reciprocals evaluation is the first important step. Since thermal power firm is a complex system of the undesirable output as new output, the new output is modelled as 𝑓(𝑈) = 1/𝑈. with multiple inputs and multiple outputs, usually including fuzzy numbers and
	Each of the above methods has its own pros and cons. Therefore, which method is undesirable outputs in the production, in this chapter, we build an integrated Enhanced
	chosen for dealing with undesirable outputs depends on the specific research problem Russell measure model based on data envelopment analysis for evaluating the
	and research background. performance of decision making units in the presence of the undesirable outputs in
	fuzzy circumstance. Then, this new model is applied to analyze the environmental
	efficiency and provide the benchmarks for the thermal power firms in China which can

CHAPTER 3. Environmental efficiency evaluation of a single-stage system with fuzzy numbers

Table 3 .1 Statistical description

 3

		𝑥 1	𝑥 2	𝑦	𝑢 𝐿	𝑢 𝑀	𝑢 𝑈
	Mean	6344.067 1311113 92971.06 918822.3 1020914 1123005
	Standard. Deviation	1878.096 1230200 90928.34 2481782 2757536 3033289
	Min	2000	24245	350	4470.3	4967	5463.7
	Max	8760	3189931 243990.9 14096088 15662320 17228552

Table 3 .2

 3 The lower and upper bounds of the environmental efficiency

	DMU	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7

Table 3 .

 3

			2 (continued)
	DMU	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
		L 0.7709 0.7712 0.7715 0.7718 0.7720 0.7723 0.7726 0.7729 0.7732 0.7735 0.7738
		U 0.7766 0.7763 0.7760 0.7758 0.7755 0.7752 0.7749 0.7746 0.7743 0.7740 0.7738
		L 0.6608 0.6608 0.6608 0.6608 0.6609 0.6609 0.6609 0.6609 0.7716 0.6609 0.7714
		U 0.6611 0.6611 0.6611 0.6610 0.6610 0.6610 0.7645 0.6610 0.6610 0.6610 0.7714
		L 0.6424 0.6425 0.6427 0.6428 0.6429 0.6431 0.6432 0.6434 0.6435 0.6436 0.6438
		U 0.6451 0.6450 0.6449 0.6447 0.6446 0.6445 0.6443 0.6442 0.6440 0.6439 0.6438
		L 0.6838 0.6841 0.6844 0.6847 0.6850 0.6852 0.6855 0.6858 0.6861 0.6864 0.6866
		U 0.6894 0.6892 0.6889 0.6886 0.6883 0.6880 0.6878 0.6875 0.6872 0.6869 0.6866
		L 0.6805 0.6809 0.6812 0.6815 0.6819 0.6822 0.6826 0.6829 0.6832 0.6836 0.6839
		U 0.6873 0.6870 0.6866 0.6863 0.6859 0.6856 0.6853 0.6849 0.6846 0.6843 0.6839
		L 0.7786 0.7789 0.7792 0.7795 0.7798 0.7800 0.7803 0.7806 0.7809 0.7812 0.7815

Table 3 .3

 3 Ranking of the firms

	Rank	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
		1	1	1	1	1	1	1	1	1	1	1
		6	6	6	6	6	6	6	6	6	6	6
	1	9 14	9 14	9 14	9 14	9 14	9 14	9 14	9 14	9 14	9	9 14
		29	29	29	29	29	29	29	29	29		29
		30	30	30	30	30	30	30	30	30		30
	7	5	5	5	5	5	5	5	5	5	5	5
	8	2	2	2	2	2	2	2	2	2	2	2
	9	12	12	12	12	12	12	12	12	12		12
	10	3	3	3	3	3	3	3	3	3	3	3
	11	10	10	10	11	10	10	7	10	11		10
	12	8	8	8	10	8	8	10	8	10	8	8
	13	20	20	20	8	20	20	8	20	8		20
	14	15	15	15	20	15	15	20	15	20		15
	15	7	7	7	15	7	7	15	7	15	7	16
	16	23	23	23	7	23	26	23	23	7		7
	17	27	27	27	23	27	23	27	27	23		23
	18	18	18	18	27	18	27	16	18	27		27
	19	19	19	19	18	21	18	18	19	16		18
	20	11	11	11	19	19	19	19	11	18		19
	21	21	21	21	21	11	11	11	21	19		11
	22	16	16	16	16	16	21	21	16	21		21
	23	17	17	17	17	17	16	17	17	17		17
	24	26	26	26	26	26	17	26	26	26		26
	25	25	25	25	25	25	25	25	25	25		25
	26	22	22	22	22	22	22	22	22	22		22
	27	24	24	24	24	24	24	24	24	24		24
	28	13	13	13	13	13	13	13	13	13		13

Application to the environmental efficiency evaluation of thermal power firms in

	China											39
	29	4	4	4	4	4	4	4	4	4	4	4
	30	28	28	28	28	28	28	28	28	28	28	28

Table 3 .4

 3 Proportion for firms to be efficient in the fuzzy circumstance when 𝛼 = 0.5

	DMU	Production Time	Coal Consumption	Total industrial output value	Solid waste
	1	1.0000	1.0000	1.0000	1.0000
	2	0.9740	0.8838	1.0000	1.0017
	3	0.8666	0.9269	1.0000	1.0594
	4	0.4635	1.0000	2.6442	1.0000
	5	0.9291	1.0000	1.0000	1.0000
	6	1.0000	1.0000	1.0000	1.0000
	7	0.6020	0.9505	1.0000	1.0252
	8	0.7152	1.0000	1.1899	1.0000
	9	1.0000	1.0000	1.0000	1.0000
		0.8086	0.8784	1.0000	1.0731
		0.4331	0.9187	1.0000	1.0078
		0.8727	0.9650	1.0000	1.0740
		0.6430	1.0000	2.6779	1.0000
		1.0000	1.0000	1.0000	1.0000
		0.6433	0.9461	1.0000	1.0503
		0.5614	0.7618	1.0000	1.0018
		0.4450	0.8624	1.0000	1.0287
		0.5431	0.8718	1.0000	1.0565
		0.4682	0.9570	1.0000	1.0788
		0.6070	1.0000	1.0000	1.0524
		0.4737	0.8958	1.0000	1.0412
		0.3190	0.7244	1.0000	1.0141
		0.5705	0.9764	1.0000	1.0609
		0.2978	0.6410	1.0000	1.0200
		0.2605	0.8638	1.0000	1.0059
		0.8363	0.9733	1.0000	1.0218
		0.5407	0.9516	1.0000	1.0725
		0.2358	0.4205	1.0000	7.3331
		1.0000	1.0000	1.0000	1.0000

Environmental efficiency evaluation of a single-stage system with fuzzy numbers

	30	1.0000	1.0000	1.0000	1.0000

Environmental efficiency evaluation of a single-stage 44 system considering performance improvement path approach

  are more acceptable for DMUs to improve the performance on their economy

	and environment.
	4.1 Introduction
	Xiangjiang River, as the largest river in Hunan Province in China, is the mother
	river of Hunan province. Xiangjiang River Basin is the most densely populated region
	with the highest level of urbanization and the most developed economy in Hunan
	Province. However, the large population and rapid economic development have
	resulted in the greatest pressure on resources and environment. Recently, with the
	gradual acceleration of the modernization process, many environmental pollution

4.1 Introduction ........................................................................................................ 44 4.2 Traditional RAM model and the closest target .................................................. 46 4.3 Closest target RAM model considering undesirable outputs ............................. 48 4.4 Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China ................................................................................................ 52 4.4.1 Data and variables .................................................................................................. 53 4.4.2 Results analysis ...................................................................................................... 55 4.5 Conclusions ........................................................................................................ 60

In recent decades, with the rapid economic development of Xiangjiang River Basin in China, the discharge of industrial waste gas, wastewater and domestic waste gas, wastewater also increased significantly, which caused great damage to the ecological environment of Xiangjiang River Basin and violated the sustainable development of economy. In order to solve the environmental pollution problem, many scholars have adopted data envelopment analysis (DEA) to measure and improve the environmental efficiency of various industries and entities in China. However, as the target (benchmark) set by these works is usually the furthest one for a decision making unit (DMU) to be efficient, thus it may be hardly accepted by the DMU. In this chapter, considering the undesirable outputs, a new closest target DEA model based on range adjusted measure (RAM) is proposed. Finally, the proposed model is applied to the water environmental efficiency evaluation of Xiangjiang River basin in China. The results show that the environmental efficiency of Xiangjiang River basin has an increasing trend during the year of 2008-2014, but the deviations among the areas are still at a larger value. Compared to the "furthest" target methods, the targets by our

CHAPTER 4. problems, such as haze, water resources shortage, water and atmospheric pollution, heavy metal pollution, have seriously threatened the ecological environment of Xiangjiang River Basin. Environmental pollution seriously restricts the sustainable development of economy and society. The Chinese government and the local government of Hunan Province issued many related environmental laws and regulations to promote the implementation of cleaner production technology and pollution reduction, so as to achieve sustainable economic and environmental development

system considering performance improvement path distance

  function approach to determine the targets for the DMUs.[START_REF] Jahanshahloo | Using the minimum distance of DMUs from the frontier of the PPS for evaluating group performance of DMUs in DEA[END_REF] conducted a DEA method to obtain the minimum distance of DMUs to the frontier by ||•||1.Briec and[START_REF] Briec | Technical efficiency and distance to a reverse convex set[END_REF] Briec and[START_REF] Briec | Dual representations of non-parametric technologies and measurement of technical efficiency[END_REF] used Hölder distance functions to obtain the evaluated DMU' minimum distance to the frontier.

	Ando et al. (2012) pointed out that least distance measures based on Hölder norms meet
	neither weak nor strong monotonicity on the strongly efficient frontier and provided a
	method to guarantee the function is weak monotonicity. To realize the strong
	monotonicity, Aparicio and Pastor (2014b) provided a solution for output-oriented
	models based on an extended production possibility set which is strongly monotonic;
	Fukuyama et al. (2014) employed least distance p-norm inefficiency measures that
	4.2 Traditional RAM model and the closest target	gave the closest
	targets by minimizing the Euclidean distance or weighted Euclidean distance to the
	efficient frontier, more extensions in this direction see Baek and Lee (2009), In this section, we firstly introduce the approach of RAM, and then show Aparicio
	Amirteimoori and Kordrostami (2010), Aparicio and Pastor (2014a). Gonzalez and et al.'s (2007) approach which finds the closest targets. As two representative

Alvarez (2001)

gained the relative targets by minimizing the sum of input contractions required to reach the frontier of the technology.

[START_REF] Portela | Negative data in DEA: A directional distance approach applied to bank branches[END_REF]

applied directional satisfy strong monotonicity over the strongly efficient frontier to obtain the targets for the DMUs. The other category is minimizing (or maximizing) the efficiency measure.

[START_REF] Portela | Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies[END_REF]

maximized the BRWZ measure proposed by

[START_REF] Brockett | Implementation of DEA models using GAMS[END_REF]

to obtain the closest targets.

[START_REF] Aparicio | Closest targets and minimum distance to the Pareto-efficient frontier in DEA[END_REF][START_REF] Aparicio | A well-defined efficiency measure for dealing with closest targets in DEA[END_REF]

proposed several mathematical programming problems to find the closest targets where some efficiency measures, such as range adjusted measured, Russell measure, slacks-based measure, are chosen as criterion of similarity. These programming problems can be easily solved, and the results guarantee the evaluated DMU can reach the closest projection point on the Pareto-efficient frontier.

To measure the environmental efficiency of the water system in Xiangjiang River Basin and set the closest target for the evaluated DMU to be efficient, in this chapter, considering the undesirable outputs, we propose a new closest target model based on Range Adjusted Measure (RAM). The RAM is chosen as the basic model because it is not only a non-radial DEA model, but also can deal with non-positive data in the input and output indicators

[START_REF] Ding | Production efficiency, environmental governance efficiency and comprehensive efficiency of Marine Economy in China[END_REF]

. Then, the new closest target model is applied to environmental efficiency evaluation of the water system in Xiangjiang River Basin. approaches in DEA for measuring efficiency and finding the closest targets, these two approaches have been largely studied and extended respectively

(Sueyoshi and Sekitani, 2007; Tavassoli et al., 2016; Aparicio and Pastor, 2014b;[START_REF] Wu | Closest target for the orientationfree context-dependent DEA under variable returns to scale[END_REF]

. 4.

2 Traditional RAM model and the closest target

  Consider we have 𝑛 DMUs, and each DMU 𝑗 (𝑗 = 1, … , 𝑛) uses 𝑚 inputs to produce 𝑠 outputs which are denoted by (𝑋 𝑗 , 𝑌 𝑗 ), 𝑗 = 1, … , 𝑛. It is assumed that 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ) ≥ 0 , 𝑋 𝑗 ≠ 0 , 𝑗 = 1, … , 𝑛 , and 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 ) ≥ 0 , 𝑌 𝑗 ≠ 0 , 𝑗 = 1, … , 𝑛. The range adjusted measure (RAM) model[START_REF] Cooper | RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA[END_REF] under constant returns to scale is shown as follows.

	Min		1	00 11 ms ir ir ir  ss R R    1 ( m s  	)
			n
	. . s t	1   j		00 i x i , 1,...,  i x s j ij   	m	(4.1)
			n
		1   j		j rj y s 	00 i y r , 1,...,  r  	s
		j	_ 00 , , i r s s 	0;  j	1,..., . n
	where

j  represents unknown variable (often referred to as "structural" or "intensity" variables) for connecting the input and output vectors by a convex combination. 𝑅 𝑖 -= 𝑚𝑎𝑥 𝑗 {𝑥 𝑖𝑗 } -𝑚𝑖𝑛 𝑗 {𝑥 𝑖𝑗 } is the range of ith input and 𝑅 𝑟 -= 𝑚𝑎𝑥 𝑗 {𝑦 𝑟𝑗 } -𝑚𝑖𝑛 𝑗 {𝑦 𝑟𝑗 } is the range of rth output; 𝑠 𝑖0 -and 𝑠 𝑟0 + are the slacks of the ith input and the rth output of 𝐷𝑀𝑈 0 , respectively. Denote (𝜆 𝑗 * , 𝑠 𝑖0 - * , 𝑠 𝑟0 + * )be an optimal solution of the model (4.1), when the optimal value of the model (4.1) is 1, then 𝐷𝑀𝑈 0 is efficient; otherwise, 𝐷𝑀𝑈 0 is inefficient. It should be noted that this model is different from the SBM model whose objective function is 0 0

Environmental efficiency evaluation of a single-stage 50 system considering performance improvement path and

  the range of rth desirable output, respectively. 𝑠 𝑖0 -, 𝑠 𝑟0 + , and 𝑠 𝑝0 --are the slacks of the ith input, the rth desirable output and the pth undesirable output of 𝐷𝑀𝑈 0 . It can be seen that model (4.4) can measure the distance between the evaluated DMU and the benchmark (reference point) from the perspective of input and output. Assume

	(𝜆 𝑗 * , 𝑠 𝑖0 - * ,𝑠 𝑟0 + * , 𝑠 𝑝0 -- * ) is an optimal solution of the model (4.4), based on the results of the
	model (4.4), we can obtain the classical environmental efficiency for 𝐷𝑀𝑈 0 , which can
	then be computed through formula (4.5).
	1	* 11 * 0 0 (	* 0	)
		1	1	1
					(4.4)
					. pq 
	where 𝑅 𝑖

-= 𝑚𝑎𝑥 𝑗 {𝑥 𝑖𝑗 } -𝑚𝑖𝑛 𝑗 {𝑥 𝑖𝑗 } , 𝑅 𝑝 --= 𝑚𝑎𝑥 𝑗 {𝑧 𝑝𝑗 } -𝑚𝑖𝑛 𝑗 {𝑧 𝑝𝑗 } and 𝑅 𝑟 -= 𝑚𝑎𝑥 𝑗 {𝑦 𝑟𝑗 } -𝑚𝑖𝑛 𝑗 {𝑦 𝑟𝑗 } are the range of ith input, the range of pth undesirable output CHAPTER 4.

CHAPTER 4. Environmental efficiency evaluation of a single-stage 52 system considering performance improvement path Theorem 4.2.

  The optimal value of model (4.8) must not be larger than that of the model (4.4).

	Assume (𝜆 𝑗 * , 𝑠 𝑖0 - * ,𝑠 𝑟0 + * ,𝑠 𝑝0 -- * ,𝑣 𝑖 * ,𝜋 𝑝 * ,𝑤 𝑟 * ,𝑑 𝑗

* ,𝑏 𝑗 *

Table 4

 4

	.1.

CHAPTER 4.

Environmental efficiency evaluation of a single-stage 54 system considering performance improvement path

Table 4 .1

 4 Descriptive statistics of inputs and outputs during 2008-2014

		Labor	Capital	Energy	DO	TP	GDP
		(10 thousands person)	(100 million RMB)	(10 thousands of TCE)	(mg/L)	(mg/L)	(100 million RMB)
	2008
	Mean	325.084	443.3067	532.8767	7.752	0.0583	1105.261
	Variance	9570.854	263485.7	31145.79	1.4982	0.0013	622951.1
	Max	422.84	1702.3	888.24	11.14	0.139	3000.98
	Min	159.63	174.55	184.26	6.1	0.01	528.4
	2009
	Mean	334.9227	637.028	557.576	7.9013	0.0639	1303.315
	Variance	407564.7	10825.21	32527.86	1.5125	0.0012	1031122
	Max	440.03	2200.62	891.75	11.18	0.138	3744.76
	Min	175.66	242.05	196.76	5.89	0.007	568.31
	2010
	Mean	344.5127	833.5107	592.6167	7.6727	0.0794	1588.619
	Variance	12402.9	638096.8	37822.98	0.5239	0.0016	1517310
	Max	458.31	2785.99	969.25	9.16	0.146	4547.06
	Min	172.72	305.1	219.62	6.15	0.007	678.71
	2011
	Mean	341.3636	1100.734	498.0357	7.7936	0.0683	1974.079
	Variance	13321.07	990766.4	27342.7	0.8571	0.0014	2489730
	Max	466.39	3433.33	804.04	9.93	0.141	5619.33
	Min	169.33	425.25	168.43	6.82	0.005	847.26
	2012
	Mean	354.9207	1373.709	570.002	7.6893	0.0715	2220.991
	Variance	13447.33	1123715	39811.78	0.3275	0.0019	3009651
	Max	470.18	3956.06	1052.41	8.47	0.161	6399.91
	Min	175.46	581.91	225.09	6.27	0.005	1002.65
	2013
	Mean	360.392	1741.072	532.8767	7.5767	0.0653	2472.869
	Variance	13443.71	1332636	31145.79	0.3448	0.0013	3768624
	Max	475.44	4539.39	888.24	8.75	0.143	7153.13
	Min	184.48	787.57	184.26	6.5	0.008	1118.17
	2014
	Mean	361.268	2116.535	557.576	7.4107	0.0653	2718.79
	Variance	13709.77	1882373	32527.86	0.3259	0.002	4494915
	Max	476.45	5435.75	891.75	8.54	0.172	7824.81
	Min	180.3	938.94	196.76	6.68	0.005	1210.86

Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China 55

  From Table4.1, it can be observed that the mean values of labor force, capital, and energy consumption increased year by year, which means that the investments of each area increased year by year. Meanwhile, the overall downward trend of the average dissolved oxygen and the overall growth trend of the average total phosphorus indicated the overall water quality had deteriorated during this period. Although GDP of all areas increased greatly, but from the large variance of GDP, we can know economic development among different areas were largely different.4.4.2 Results analysisIn this section, we evaluate the water environmental efficiency of 15 monitoring areas in 7 cities. In order to assess the annual water environmental efficiency of each area, each area of each year is treated as a DMU. The classical water environmental efficiency of each area can be derived by using model (4.4) and formula (4.5). The results are shown in table 4.2.

Table 4

 4

	City	Area	2008	2009	2010	2011	2012	2013	2014	Mean
	Yongzhou Xiaoshui	1.0000 0.6755 0.6754 0.6952 0.6952 0.6704 0.6771 0.7270
		Trunk	0.9941 0.6695 0.6634 0.6894 0.6894 0.6718 0.6593 0.7196
	Hengyang Chunlingshui 0.9674 1.0000 0.9965 1.0000 1.0000 0.5784 0.5606 0.8719
		Zhengshui	0.9666 0.9391 1.0000 0.9752 0.9752 0.5306 0.5676 0.8506
		Leishui	0.9560 0.8722 0.9359 0.9615 0.9615 0.5711 0.5663 0.8321
		Mishui	1.0000 0.9456 1.0000	\	\	0.5610 0.5659 0.8145
		Trunk	0.9836 0.9521 0.9864 0.9800 0.9800 0.5590 0.5567 0.8568
	Zhuzhou	Lushui	0.8982 0.7253 0.6245 0.7205 0.7205 0.6548 0.6567 0.7144
		Trunk	1.0000 0.7586 0.7150 0.8424 0.8424 0.6713 0.7125 0.7917
	Xiangtan Lianshui	0.7409 0.7129 0.6545 0.7098 0.7098 0.6717 0.6483 0.6926
		Trunk	0.7094 0.6209 0.5922 0.6513 0.6513 0.6559 0.6641 0.6493
	Changsha Liuyanghe	0.8693 0.9060 0.7856 1.0000 1.0000 0.9459 0.8951 0.9146
		Trunk	0.8860 0.8713 0.8367 1.0000 1.0000 1.0000 1.0000 0.9420
	Chenzhou Leishui	1.0000 0.7939 0.7799 1.0000 1.0000 0.8781 1.0000 0.9217
	Loudi	Lianshui	0.6062 0.5503 0.5284 0.5596 0.5596 0.5126 0.4563 0.5390
		Mean	0.9052 0.7996 0.7850 0.8418 0.8418 0.6755 0.6791

.2 Classical water environmental efficiencies of 15 monitoring areas in Xiangjiang river basin In Table 4.2, the areas with the efficiency value of 1 are classical water environmental efficient. Due to the data of Mishui area of Hengyang in 2011 and 2012 CHAPTER 4.

Environmental efficiency evaluation of a single-stage 56 system considering performance improvement path is

  unavailable, the classical water environmental efficiency of this area could not be obtained. From table 4.2, it can be found that the overall classical water environmental efficiency of Xiangjiang River Basin was decreasing year by year. Liuyanghe area of Changsha, Trunk area of Changsha, and Leishui area of Chenzhou performed well, and their water environmental efficiencies were all greater than 0.9. Lianshui area of Loudi performs the worst. According to the locations of the 15 monitoring areas, we can get the classical water environmental efficiencies of the seven cities in Xiangjiang River Basin, which were shown in table 4.3.

Table 4

 4 It can be seen from table 4.3, the overall classical water environmental efficiencies of Xiangjiang River Basin had become worse and worse from 2008 to 2014. Changsha performed the best, followed by Chenzhou and Loudi performs the worst. As the capital city of Hunan province, Changsha has the largest economy and pays more attention to environmental protection than other cities. For the worst performance city Loudi, the local government needs to coordinate the development of economy and the environment. Besides, the classic water environmental efficient areas in table 4.2 forms the efficient set H of model (4.8), by model (4.8), the water environmental efficiency and the closest target of each area of each year can be obtained.

	.3 Average classical water environmental efficiencies of seven cities in Xiangjiang
					river basin
		2008	2009	2010	2011	2012	2013	2014	Mean
	Yongzhou	0.9971 0.6725 0.6694 0.6923 0.6923 0.6711 0.6682	0.7233
	Hengyang	0.9747 0.9418 0.9838 0.9792 0.9792 0.5600 0.5634	0.8546
	Zhuzhou	0.9491 0.7420 0.6698 0.7814 0.7814 0.6631 0.6846	0.7530
	Xiangtan	0.7252 0.6669 0.6234 0.6805 0.6805 0.6638 0.6562	0.6709
	Changsha	0.8776 0.8886 0.8112 1.0000 1.0000 0.9730 0.9475	0.9283
	Chenzhou	1.0000 0.7939 0.7799 1.0000 1.0000 0.8781 1.0000	0.9217
	Loudi	0.6062 0.5503 0.5284 0.5596 0.5596 0.5126 0.4563	0.5390

4.

4 Application to the water environmental efficiency evaluation of Xiangjiang River Basin in China 57Table 4 .4

 4 Water environmental efficiencies of the 15 monitoring areas from 2008 to 2014 During this period, the best performing year is 2009, and the worst year is 2014, while the efficiency difference is small and can be ignored. Comparing the efficiencies of the 15 areas, we find the Trunk area of Changsha, the Mishui area of Hengyang, the Trunk area of Hengyang, and the Chuling area of Hengyang performed well, and the efficiencies were all higher than 0.99. From the average efficiency of each area listed in the last column of table 4.4, except the Lianshui area of Xiangtan, the Trunk area of Xiangtan and the Lianshui area of Loudi, other 12 areas' average efficiencies were above 0.9 which indicated that the overall

	City	Area	2008	2009	2010	2011	2012	2013	2014 Mean
	Yongzhou Xiaoshui	1.0000 0.9857 0.9943 0.9086 0.9086 0.9142 0.8631 0.9392
		Trunk	0.9941 0.9806 0.9836 0.9000 0.9000 0.9171 0.8692 0.9349
	Hengyang Chunlingshui 0.9674 1.0000 0.9987 1.0000 1.0000 0.9916 0.9751 0.9904
		Zhengshui	0.9666 0.9996 1.0000 0.9814 0.9814 0.9896 0.9642 0.9833
		Leishui	0.9560 0.9839 0.9925 0.9771 0.9771 0.9969 0.9969 0.9829
		Mishui	1.0000 0.9805 1.0000	\	\	0.9898 0.9962 0.9933
		Trunk	0.9836 0.9996 1.0000 0.9929 0.9929 0.9855 0.9778 0.9903
	Zhuzhou	Lushui	0.8982 0.9548 0.8768 0.9038 0.9038 0.9111 0.8718 0.9029
		Trunk	1.0000 0.9751 0.9340 0.9291 0.9291 0.9143 0.8693 0.9358
	Xiangtan Lianshui	0.7433 0.7339 0.7729 0.7695 0.7695 0.7814 0.7787 0.7642
		Trunk	0.8682 0.8300 0.7759 0.7898 0.7898 0.7588 0.7515 0.7948
	Changsha Liuyanghe	1.0000 1.0000 0.9845 1.0000 1.0000 0.9459 0.8951 0.9751
		Trunk	0.9875 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9982
	Chenzhou Leishui	1.0000 0.9634 0.9531 1.0000 1.0000 0.9951 1.0000 0.9874
	Loudi	Lianshui	0.6267 0.6558 0.7080 0.8678 0.8678 0.8610 0.8616 0.7784
		Mean	0.9328 0.9362 0.9316 0.9300 0.9300 0.9302 0.9114

The water efficiencies of the 15 monitoring areas are shown in table 4.4. The areas in a certain year having the efficiency of 1 are water environmental efficient. It can be seen from table

4

.4 that the average water environmental efficiencies of these areas tended to be the same, with an efficiency value of about 0.93, which was obviously different from the classical water efficiency. ecological environment level of water system in Xiangjiang River Basin were all at a higher level. The results indicated that Hunan Province had made some achievements in the control of water quality pollution in Xiangjiang River. CHAPTER 4.

Environmental efficiency evaluation of a single-stage 58 system considering performance improvement path

  Comparing the results in tables 4.2 and 4.4, it is found the average water environmental efficiency of each area based on the closest target model (4.8) was higher than the average classical water environmental efficiency. Compared with the classical

	environmental efficiency evaluation model (4.4), the water environmental inefficient
	areas can achieve efficient with the "least" effort through our proposed model (4.8),
	besides, the closest target for each water environmental inefficient area can be obtained.
	Furthermore, the water environmental efficiencies of seven cities in Xiangjiang river
	basin from 2008-2014 were listed in table 4.5.

Table 4 .5

 4 Water environmental efficiencies of seven cities in Xiangjiang river basin

		2008	2009	2010	2011	2012	2013	2014	Mean
	Yongzhou	1.0000 1.0000 0.9803 1.0000 1.0000 1.0000 0.9455	0.9894
	Hengyang	1.0000 0.8609 1.0000 1.0000 0.6969 0.7604 0.6946	0.8590
	Zhuzhou	1.0000 0.9858 0.9436 1.0000 1.0000 1.0000 0.9591	0.9841
	Xiangtan	1.0000 0.9546 0.9363 1.0000 0.9811 0.9287 1.0000	0.9715
	Changsha	0.8884 0.9207 0.9044 0.9752 1.0000 1.0000 1.0000	0.9555
	Chenzhou	1.0000 1.0000 0.9244 0.9911 0.8847 0.9203 0.8915	0.9446
	Loudi	1.0000 0.9093 0.8789 0.8639 0.8803 0.9016 0.8623	0.8995

  used total-factor energy efficiency to evaluate the energy efficiencies of 29 administrative regions in China for the period 1995-2002 and found a U-shape relation between TFEE and per capita income in these regions of China.

		CHAPTER 5. Environmental efficiency evaluation of a two-stage
	64	system via total-factor energy efficiency
	undesirable outputs, Zhou and Ang (2008) proposed several DEA-type linear
	programming models which consider both desirable and undesirable outputs in
	measuring economy-wide total-factor energy efficiency performance. Shi et al. (2010)
	developed an extended DEA model by treating undesirable outputs as inputs to evaluate
	the industrial energy efficiency and investigated the maximum energy-saving potential
	in 28 administrative regions in China. After that, Bai et al. (2012) used a super
	efficiency DEA method to measure the energy efficiency of 11 provinces in western
	China from 1989 to 2009, under the framework of total-factor energy efficiency where
	both desirable outputs and undesirable outputs are considered. Wang et al. (2013)
	Zhang et al. (2011) used DEA window analysis to investigate the dynamic trends in the
	total-factor energy efficiency of a sample of developing countries. Zhao et al. (2014)
	applied a total-factor energy efficiency index to evaluate the changes of TFEE at the
	sector and provincial levels. They found that technology progress, energy price and
	economic development have a positive influence on TFEE based on Tobit regression.

In this category of research, not only energy inputs but also non-energy inputs (e.g., labor, capital) are considered when analyzing the desirable outputs. Considering

2 Modeling of environmental efficiency evaluation of the two-stage system of China

		CHAPTER 5. Environmental efficiency evaluation of a two-stage 's
	68 industry	system via total-factor energy efficiency 69
	Investments in pollution In our study of industrial environmental efficiency, the undesirable outputs ( , , , , , ) |
	treatment (pollutants) are mainly generated by energy inputs in the production process and should Stage 1 constraints:
	n be reduced if energy consumption is reduced. Therefore, we apply the weak ( ) , j j j j j 1,..., mm
	Energy Utilization Process 1 j disposability assumption to deal with undesirable outputs. As expressed in Fä re and Pollution Treatment n POVW Non-energy inputs Grosskopf (2004), weak disposability indicates that a Null-Joint relationship exists ( ) , j j j 1,..., kk Process 1 j Pollution between desirable outputs and undesirable outputs in the production process, which n
	Energy inputs means desirable outputs and undesirable outputs should be reduced in a proportional , jj 1,..., ss 1 j GIOV n way (see more details about this assumption in Fä re et al., 1989; Tone, 2004; Zhou et , jj 1,..., ff al., 2008). The assumption of weak disposability is important because it enables us to 1 j
	model undesirable outputs in DEA models, considering the possible tradeoffs between Stage 2 constraints:
	the desirable outputs and the undesirable outputs. Analogous to Kuosmanen (2005)'s n T= , jj two stage 1,..., ff
	way of defining production technology under the variable return to scale that satisfies 1 j
	weak-disposability assumption, the related production possibility set (PPS) of the ( j
	industrial two-stage system shown in Figure 5.1 is given as follows.

). Denote the DMU being evaluated by 𝐷𝑀𝑈 0 .

5.

Environmental efficiency evaluation of a two-stage 74 system via total-factor energy efficiency

  Table 5.1.

CHAPTER 5.

Table 5 .1

 5 Descriptive statistical analysis of inputs and outputs

	Variables ILF	IC	IEC	GLOV	ISWG IWGE IWWD	IIPT	POVW
	Mean	172.3 1690.9	6779.2	3418.4	5051.1	74.4 80038.5 161311.9 342258.6
	Std.dev. 124.8 1543.9	4391	3296.7	3759.6	44.7 70312.9 142217.9 377342.1
	Max	496.4 6894.8 18731.3 12500.2 14229	168.7 287181 596643.1 1497950.1
	Min	13	134.8	644	217.6	147	2.3	7168	7773.2	10369.2
	Mean	178.4 2021.7	7442.7	4110.4	5854.2	71.3 82187.9 184123	450404.5
	Std.dev. 130.3 1734.1	4816	3872.2	4503.9	42	72683.2 159263.5	523786
	Max	505.9 7177.8 20423.9 14910	18688	158.3 268762	673420 2240597.9
	Min	14.1	83.3	739.9	278.4	158	2.5	5960	3889	20431.2
	Mean	178.4 2541.7	7879.7	4965.1	6337.3	66.4 80519.6 180880	540441.2
	Std.dev. 132.5 2053.4	5032.7	4517	4857.2	38.9 71152.9 168893.4 592634.8
	Max	498	8342.4	21399	17254	19769	146.6 259999	844159	2409843
	Min	14.7	119.5	794.5	321.2	220	2.1	5991	3774	41309
	Mean	184.3 3176.9	8335.6	5248.8	6797.7	62.2 78097.2 147540.3 536073.5
	Std.dev. 139.6 2502.9	5293.6	4750.7	5160.8	36.3 67539.6 108913	581425.5
	Max	528.5 10304.6 22694 18091.6 21975.8 136.6 256160	515832	2513210
	Min	16	144	863.1	300.6	200.9	2.1	7031	3563	24440
	Mean	192.5 3903.5	9088.6	6442.6	8031	62.1 79133.2 132325.7 592826.5
	Std.dev.	150	2978	5720.7	5475.8	6635.8	36.1 70357.6 105065.6 650121.4
	Max	563.2 12463.1 24365.6 21462.7 31688	138.3 263760	456759 2863867.2
	Min	17.1	191.6	951.3	385.2	212	2.8	5782	4354	31623.2

Table 5

 5

.2.

Table 5 .2

 5 Four kinds of efficiencies of industry in 30 regions of China from 2006-2010

		Total factor energy efficiency	Overall environmental efficiency
		2006 2007 2008 2009 2010	2006 2007 2008 2009 2010
	Beijing	0.934 0.957 1.000 1.000 1.000	0.737 0.759 1.000 1.000 1.000
	Tianjin	0.606 0.680 1.000 0.933 1.000	0.662 0.663 1.000 0.947 1.000
	Hebei	0.578 0.955 1.000 0.822 1.000	0.416 0.516 1.000 0.634 1.000
	Shanxi	0.701 0.715 0.895 0.500 0.732	0.312 0.415 0.458 0.394 0.453
	Inner Mongolia	0.604 0.665 0.921 0.932 1.000	0.296 0.451 0.646 0.807 1.000
	Liaoning	0.424 0.662 0.643 0.669 0.635	0.313 0.404 0.458 0.471 0.579
	Jilin	0.264 0.484 0.626 0.625 1.000	0.413 0.445 0.524 0.567 1.000
	Heilongjiang 0.347 0.390 0.967 0.603 0.800	0.485 0.489 0.662 0.500 0.843
	Shanghai	0.975 0.734 0.850 1.000 1.000	0.814 0.735 0.842 1.000 1.000
	Jiangsu	0.835 1.000 1.000 1.000 1.000	0.646 0.759 1.000 0.912 1.000
	Zhejiang	0.904 1.000 1.000 0.923 1.000	0.683 1.000 0.938 0.876 1.000
	Anhui	0.735 0.675 0.660 0.674 0.758	0.360 0.398 0.514 0.503 0.666
	Fujian	0.478 0.319 0.499 0.612 0.338	0.396 0.423 0.455 0.505 0.550
	Jiangxi	0.751 0.567 0.649 0.665 0.705	0.376 0.416 0.477 0.549 0.642
	Shandong	0.579 0.729 1.000 1.000 1.000	0.520 0.596 0.797 0.931 1.000
	Henan	0.485 0.712 0.657 0.599 0.829	0.403 0.436 0.554 0.563 0.740
	Hubei	0.546 0.549 0.636 0.800 0.754	0.431 0.475 0.516 0.541 0.609
	Hunan	0.937 0.938 0.863 0.758 0.785	0.394 0.445 0.515 0.529 0.655
	Guangdong 1.000 1.000 1.000 1.000 1.000	1.000 1.000 1.000 1.000 1.000
	Guangxi	0.439 0.834 0.789 0.786 0.871	0.362 0.408 0.455 0.443 0.543
	Hainan	1.000 1.000 1.000 1.000 1.000	1.000 1.000 1.000 1.000 1.000
	Chongqing 0.279 0.653 0.571 0.759 0.736	0.312 0.327 0.388 0.491 0.579
	Sichuan	0.667 0.834 0.545 0.563 0.745	0.345 0.354 0.400 0.464 0.640
	Guizhou	0.575 0.804 0.836 0.752 0.808	0.371 0.408 0.457 0.402 0.436
	Yunnan	0.908 0.990 1.000 0.975 1.000	0.507 0.585 1.000 0.634 1.000
	Shaanxi	0.840 0.594 0.599 0.613 0.707	0.359 0.383 0.415 0.432 0.520
	Gansu	0.889 0.719 0.884 0.762 0.725	0.349 0.436 0.484 0.495 0.527
	Qinghai	1.000 0.921 1.000 0.972 1.000	1.000 0.896 1.000 0.771 1.000
	Ningxia	0.278 0.592 0.702 0.628 0.862	0.320 0.331 0.375 0.373 0.557
	Xinjiang	0.671 0.398 0.744 0.582 0.721	0.391 0.399 0.457 0.407 0.559
	Average	0.674 0.736 0.818 0.784 0.850	0.499 0.545 0.660 0.638 0.770

Environmental efficiency evaluation of a two-stage 76 system via total-factor energy efficiency

Table 5 .

 5 2 (continued)

		Efficiency of the first stage	Efficiency of the second stage
		2006 2007 2008 2009 2010	2006 2007 2008 2009 2010
	Beijing	0.771 0.811 1.000 1.000 1.000	0.702 0.707 1.000 1.000 1.000
	Tianjin	0.672 0.732 1.000 0.975 1.000	0.652 0.593 1.000 0.920 1.000
	Hebei	0.383 0.556 1.000 0.600 1.000	0.448 0.477 1.000 0.667 1.000
	Shanxi	0.398 0.422 0.517 0.368 0.469	0.227 0.408 0.399 0.420 0.438
	Inner Mongolia	0.353 0.464 0.638 0.806 1.000	0.239 0.437 0.654 0.809 1.000
	Liaoning	0.329 0.452 0.491 0.514 0.562	0.296 0.356 0.424 0.429 0.595
	Jilin	0.341 0.439 0.545 0.583 1.000	0.485 0.451 0.504 0.550 1.000
	Heilongjiang 0.403 0.432 0.720 0.505 0.816	0.566 0.546 0.603 0.495 0.870
	Shanghai	0.807 0.745 0.843 1.000 1.000	0.822 0.725 0.841 1.000 1.000
	Jiangsu	0.661 0.809 1.000 0.939 1.000	0.631 0.709 1.000 0.885 1.000
	Zhejiang	0.744 1.000 0.948 0.900 1.000	0.621 1.000 0.927 0.852 1.000
	Anhui	0.454 0.471 0.536 0.545 0.670	0.266 0.325 0.492 0.461 0.662
	Fujian	0.432 0.406 0.499 0.554 0.513	0.359 0.439 0.411 0.457 0.588
	Jiangxi	0.470 0.438 0.508 0.549 0.657	0.282 0.394 0.446 0.548 0.626
	Shandong	0.542 0.628 0.840 0.948 1.000	0.498 0.564 0.753 0.914 1.000
	Henan	0.404 0.512 0.562 0.539 0.723	0.402 0.359 0.547 0.586 0.757
	Hubei	0.415 0.442 0.511 0.604 0.650	0.447 0.507 0.520 0.478 0.569
	Hunan	0.514 0.545 0.581 0.565 0.660	0.275 0.346 0.449 0.493 0.650
	Guangdong 1.000 1.000 1.000 1.000 1.000	1.000 1.000 1.000 1.000 1.000
	Guangxi	0.309 0.454 0.462 0.473 0.553	0.416 0.361 0.448 0.414 0.532
	Hainan	1.000 1.000 1.000 1.000 1.000	1.000 1.000 1.000 1.000 1.000
	Chongqing 0.263 0.414 0.427 0.555 0.619	0.362 0.240 0.350 0.427 0.540
	Sichuan	0.400 0.472 0.415 0.455 0.602	0.291 0.237 0.386 0.473 0.679
	Guizhou	0.343 0.442 0.490 0.439 0.478	0.399 0.375 0.424 0.364 0.394
	Yunnan	0.536 0.606 1.000 0.664 1.000	0.479 0.563 1.000 0.605 1.000
	Shaanxi	0.499 0.435 0.467 0.492 0.592	0.219 0.331 0.362 0.371 0.449
	Gansu	0.489 0.448 0.528 0.531 0.565	0.210 0.424 0.441 0.460 0.488
	Qinghai	1.000 0.873 1.000 0.849 1.000	1.000 0.919 1.000 0.693 1.000
	Ningxia	0.258 0.363 0.423 0.395 0.617	0.381 0.299 0.327 0.351 0.497
	Xinjiang	0.430 0.346 0.495 0.410 0.555	0.352 0.451 0.419 0.403 0.564
	Average	0.521 0.572 0.682 0.659 0.777	0.478 0.518 0.638 0.617 0.763

Table 5

 5

	Shandong, Henan, Hubei, Hunan, Chongqing, Sichuan, Shaanxi, and Gansu. Two other
	regions improved their industrial overall environmental efficiencies to be efficient and
	then maintained that efficiency, namely Beijing and Shanghai. Two other provinces,
	namely Guangdong and Hainan, were efficient for the whole study period. All the other
	regions' industrial overall environmental efficiencies fluctuated during these years.
	The average value of overall environmental efficiencies of all regions increased
	year by year from 0.499 in 2006 to 0.770 in 2010, which shows that China's industrial

.2 are relative efficiencies which are obtained by comparison with other regions' performances. In this chapter, the overall environmental efficiency measures the efficiency of a whole industrial production process, considering both the first and second stages. The overall environmental efficiency of a region's industry is calculated as the average of the efficiencies of its two stages. The overall environmental efficiencies listed from column 7 to 11 show four kinds of scenarios. 13 regions' overall environmental efficiencies of industry increased year by year, namely Inner Mongolia, Liaoning, Jilin, Fujian, Jiangxi, performance became better during the "11th Five-Year Plan". Similar phenomena can also be seen in the divisional efficiencies in Table

5

.2. Comparing the efficiencies of CHAPTER 5.

Environmental efficiency evaluation of a two-stage 78 system via total-factor energy efficiency two

  stages, we find that the first stage efficiencies were better than the second stage, but the gap decreased. At the end of 2010, the average efficiencies of two stages were at almost the same level. the statistical 0This phenomenon was because Chinese

	government paid more and more attention to environmental pollution. During this
	period, the government enacted many policies for environment protection which
	encouraged green industry and punished polluting enterprises. Examples of such
	policies are the "China National Environmental Protection Plan in the Eleventh Five-
	Years (2006-2010)" and the "Measures for the Administrative Penalties for
	Environmental Protection (2010)".
	In order to analyze the efficiency trends of provinces from a larger scale viewpoint,
	we classify these 30 regions into six administrative areas: North China, Northeast China,
	East China, South Central China, Southwest China, and Northwest China, according to
	the administrative area division of China. The provinces of each area are shown in Table
	5.3.

Table 5 .3

 5 Six administrative areas

	Area	Provinces
	North China	Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia
	Northeast China	Liaoning, Jilin, Heilongjiang
	East China	Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong
	South Central China	Henan, Hubei, Hunan, Guangdong, Guangxi, Hainan
	Southwest China	Chongqing, Sichuan, Guizhou, Yunnan
	Northwest China	Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang
	Based on the area division, we can obtain the total factor energy efficiencies,
	overall environmental efficiencies, efficiencies of stage 1, and efficiencies of stage 2 of
	the six areas during 2006-2010 by averaging all corresponding provincial efficiencies.
	The results are shown in Figure 5.2.

Table 5 .4

 5 Average efficiency of six administrative areas during 2006-2010

		Total factor energy efficiency	Overall environmental efficiency	Efficiency of stage 1	Efficiency of stage 2
	North China	0.8452	0.7026	0.7174	0.6879
	Northeast China	0.6094	0.5435	0.5422	0.5448
	East China	0.7889	0.6936	0.7159	0.6714
	South Central China 0.8189	0.6673	0.6826	0.6519
	Southwest China	0.7500	0.5051	0.5310	0.4792
	Northwest China	0.7362	0.5294	0.5624	0.4964

Environmental efficiency evaluation of a two-stage 80 system via total-factor energy efficiency

  Through Figure5.2 (a), we know that Northeast China's total factor energy efficiencies increased the most, being only 0.345 in 2006 but 0.812 in 2010. The other areas' total factor energy efficiencies were fluctuant with an increasing trend. North China had the largest total factor energy efficiency starting in 2008. Combining the data in Table5.4, we see that North China also had the largest average total factor energy efficiency, followed by South Central China, East China, Southwest China, Northwest China and Northeast China. North China had the best performance because many industrial enterprises there, such as enterprises in Beijing and Tianjin, employed high technology instead of the traditional technology for production. As for the Northwest area, although it has a large amount of natural resources, its average total factor energy efficiency was the lowest, which may be because the local government did not pay enough attention to the technology of energy utilization.

Table 5

 5 , it should reduce its industrial labor force to 82.572 ten thousand employees, its net value of fixed assets to 742.873 billion RMB, and its industrial energy consumption to 9941.777 ten thousand tons of standard coal in the first stage. In addition, it should reduce industrial solid wastes generated, industrial waste gas emitted, industrial waste water discharged to 1744.545 million tons, 15.783 tons, and 26151.07 million tons respectively. In the second stage, it should reduce the industrial labor force to 89.597 ten thousand employees, the net value of fixed assets to 797.413 billion RMB, and its investments in industrial pollution treatment to 80172.528 million RMB. By

				.5 Benchmarks for China's industry
		ILF	IC	IEC	ISWG	IWGE	IWWD	ILF	IC	IIPT
	Beijing	58.382	200.886	6954	1269	5.684	8198	92.866	319.543	19340
	Tianjin	25.217	733.129	6818	1862	21.762	19680	72.523 2108.457 164684
	Hebei	64.432 2093.505	27531	31688	99.418	114232 139.467 4531.512 108588
	Shanxi	82.572	742.873 9941.777 1744.545 15.783 26151.07 89.597	797.413 80172.53
	Inner Mongolia	59.409 3299.688	16820	16996	119.298	39536	20.015 1111.660 132400
	Liaoning	113.473 1025.251 13544.2 2922.899 34.153 63624.26 113.714 1028.993 124530.2
	Jilin	56.150 2608.266	8297	4642	30.064	38656	41.843 1943.682	63366
	Heilongjiang 75.186	863.894 9853.724 4714.134 22.853	38921	75.186 1155.685	49494
	Shanghai	147.556 1306.324	11201	2448	22.148	36696	10.596	93.809	94107
	Jiangsu	243.422 7340.785	25774	9064	100.245 263760 169.858 5122.347 185995
	Zhejiang	143.657 1318.511	16865	4268	65.389	217426 402.567 3694.840 119568
	Anhui	79.927 1384.349 8542.741 2265.759 24.257 61897.79 79.927	940.203	58895
	Fujian	53.963	496.542	9809	2135.6	26.334 55004.01 125.710 1129.996 87267.1
	Jiangxi	59.730 1032.312 6291.003 1929.706 22.432 62606.46 59.730 1391.847 42065.72
	Shandong	48.808 1043.426	34808	16038	138.287 208257 464.957 9940.008 456759
	Henan	163.112 2712.498 17475.43 4734.086 59.950	136763 163.112 2782.342 125120
	Hubei	116.360 1050.719 10545.13 2400.085 28.466 74670.56 110.001 995.362	81824.4
	Hunan	104.675 1171.939 9390.738 2416.616 29.579 82909.01 104.675 1325.357 69105.21
	Guangdong	77.158	719.879	26908	5456	98.909	187031 486.040 4534.710 310584
	Guangxi	53.176	950.303 5782.762 1744.672 19.985 54994.36 53.176 1190.213 38642.68
	Hainan	2.489	27.017	1359	212	2.817	5782	15.161	164.593	4354
	Chongqing	62.960	563.021 6570.865 1352.422 14.078 30830.37 50.484	447.059	50810.5
	Sichuan	122.602 1350.966 12295.81 3107.189 33.172 74944.66 115.704 1852.948	71627
	Guizhou	39.470	349.880 4072.245 568.1118	5.140	8516.107 29.028	253.859 29163.46
	Yunnan	77.827 1148.954	8674	9392	43.955	30926	42.276	624.123	106272
	Shaanxi	69.215	618.611 7918.749 1677.669 16.866 34821.22 61.630	546.276 63052.76
	Gansu	33.281	345.834 3773.662 585.1506	6.618	15352	33.281	314.605 31768.91
	Qinghai	7.249	197.721	2568	1783	13.315	9031	9.807	267.504	9747
	Ningxia	11.527	262.327	2501.79 1253.212	8.693	10575.18 11.527	114.641 14924.62
	Xinjiang	32.282	367.586 3779.761 931.4257 10.001 25375.37 32.282	476.851 25419.72

These benchmarks provide the targets for China's local governments to balance the development of the industrial economic growth with environmental protection so as to achieve overall environmental efficient. For example, if Shanxi province intends to be efficient

  the total values of shared inputs and shared undesirable output and shared desirable output are fully divided into four subsystems. 𝑗 ∈ 𝑃𝑃𝑆 refers to all the DMUs which operate in the production possibility set (or technology set) 𝑃𝑃𝑆.

	Model (6.3) is a non-linear programming model. By substituting 𝜉 𝑔 𝛾 𝑔 𝑝 ,𝜔 𝑖 𝛼 𝑖 𝑝 ,
	and 𝑣 ℎ 𝛽 ℎ 𝑝 by 𝜁 𝑔 𝑝 ,𝑤 𝑖 𝑝 , and 𝑢 ℎ 𝑝 respectively, it can be transformed into the following linear
	model.

  𝐵𝑃𝐺 𝑡 , and 𝑇𝐺𝑅 𝑡 are respectively the level of technical efficiency of a DMU (such as a provincial transportation sector) within Group R, the best practice gap of the observation within Group R, and the technology gap of the observations for the DMU in Group R to the global technology, all at time t[START_REF] Battese | A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies[END_REF][START_REF] Oh | A metafrontier approach for measuring Malmquist productivity index[END_REF].

				t x x y y z t t t G t t t t D x x y y z D x x y y z t I t t t t I t t t t         D x x y y z t t 	t		(6.5)
		t TE TE	t 		t BPG BPG  t		t TGR  t TGR
		EC BPC TGC  
	where 𝑇𝐸 𝑡 ,

  , we thus use the fuel-based carbon calculation

	model based on the conversion factor to estimate provincial transportation CO2
	emissions. Based on the Intergovernmental Panel on Climate Change guidelines for
	National Greenhouse Gas Inventories (IPCC, 2006), CO2 emissions can be estimated
	using the following equation.
	2 CO		1 n   i	i A CCF HE COF i i   		44 12	(6.6)
	Through formula (6.6), CO2 emissions are related to the amount of all
	carbonaceous fuel combusted (A), the carbon content factor (CCF), the heat equivalent
	(HE), and the carbon oxidation factor (COF) of carbonaceous fuel. The constant (44/12)
	represents the ratio of the molecular weight of CO2 (44) to the molecular weight of
	carbon (12). Thus, 𝐶𝐶𝐹 𝑖 × 𝐻𝐸 𝑖 × 𝐶𝑂𝐹 𝑖 ×	44 12	is the CO2 emission factor of a fuel.
	Following the method of Chang et al. (2013), we use the domestic report from the
	Energy Research Institute (ERI) of the National Development and Reform Commission
	(NDRC) (2007) in China to represent the true carbon emission factors. The CO2
	emission factors shown in Table 6.2 reflect several major types of carbonaceous fuels
	in China.

Table 6 .

 6 2 CO2 emission factors by major carbonaceous fuel types in China

	Fuel	Coal	Petrol	Kerosene	Diesel	Fuel Oil	Natural gas
	CCF	27.28	18.9	19.6	20.17	21.09	15.32
	HE	192.14	448	447.5	433.3	401.9	0.384
	COF(%)	92.3	98	98.6	98.2	98.5	99

Table 6 .3

 6 Transformation coefficient to standard coal

	Fuel	Coal	Coke	Petrol	Kerosene Diesel Fuel Oil	Natural gas	Electricity
	Rate 0.7143 0.9714 1.4714	1.4714	1.4571	1.4286	12.143	1.229

Table 6 .4

 6 Distribution of 30 administrative regions in three areas of China

	Area	Administrative regions
	Eastern China	Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu,
		Zhejiang, Fujian, Shandong, Guangdong, Hainan
	Central China	Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan
	Western China	Sichuan, Chongqing, Guizhou, Yunnan, Shaanxi, Gansu,
		Qinghai, Ningxia, Xinjiang, Guangxi, Inner Mongolia

Table 6 .5

 6 The average metafrontier Malmquist-Luenberger index and its decompositions for With the results shown in Table6.5, among the 30 regions, only 6 regions showed a downward trend in the MMLPI. Considering specific regions, Shangdong showed the largest increase in the average MMLPI, while Hainan showed the largest decrease. For the EC index, 6 regions lagged further behind from the frontiers, one region kept unchanged, and the other regions showed increases in the average EC. Considering the three different areas, in Eastern China, Shandong had the highest EC (1.5063), while Hainan had the lowest (0.9587). In Central China, Heilongjiang had the highest EC (1.1068) and Hubei had the lowest (0.9675). In Western China, Inner Mongolia had the highest EC (1.2423) and Qinghai had the lowest (0.9463). This indicates that Shandong, Heilongjiang, and Inner Mongolia had a high catching-up effect in the transportation sector during 2007-2013, which may have been caused by the Chinese government

			each region 2007-2013
		EC	BPC	TGC	MMLPI
	Beijing(E)	0.9840	0.8964	1.0443	0.9211
	Tianjin(E)	1.2496	1.1604	0.9843	1.4272
	Hebei(E)	1.0623	1.1521	1.0050	1.2300
	Liaoning(E)	1.4145	1.0779	1.0008	1.5260
	Shanghai(E)	1.0036	0.8924	1.0497	0.9402
	Jiangsu(E)	1.3125	1.1791	0.9949	1.5396
	Zhejiang(E)	1.1464	0.9188	1.0049	1.0585
	Fujian(E)	0.9991	1.0455	0.9969	1.0413
	Shandong(E)	1.5063	1.2533	0.9692	1.8296
	Guangdong(E)	1.0338	0.8352	1.0241	0.8842
	Hainan(E)	0.9587	0.8037	0.9943	0.7661
	Shanxi(C)	1.0060	0.8522	1.2343	1.0582
	Jilin(C)	1.0200	1.0026	1.1286	1.1540
	Heilongjiang(C)	1.1068	1.0744	1.1240	1.3365
	Anhui(C)	1.0021	1.1054	1.0247	1.1351
	Jiangxi(C)	1.0470	0.9850	1.1017	1.1362
	Henan(C)	1.0534	0.9561	1.0770	1.0847
	Hubei(C)	0.9675	0.8731	1.3248	1.1191
	Hunan(C)	1.0000	0.9106	1.4583	1.3280
	Guangxi(W)	1.0331	1.0280	1.0311	1.0951
	Chongqing(W)	1.0499	0.9677	1.0117	1.0279
	Sichuan(W)	1.0492	0.9642	0.9996	1.0112
	Guizhou(W)	1.0540	1.1693	0.9970	1.2287
	Yunnan(W)	1.0255	1.2486	0.9062	1.1603
	Shaanxi(W)	1.0352	1.0864	1.0140	1.1404
	Gansu(W)	0.9765	0.9805	1.0071	0.9643
	Qinghai(W)	0.9463	1.2816	0.9861	1.1960
	Ningxia(W)	1.1872	1.0624	1.1349	1.4314
	Xinjiang(W)	1.0272	0.9998	0.9659	0.9920
	Inner Mongolia(W)	1.2423	1.0615	0.9640	1.2712
	Note: E, C, and W in parentheses refer to the Eastern, Central, and Western areas
	respectively.

Table 6 .6

 6 Changes in MMPI and its decompositions of China's transportation sector 2007-

	2013

Table 6

 6

	.6 (Continued)
			Western China		China
	Year
		EC	BPC	TGC MMLPI	EC	BPC	TGC MMLPI
	2007-2008	0.7432 1.2888 1.0667 1.1183	0.7096 1.4764 1.0811 1.1480
	2008-2009	1.4137 0.9783 1.0544 1.7396	1.7143 0.7612 1.0164 1.3127
	2009-2010	1.1447 0.9813 1.0060 1.0655	1.0503 1.0318 1.0008 1.0622
	2010-2011	1.0501 1.0469 0.8302 0.9243	1.0260 0.8881 1.1763 0.9521
	2011-2012	0.8525 1.3888 0.9880 1.1354	0.9330 1.1705 0.9919 1.0566
	2012-2013	1.1376 0.7795 1.0642 0.9625	1.0668 0.8368 1.0454 0.9146
	Mean	1.0570 1.0773 1.0016 1.1576	1.0833 1.0275 1.0520 1.0744

  les DEA de base Dans cette section, deux modè les DEA de base, à savoir le modè le CCR et le modè le BCC, sont introduits. En supposant qu'il y ait n DMU évaluées, chaque DMU utilise les mêmes entrées pour produire les mêmes sorties. 𝑋 𝑗 = (𝑥 1𝑗 , … , 𝑥 𝑚𝑗 ) 𝑇 et 𝑌 𝑗 = (𝑦 1𝑗 , … , 𝑦 𝑠𝑗 )

	A.3 Evaluation de l'efficacité environnementale d'un systè me à une seule
	é tape avec paramè tres flous
	3.1 Introduction
	Ces derniè res anné es, avec le dé veloppement rapide de l'é conomie chinoise, la
	Chine est confronté e à une consommation d'é nergie é norme et à de graves problè mes
	de pollution de l'environnement. Parmi tous les types d'é nergie, l'é lectricité est la
	principale source d'é nergie en Chine depuis de nombreuses anné es.
	En outre, parmi les divers modes de production d'é lectricité , la Chine s'appuie
	fortement sur l'é nergie thermique, l'é nergie hydraulique et la thermoé lectricité . En
	particulier, l'é nergie thermique repré sentait environ 74,4% de toute l'é lectricité en 2016.
	Jusqu'à pré sent, de nombreux modè les DEA ont é té proposé s pour traiter les
	ré sultats indé sirables et finalement obtenir l'efficacité environnementale (Fä re et al.,
	1989; Seiford et Zhu, 2002; Zhou et al., 2008). Dans ce chapitre, une nouvelle approche
	utilisant la mesure Russell prenant en compte les extrants indé sirables est proposé e pour
	mesurer l'efficacité environnementale d'une entreprise de production d'é nergie
	thermique.
	3.2 Examen de Russell Measure, de DEA floue et de ré sultats indé sirables
	(1) Mesure Russell
	La mesure Russell a é té introduite pour la premiè re fois par Fä re et Lovell (1978).

𝑇 sont le vecteur d'entr é e et le vecteur de sortie de 𝐷𝑀𝑈 𝑗 , respectivement, o ù T dans le superscript indique Transpos L'efficacité de chaque DMU est le rapport des sorties Cette situation sera maintenue pendant longtemps. Étant donné que la production d'énergie thermique gé nè re gé né ralement un grand nombre de pollutions (rendements indé sirables), mais avec moins de traitement, elle est devenue la principale source de problè mes environnementaux en Chine. Il est donc essentiel pour nous de mesurer l'efficacité des entreprises thermiques afin d'accroî tre leur productivité et de ré duire leurs é missions.

3 Evaluation de l'efficacité environnementale d'un systè me à une seule é tape avec paramè tres flous 123

  Comme nous le savons, les modè les DEA traditionnels supposent que toutes les donné es pour les entré es et les sorties sont pré cises, ils ne peuvent donc pas traiter de donné es impré cises. Pour ré soudre cette situation incertaine, la thé orie des nombres flous est introduite dans la zone DEA. Le concept d'ensemble flou a é té proposé par[START_REF] Zadeh | Fuzzy sets[END_REF] pour traiter des estimations impré cises dans des circonstances incertaines.

	Ces derniè res anné es, de nombreux modè les DEA ont é té dé veloppé s dans les
	environments flours (Kao et Liu 2000a; Kao et Liu 2000b; Leon et al., 2003;
	Lertworasirikul et al., 2001; Wang et Li 2014).
	(3) Sorties indé sirables et efficacité environnementale
	La litté rature dans ce domaine peut ê tre classé e en deux caté gories: les approches
	directes et les approches indirectes. Les approches directes sont principalement basé es

A.

sur

Fä re et al. (1989)

, qui a remplacé l'hypothè se forte des ré sultats en termes de disponibilité par des hypothè ses faiblement disponibles. Ce travail a é té largement dé veloppé (Fä re et al.

  𝑦 𝑟𝑗 (𝑟 = 1, … , 𝑠) ≥ 0 et sorties indé sirables 𝑢 𝑘𝑗 (𝑘 = 1, … , g) ≥ 0 .Notons 𝑥 ̃𝑖𝑗 , 𝑦 ̃𝑟𝑗 et 𝑢 ̃𝑘𝑗 sont les é quivalents flous de 𝑥 𝑖𝑗 , 𝑦 𝑟𝑗 et 𝑢 𝑘𝑗 , respectivement. Le modè le ERM flou permettant de mesurer l'efficacité de 𝐷𝑀𝑈 0 avec des sorties

	indé sirables est le suivant:
		1
	min	1 (	1		)
		1			1
	. .	0	; 1,..., ,
	1
			0	;	1,..., ,
	1
			0	;	1,..., ,
	1
	Bien que l'efficacité environnementale ait déjà été largement appliquée dans de
	nombreux domaines, elle n'est que rarement visible dans les circonstances floues, y
	compris les travaux thé oriques et pratiques. Dans ce chapitre, un modè le de mesure
	Russell amé lioré inté gré est proposé pour é valuer l'efficacité environnementale avec la
	pré sence de sorties indé sirables dans des circonstances floues. Il est ensuite appliqué
	aux entreprises thermiques en Chine.
	3.3 Modé lisation d'un systè me à une é tape avec des sorties indé sirables et des
	nombres flous

Supposons qu'il y a n DMU dans l'ensemble N à é valuer. Pour 𝐷𝑀𝑈 𝑗 (j = 1,2, … , n) , il applique les entré es 𝑥 𝑖𝑗 (𝑖 = 1, … , 𝑚) ≥ 0 , pour produire les sorties souhaitables

4 Évaluation de l'efficacité environnementale d'un systè me à une seule é tape tenant compte de l'amé lioration des performances 129

  Pour mesurer l'efficacité environnementale du systè me d'alimentation en eau dans le bassin de la riviè re Xiangjiang et dé finir la cible d'efficacité la plus proche pour la DMU é valué e, nous proposons dans ce chapitre un nouveau modè le de cible la plus Modè le de RAM cible le plus proche prenant en compte les sorties indé sirables Supposons que n DMU soient évalués. 𝐷𝑀𝑈 𝑗 (𝑗 = 1, … , 𝑛) utilisent chacun m entrées pour produire s sorties souhaitables tout en générant q sorties indésirables. Les notations sont données comme suit. 𝑥 𝑖𝑗 (𝑖 = 1, . . , 𝑚) est la ième entrée de 𝐷𝑀𝑈 𝑗 , 𝑦 𝑟𝑗 (𝑟 = 1, . . , 𝑠) est la troisième sortie souhaitable de 𝐷𝑀𝑈 𝑗 et 𝑧 𝑝𝑗 (𝑝 = 1, . . , 𝑞) est la pth sortie indésirable de 𝐷𝑀𝑈 𝑗 . Sur la base du modè le RAM, nous construisons le modè le cible suivant le plus proche pour mesurer l'efficacité environnementale de la 𝐷𝑀𝑈 𝑜 é valué e.

	proche basé sur la mesure de distance ajusté e (RAM). La RAM est choisie comme modè le de base, car il ne s'agit pas uniquement d'un modè le DEA non radial, elle peut é galement traiter des donné es non positives dans les indicateurs d'entré e et de sortie (Ding et al., 2018). 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 ( ) . . , 1,..., , , 1,..., , , 1,..., , 0, , q m s p i r i p r i p i j ij i i jH j rj r r jH j pj p p jH q m s i ij p ij r rj j i p r s s s Max m p s R R s R s t x s x i m y s y r s z s z p q v x z w y d j H 4.2 0 1 ( i v m q s
	. Cependant, les é tudes pré cé dentes fixaient presque l'objectif "le
	plus é loigné " qu'une unité de gestion soit à mê me d'atteindre l'efficacité tout en
	mesurant l'efficacité environnementale. Ainsi, la ré fé rence (cible) peut ne pas ê tre
	facilement acceptable par la DMU. Ré cemment, certains dé veloppements se
	concentrent sur la recherche de la cible « la plus proche» , de sorte que la DMU en cours
	d'évaluation puisse être efficace avec le «moindre» effort. L'idée sous-jacente de la
	cible la plus proche est que la cible la plus proche suggère des axes d'amélioration pour
	les entrées et les sorties de l'unité inefficace qui amè nera la DMU à ê tre efficace avec
	moins d'effort (Aparicio and Pastor 2014a).

A.

* "2016 Research Fronts". https://clarivate.com.cn/research_fronts_2017/2016research.pdf

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environnementale et fournir des repères aux entreprises d'énergie thermique en Chine, ce qui peut guider les décideurs dans l'élaboration de plans de production appropriés pour améliorer leurs performances. Ensuite, en prenant en compte les résultats indésirables, un nouveau modèle DEA cible plus proche basé sur une mesure de distance ajustée (RAM) est établi pour mesurer la performance environnementale d'un système à une étape. Le modèle proposé est utilisé pour mesurer l'efficacité environnementale des régions du bassin de la rivière Xiangjiang en Chine, et l'objectif le plus proche est défini pour ces régions inefficaces afin qu'elles puissent faire le minimum d'efforts pour atteindre l'efficacité. En outre, nous construisons un nouveau modèle d'analyse de l'enveloppement des données en deux étapes avec des entrées partagées pour analyser l'industrie chinoise, communément considérée comme une «boîte noire» dans les méthodes traditionnelles d'efficacité environnementale. Sur la base de l'analyse théorique du modèle, certaines suggestions de politiques sont données à cette industrie. Enfin, nous examinons le secteur des transports en Chine en le divisant en quatre sous-systèmes principaux: les chemins de fer, les autoroutes, les voies navigables et l'aviation civile, puis nous construisons un modèle d'analyse de l'enveloppement des données de réseau permettant de mesurer les performances du secteur en tenant compte des émissions indésirables de CO2. En outre, compte tenu de l'hétérogénéité des secteurs des transports dans différentes régions de Chine, un nouvel indice de productivité métafrontier Malmquist-Luenberger est proposé, fondé sur le modèle de réseau DEA, qui permet d'enquêter sur la croissance de la productivité des secteurs des transports de

Acknowledgements

I am very glad to have this chance to express my heartful gratitude to those who helped,

i supported, and accompanied me during my PhD study. This work has been carried out between the Logistique et Optimisation des Systè mes Industriels (LOSI) at would like to thank the China Scholarship Council for the financial support during my academic stay in France.

 Model (5.3) is still non-linear since 𝛽 𝑚 𝛼 0 and 𝜑 𝑚 𝛼 0 exist in some constraints. If we fix the value of variable 𝛼 0 , model (5.3) becomes a parametric linear program which can be efficiently solved by the following algorithm.

a. In computation, the initial value for 𝛼 0 will be set as the value 𝐿𝑊 0 , and then its corresponding linear program can be solved. If it is feasible, its corresponding objective optimal value can be obtained.

b. Increase 𝛼 0 by a very small positive number 𝜀 (=0.00001 for example) for each step t, resulting in 𝛼 𝑡 0 = 𝐿𝑊 0 + 𝑡 × 𝜀, 𝑡 = 1, …, until the upper bound of 𝑈𝑃 0 is reached.

For each 𝛼 𝑡 0 , we can obtain a corresponding objective optimal value 𝑒𝑑 0 𝑡 if its corresponding model is feasible.

c. Comparing all the optimal objective values, 𝑒𝑑 0 𝑡 , 𝑡 = 1,2, …, , we can obtain the CHAPTER 6. Environmental efficiency evaluation of a parallel network system considering regional heterogeneity input and multi-output data may have a certain degree of uncertainty, such as just the distribution function, which commonly exists in the environmental issues. Therefore, we will study the environmental performance evaluation with stochastic data by stochastic DEA method and its applications to some real problems.

(2) With the development of internet technology, artificial intelligence, high precision sensors and other technologies, the amount of data in the field of environment greatly increases. These fast-updated, massive environmental big data will bring the new challenge and opportunity to the environmental efficiency evaluation. Currently, the research of environmental management under big data has been widely concerned by scholars. However, in the field of environmental efficiency evaluation, the theoretical research on environmental management under the background of big data is rare. Big data in the field of environmental management provides important information for in-depth analysis of the interaction within the network system, which can be used to solve complex environmental problems. Meanwhile, the internal relationship of the system revealed by the environmental big data puts forward new requirements for the existing performance evaluation methods, thus it is necessary to construct the corresponding interactive network system environment evaluation model. Environmental big data will also greatly increase the complexity of dealing with the corresponding problems. The traditional performance evaluation methods are often inefficient in solving these environmental efficiency evaluation problems because of the large number of DMUs. The future research will study the environmental efficiency evaluation under the circumstance of big data and establish the adaptive environmental efficiency evaluation method in order to solve the more complicated environmental efficiency evaluation problem

(2) The second direction is to consider the stochastic data in the environmental efficiency evaluation. In addition to the existence of fuzzy numbers in the environmental efficiency evaluation of the single-stage system in Chapter 3, the multiinput and multi-output data may have a certain degree of uncertainty, such as just the distribution function, which commonly exists in the environmental issues. Therefore, we will study the environmental performance evaluation with stochastic data by stochastic DEA method and its applications to some real problems.

Appendix of French Abstract Contents