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This paper presents a novel super efficiency model based on the Andersen-Petersen model, which serves as a bridge between input-oriented and output-oriented models. The proposed model defines a path from the deleted decision-making unit to the efficiency frontier with the shortest step length. Initially formulated as a nonlinear programming model, the developed model is transformed into a multi-objective linear programming model and then further simplified into a linear programming model through variable changes and the application of nonlinear programming solving methods. The feasibility of the proposed path is discussed, and a weighted version of the shortest path model is introduced to incorporate preferences regarding the relative importance of inputs or outputs. Addressing a weakness of the AP methods, the inability to prioritize weights is resolved in the developed model. Real case studies in the context of Iranian education are conducted, and the results of the AP and shortest path analyses are analyzed to validate the proposed method. [ABSTRACT FROM AUTHOR]

This research aims to measure the superior efficiency of protected farms in Anbar Governorate using (Data Envelopment Analysises) for a sample that consisted of 91 farms for the year 2020 for the spring season, as well as clarifying the internal reasons behind achieving superior levels of efficiency. For the indicators of the statistical questionnaire collected from 91 operating protected farms in Anbar Governorate, a set of conclusions were reached, the most important of which are: Low efficiency levels for most of the protected farms due to the waste of resources used for these farms, efficient farms according to the high efficiency index can reduce variable costs A greater percentage than reducing fixed costs, and Fallujah district achieved the highest levels of efficiency and high efficiency, as it averaged efficiency and high efficiency 0.81 and 0.80 respectively, followed by spending his work, and the research reached a set of recommendations, the most important of which are: Provide the necessary environment for it, especially financially, in order to achieve more efficiency in order for its products to compete with the protected farms in neighboring countries, and on the other hand Owners of protected farms in Anbar Governorate are encouraged to reduce the waste in the use of their resources, especially the waste in fixed costs, a large part of which is due to the decrease in the houses on one farm optimum level.

The recent pandemic outbreak and weather-related disasters show that there is no place immune from such emergency events. Thus, it would be essential to provide disaster relief items efficiently through a disaster relief logistics network system (DRLNS). This paper considers a design problem of DRLNS. For this purpose, this study presents a process of combining the multi-objective programming (MOP) model with the three data envelopment analysis (DEA)-based methods. Through a case study, the proposed MOP-DEA design framework would help the decision-makers better evaluate the efficiency of various DRLNS configurations and identify the robust and efficient ones among them.

The recent pandemic outbreak and weather-related disasters show that there is no place immune from such emergency events. Thus, it would be essential to provide disaster relief items efficiently through a disaster relief logistics network system (DRLNS). This paper considers a design problem of DRLNS. For this purpose, this study presents a process of combining the multi-objective programming (MOP) model with the three data envelopment analysis (DEA)-based methods. Through a case study, the proposed MOP-DEA design framework would help the decision-makers better evaluate the efficiency of various DRLNS configurations and identify the robust and efficient ones among them. [ABSTRACT FROM AUTHOR]

China's power sector has received great research attention because of its large energy consumption and CO2 emissions. This study assesses the environmental efficiency and technology inequality of China's power sector from 2008 to 2017. Methodologically, this study proposes a non-radial FDH (free disposable hull) model and a super non-radial FDH model. The non-radial FDH model relaxes the convex assumption and captures all inefficiencies of inputs, desirable output and undesirable output. The super non-radial model is capable of discriminating efficient power sectors and always has feasible solutions. We also compare their performance with the non-radial data envelopment analysis (DEA) model. The main conclusions are summarized as follows: First, the environmental efficiency of China's power sector has experienced steady growth; the power sectors in the east region outperform those in other regions. Second, the proposed FDH models are more applicable and reliable than the non-radial DEA model in efficiency measurement of China's power sector, due to the indivisibility of labor. Third, there has been growing technology inequality and the main driving factor determining technology inequality is the inter-region efficiency Gini coefficient. To improve environmental efficiency and eliminate technology inequality, the government should mainly solve the issue of excessive labor input and establish a free technology market for technology trading. [ABSTRACT FROM AUTHOR]

Copyright of Revista Facultad de Ciencias Economicas: Investigacion y Reflexion is the property of Revista Facultad de Ciencias Economicas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Technology Economics is the property of Chinese Society of Technology Economics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Anbar Journal of Agricultural Sciences is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Medical academic libraries are required to exemplify and quantify the value of their services to their users and parent organizations. Using the Data Envelopment Approach (DEA) technique, this study reports and discusses the efficiency measurement of the 77 academic libraries in Type1 medical sciences universities in Iran. Eleven (11) input and outputs variables were selected to measure the efficiency and performance of the libraries. The selected variables were: Total volumes held, net volumes added during the research period, number of professional staff, and number of supporting staff (service, security, etc.). The total number of full-time students enrollment, full-time instructional faculties, total personal expenditures (professional and supporting staff), area of the libraries, library spaces, computers, and seating capacities. As representative variables of the services libraries provide to their users, we have selected as outputs opening hours per week, the number of registered readers/members (students, faculty, etc.), circulation transactions, and the number of reader visits or attendance. The input-oriented BCC model analyzed libraries' efficiency and benchmarked each inefficient unit by determining and introducing similar efficient units in terms of services and multiple parameters. Out of the 77 libraries analyzed, 30 libraries were efficient, and 47 were ranked as inefficient. By addressing the performance details of each of the introduced units as a benchmark, the finding of this study can help the gatekeeper of these universities to plan and modify their library work plans to improve performance and achieve full efficiency. [ABSTRACT FROM AUTHOR]

The framework for measuring the performance of Islamic banks is related to the concept of efficiency that has been widely implemented. However, there is a deficiency of the DEA model, especially in determining the best ranking of the DMU when there are several DMU units which are equally worth 1. In this study, Islamic banks in Indonesia were used as objects of study. After calculating the super efficiency, then the research will measure the level of influence of each variable on the relative efficiency value through sensitivity analysis. The results showed that, in super efficiency the highest value was owned by BSM bank in 2016 with a relative efficiency value of 1,351, followed by Bank Mega Syariah 2016 with 1,202 and BMI 2016 of 1,175. For sensitivity analysis, the efficiency value of Islamic banks was very sensitive to value output variables, especially operating income variables.

In response to the limitation of classical Data Envelopment Analysis (DEA) models, the super efficiency DEA models, including Andersen and Petersen (Manag Sci 39(10): 1261–1264, 1993)'s model (hereafter called AP model) and Li et al. (Eur J Oper Res 255(3): 884–892, 2016)'s cooperative-game-based model (hereafter called L–L model), have been proposed to rank efficient decision-making units (DMUs). Although both models have been widely applied in practice, there is a paucity of research examining the performance of the two models in ranking efficient DMUs. Consequently, it is unclear how close the rankings obtained by the two models are to the "true" ones. Among the very few studies, Banker et al. (Ann Oper Res 250(1): 21–35, 2017) pointed out that the ranking performance of the AP model is unsatisfactory; Li et al. (Eur J Oper Res 255(3): 884–892, 2016) and Hinojosa et al. (Exp Syst Appl 80(9): 273–283, 2017) demonstrated the L–L model's capability of ranking efficient DMUs without addressing the ranking performance. In this study, we, thus, examine the ranking performance of the two super-efficiency models. In evaluating their performance, we carry out Monte Carlo simulations based on the well-known Cobb–Douglas production function and adopt Kendall rank correlation coefficient. Unlike Banker et al. (Ann Oper Res 250(1): 21–35, 2017), we use the rankings obtained based on the two models and the "true" ones as the basis of performance evaluation in our simulations. Moreover, we consider several types of returns to scale (RS) and study the impact of changes of some parameters on the ranking performance. In view of the importance, we also carry out additional simulations to examine the influence of technical inefficiency on the two models' ranking performance. Based on the simulation results, we conclude: (1) Under different RS, the ranking performance of the two models remains the same when changing parameters, e.g., the distribution of input variables; (2) Under different RS, when technical inefficiency (in comparison with random noise) is more important, the two models have satisfactory performance by providing rankings that are close to, or the same as, the "true" ones; (3) The L–L model has better performance than the AP model and is more robust. This is especially true when technical inefficiency is less important; (4) Under different RS, when technical inefficiency is less important, both models have unsatisfactory ranking performance; and (5) The relative importance of technical inefficiency plays an prominent role in ranking efficient DMUs. [ABSTRACT FROM AUTHOR]

In the professional and competitive sport ranking and rating of players and teams in response to their performance is vital. There is no universal method of ranking which can be applied to all sports. In this study we suggest Data Envelopment Analysis super efficiency technique for ranking of football players in English Premier League 2016/17 season. Performance of 46 forwards and 31 midfielders was evaluated and subsequently ranked who had played a minimum of 1000 minutes and had scored at least 3 goals during the season based on their input and output statistics. According to the CCR DEA model, only twelve players reached the performance of 100%. This means that only 26.086% of the sample reached the efficiency frontier. The average CCR performance of the forward players during the 2016/17 was 0.85%. The results showed that midfielders were more efficient than forwards but strikers were more successful in scoring goals. The use of super efficiency analysis sets out to rank the DMUs which allows an unbiased assessment of player performance. Such an efficiency measuring system would provide useful information to management of football clubs, their coaches and to football players themselves. [ABSTRACT FROM AUTHOR]

We investigate the estimation of high-dimensional normal mean under sparsity. Most shrinkage priors in the literature are based on certain assumptions of sparsity levels and signal sizes. Violation of these assumptions can lead to unsatisfactory estimation. In this paper, we propose a new class of flexible priors, the adaptive normal-hypergeometric-inverted-Beta (ANHIB) priors, which generalize several popular shrinkage priors without requiring prior knowledge of data sparsity levels and signal sizes, and thus can be used as good default priors in a large variety of situations. We show that the ANHIB estimators provide strong suppression to noises and little shrinkage to large signals, and have consistently superior estimation performance under various sparsity levels and signal sizes. [ABSTRACT FROM AUTHOR]

In this paper, the efficiency of the performance of some independent units of police organization was evaluated to optimize the total used inputs and the total produced outputs of each unit. For this purpose, with regard to the efficiency and inefficiency of each unit, based on the location of the units to one another, and also due to the limitations on number and the way of transferring the forces of some units, and using the super effective model, a model was presented to reallocate the inputs of the organization units in order to increase and improve the efficiency of inefficient units and to emphasize maintaining the efficiency of efficient units.

Based on the undesired output super-efficient SBM model, this study measured the urban land green use efficiency of 283 prefecture-level cities and above in China from 2003 to 2017. On this basis, non-parametric kernel density estimation and exploratory spatial data analysis were used to describe and identify the temporal dynamic evolution law and spatial pattern evolution characteristics of urban land green utilization efficiency from the two-dimensional perspective of time and space. The results showed that: ① During the study period, the urban land green use efficiency of China showed an overall upward trend. The average efficiency value increased from 0. 481 in 2003 to 0. 489 in 2017, and the number of effective decision-making units increased from 20 cities to 24 cities. Highly efficient cities and effective decision-making unit cities were mostly located in the eastern coastal areas in 2003 and in the mid-western inland areas in 2017. ② During the study period, the green utilization efficiency of urban land experienced a decline-elevation evolution characteristic, and the urban efficiency difference experienced an evolution characteristic of shrinking-expanding-reducing, and there always existed a two-level differentiation phenomenon. The kernel density curves of the three regions had their own shape and trajectory in position, kurlosis, peak number and tailing, which was the result of superposition of regional characteristics and time period characteristics. ③ During the study period, there was always a significant and positive global spatial autocorrelation of urban land green use efficiency, which evolved from a strong correlation lo a weak correlation. The local spatial pattern was dominated by HH and LL, supplemented by LH and HL, and a spatial neighboring companion effect and a spatial proximity spillover effect existed geographically, forming a spatial pattern of 'urban agglomeration and separation'. Finally, this study suggests that the concept of ' lucid waters and lush mountains are invaluable assets' should be followed to guide the development and utilization of urban land, to build an urban eco-environment community, lo use the space spillover effect between neighboring cities, and to encourage the cities to play a cooperative and coordinating role in the improvement of land green use efficiency. [ABSTRACT FROM AUTHOR]

Sustainable airline operations have become an increasingly important issue in recent years. With this respect, several initiatives for reducing pollutant emissions—such as carbon dioxide (CO2)—in the airline industry are now under consideration by regulators, policymakers, and companies. The impact of these initiatives upon efficiency levels of airline operations is still being analysed by different authors. This article is focused on the efficiency assessment of 13 major Chinese airlines from 2008 to 2015, applying a modified slack‐based measure model to account for CO2 emissions. The impact of contextual variables related to the airline's age, fleet mix, stock market governance, ownership type, network span, and whether or not it has undergone a previous merger and acquisition process is tested by means of a stochastic non‐linear robust regression approach. Findings suggest that sustainability in Chinese airline operations is dependent upon a number of economic factors such as learning curve, economies of scale, technology type, and network management. Policy implications are derived for Chinese airlines. [ABSTRACT FROM AUTHOR]

India is expected to be ranked among the top three healthcare markets in terms of growth by 2020. The scale and scope for delivery of quality healthcare services demand high levels of service performance to provide effective and efficient services to patients. The purpose of this study is to assess the performance efficiency of Indian private hospitals using data envelopment analysis (DEA) and super-efficiency DEA. The analysis uses an output-oriented approach with a mix of four inputs and one output variables to identify the most efficient hospitals. In the first stage, a sample of 25 private hospitals is evaluated using DEA, and in the second stage, the same sample is analysed using super-efficiency DEA for discriminating the performance of the efficient hospitals. The results show seven hospitals as the most efficient ones using DEA in the first stage. Fortis Hospital Ltd emerges as the super-efficient hospital using super-efficiency DEA analysis in the second stage. The results obtained have managerial implications and provide the decision maker (DM) the requisite guidance for corrective actions. [ABSTRACT FROM AUTHOR]

Copyright of OPUS - International Journal of Society Researches is the property of OPUS - International Journal of Society Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

League tables associated with various forms of service activities from schools to hospitals illustrate a public need for ranking institutions by their productive performance. We present a new approach for ranking production units which is based on each unit's marginal contribution in terms of structural efficiency. The approach is radically different from conventional methods based on super-efficiency indexes in Data Envelopment Analysis. We illustrate the mechanics of our method by numerical examples as well as an empirical illustration. We further demonstrate that our new indexes inherit all relevant and desirable properties of the Farrell efficiency index upon which they are constructed. [ABSTRACT FROM AUTHOR]

Turkey has gone through great changes with "Health Transformation Program" and made a substantial transformation. However, much statistical data have been recorded regarding the practices and behavior of hospitals in Turkey since the implementation of health transformation program. While these records pointed to various problems arising from the reforms, a methodological analysis is rarely found. Based on five years of province level health care data, this paper analyzes the productive efficiency of Turkey's health care sector in the post reform period. Efficiency measures are calculated by a nonparametric approach known as data envelopment analysis. Productivity between the years 2011 and 2015 is measured by the Malmquist index. Furthermore, in order to classify the provinces with the assessment value of 1; the super-efficiency model is applied for further sorting. According to the computed Malmquist index, results show that 51 provinces increased their productivity however 30 provinces decreased their productivity in Turkey's health care sector. On the other hand, by the evaluation of the results, it is seen that the level of economic development and the efficiency performance of hospitals could not necessarily act cooperatively. [ABSTRACT FROM AUTHOR]

The scarcity of primary energy sources and depletion of the world's fossil fuel reserves combined with wildly fluctuating energy prices in recent years have posed financial, cyclical, and environmental problems for European countries. These countries have a promising energy sector within the global energy markets, and measuring their technical efficiencies is of great importance. The goal of this study is to find and compare the efficiency scores of European countries and regions for the period of 2011-2015 using super efficiency and super slack-based measure (super SBM) data envelopment analysis (DEA) models. The empirical results revealed that efficiency scores of Eastern Europe, Baltic States, and the European Union-13 (EU-13) have remained lower than the efficiency scores registered for Northern Europe, Western Europe, Southern Europe, Scandinavia, and the European Union-15 (EU-15) for the same period. Besides, Greece, Luxembourg, Norway, and Denmark have been found efficient for the whole period. Additionally, SBM model analyses have shown better results in comparison to super efficiency approach. In conclusion, both the efficiency results and policy recommendations for the European countries and regions would provide valuable contribution to the decision-making processes in terms of energy policies. [ABSTRACT FROM AUTHOR]

Abstract One of the main challenging issues in the conventional data envelopment analysis (DEA) is ranking efficient decision-making units (DMUs) when more than one DMU have the efficiency score equal to one. It must be mentioned that most of the DMUs have internal structures. In this regard, in order to measure the efficiency score of these DMUs, network DEA methods are applied. Most researches are focused on assessing the efficiency of these DMUs and just like the classic DEA, several DMUs are efficient. To identify the sources and estimate the amount of inefficiencies in DMUs with network structure and overcome some shortcomings in the previous ranking models, in this paper, a slack-based network model of super efficiency, considering the optimal value of intermediate measures in the objective function and right handset for ranking overall efficient DMUs, are suggested to have more accurate and comprehensive ranking DMUs with internal structures. Finally, two numerical and empirical examples are provided to verify the discriminative power of the proposed model. [ABSTRACT FROM AUTHOR]

The science of Data Envelopment Analysis (DEA) evaluates the effectiveness of decision making units. But, one of the problems of Data Envelopment Analysis (DEA) is that, if the number of units with the same efficiency equal to one was more than one, then we couldn’t select the best between them. It means that, we can’t rank them. Therefore, the need for ranking these units is considered by the managers. Different methods were proposed in this context. Most of these methods are modeled by DEA models. Due to the variety of ranking methods in DEA, this paper will describe ranking methods which are based on super-efficiency. More precisely, we introduced methods that rank using elimination (removing) of decision making units under the evaluation of observations(set). These methods have some advantages and disadvantages such as, model feasibility or infeasibility, stability or instability, being linear or nonlinear, being radial or non-radial, existence or non- existence of bounded optimal solution in objective function, existence or non- existence of multiple optimal solution, non-extreme efficient units ranking, complexity or simplicity of computational processes, that in this paper, Super Efficiency methods are compared with these eight properties.

This paper analyzes the efficiency of thermal power plants in Angola by means of a two-stage Data Envelopment Analysis (DEA) approach. In the first stage, a novel super-efficiency DEA model for undesirable outputs (CO2 emission levels and discharge of polluted water) is initially used to measure their efficiency levels. Then, in the second stage, relevant cost structure variables frequently used to describe a productive technology are employed as analytical thresholds for assessing energy production performance either in terms of capital or labor-intensity levels. Precisely, bootstrapped regression trees are used to discriminate super-efficiency scores yielding an energy production performance predictive model based on the technology type as proxied by its cost structure and their respective thresholds, since Angolan thermal plants are heterogeneous. Findings suggest that Angolan power plants are old and labor intensive, as some of them date back to the colonial era, and that lack of capital investment should be revised in favor of installing carbon capture devices. The approach developed here consists of a valuable approach for identifying priorities when technologically updating a heterogeneous thermal industry to face pollutant concerns.

Turkey has gone through great changes with "Health Transformation Program" and made a substantial transformation. However, much statistical data have been recorded regarding the practices and behavior of hospitals in Turkey since the implementation of health transformation program. While these records pointed to various problems arising from the reforms, a methodological analysis is rarely found. Based on five years of province level health care data, this paper analyzes the productive efficiency of Turkey's health care sector in the post reform period. Efficiency measures are calculated by a nonparametric approach known as data envelopment analysis. Productivity between the years 2011 and 2015 is measured by the Malmquist index. Furthermore, in order to classify the provinces with the assessment value of 1; the super-efficiency model is applied for further sorting. According to the computed Malmquist index, results show that 51 provinces increased their productivity however 30 provinces decreased their productivity in Turkey's health care sector. On the other hand, by the evaluation of the results, it is seen that the level of economic development and the efficiency performance of hospitals could not necessarily act cooperatively. [ABSTRACT FROM AUTHOR]

The problem of aviation four-station material support has always been the most important task in the air force logistics support, especially in the emergency condition. In order to improve the material supply capacity of the four stations in emergency situation and the efficiency of combat mission and security tasks, a three-echelon supply strategy is proposed. Being different from the traditional single-objective supply scheme, a multi-objective optimization model of four-station equipment supply is constructed to ensure the optimal supply time and satisfaction simultaneously. In order to improve the implementation capacity of the program, the supply time is taken as input and the rate of satisfaction at each point of demand is taken as the output. The SE-DEA model is used to evaluate the Pareto optimal solutions, so as to reduce the size of the alternatives. A numerical example is given to prove if the proposed model is effective and feasible. The example suggests that this strategy can provide decision-maker with effective supply strategy, which is applicable to the supply decision of four station material in emergency situation. [ABSTRACT FROM AUTHOR]

An alternatve approach of super efficiency slack-based measure data envelopment analysis has been proposed to make the projection of an efficient decision making unit strongly-Pareto efficient. The approach however did not examine the simultaneous effect of non-discretionary factors and integer requirements on efficiency measures. To obtain more accurate efficiency measures, this paper proposes a two-stage approach of super efficiency slack-based measure in non-discretionary factors and mixed integer requirements. Both new factors and requirements were first integrated into the existing approach. The optimal solution of the proposed approach was then obtained by transforming its fractional form to a linear form. Thus, the scalar measures of the proposed approach can now deal directly with discretionary mixed integer input saving-output surplus and discretionary mixed integer input excess-output shortfall. The practicability of the proposed approach was tested using empirical data of Malaysian community colleges. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis (DEA) is one of the scientific method that computes the efficiency by using a powerful mathematics basic. Data Envelopment Analysis is a non-parametric technique to evaluate the efficiency of a set of decision making units (DMU) with multi inputs and outputs . since DEA’s models classifies decision making units into two categories of efficient and inefficient, so most of the Decision makers are seeking a full ranking DMUs. In this paper, we will extend a model for ranking of efficient units in DEA. so first we propose two new nonlinear models which one can compute the efficiency by first model and rank the efficient DMUs by second one such that These models have a feasible solution always And at least we will compare models of this paper with the others ranking models by some numerical examples and Results have confirm the model performance.

Data Envelopment Analysis (DEA) is used to examine the Super efficiencies and relative technical efficiency of 15 Co-operative Sugar mills in Tamilnadu using Charnes, Cooper & Rhodes (CCR) model and Banker, Charnes and Cooper (BCC) model. Based on the analysis, the efficient sugar mills are found. For inefficient sugar mills, the degree to which each inputs needs to be reduced for optimum output is derived using Benchmarking. Super efficiency analysis indicates that Kallakurichi-II sugar mill dominates the sugar mills under study with a super-efficiency score equal to 1.5471. Cheyyar, Dharmapuri, Subramania Siva and Kallakurichi- I sugar mills occupy second, third, fourth and fifth place respectively. [ABSTRACT FROM AUTHOR]

Environmental efficiency (EE) assessment is an efficient way to evaluate the degree of coordination between economy and environment. Most of the studies measured country- or region-level EEs, while the EE disparities among cities were not well investigated. By incorporating the socioeconomic and remote sensing data, this study measured the static and dynamic EEs of 11 provinces and 131 cities in the Yangtze River Economic Zone (YREZ) in China based on a super efficiency data envelopment analysis (SEDEA) and Malmquist index (MI) methods during 2003–2014. The influential factors of EE imbalance in the YREZ area were explored by the panel tobit model. Results show that large gaps exist in city's environmental efficiency. Cities in the Yangtze River Delta (YRD) show higher EEs than that in the Chengyu Urban Agglomeration (CUA) and Urban Agglomeration in the Middle Reaches of the Yangtze River (UAMR) areas. 15 cities have an EE below 0.2 and only 2 cities above 1 in 2014. The overall average EE exhibited a declining trend during 2003–2014. The number of cities below the average environmental efficiency increased from 70 (53.4%) to 83 (63.4%) over the time period studied. The MI results indicate that management and scale optimization level is the main factor hindering total factor productivity (TFP) growth. The tobit experiment reveals that GDP per capita played a negative impact on EE for most of the YREZ area during 2003–2014. The degree of opening up and industrial structure acted positively on city's environmental efficiency. These conclusions may be a helpful reference for decision makers to coordinate the economy and environment in the YREZ area. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of four dual problems of a primal vector optimization problem involving nearly subconvexlike set-valued mappings. For each dual problem, a strong duality theorem with super efficiency is established. The strong duality result can be expressed as follows: starting from a super minimizer of the primal problem, a super maximizer of the dual problem can be constructed such that the corresponding objective values of both problems are equal. The results improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]