Super Slacks-based Measure Research Articles

A modified slacks-based super-efficiency measure in the presence of negative data

As a non-radial super-efficiency model, Super slacks-based measure (SBM) can rank efficient decision making units (DMUs) while it cannot deal with negative data. This paper proposes an improved Super SBM model and the corresponding improved SBM model under the condition of variable returns to scale, both of which are feasible and allow input-output variables to take negative values. Based on them, a two-stage approach is provided, which has the following advantages in the presence of negative data: compared with radial super-efficiency models capable of dealing with negative data, it can judge the efficiency of DMUs just by the resulting super-efficiency score; it yields a strongly Pareto efficient projection for each DMU; for inefficient DMUs, it provides better target; for efficient DMUs with the super-efficiency score greater than one, it reduces or expands at least one of outputs or inputs to reach the super-efficiency frontier; it is monotonous, units-invariant and translation invariant for both inputs and outputs. The proposed method successfully overcomes the drawbacks of the current super-efficiency models capable of handling negative data and extends Super SBM to the situation where negative data exist.

The influence of market reform on the CO2 emission efficiency of China

In recent years, the constant advancement of market reform in China improves the market allocation efficiency of production factors and further promotes the rapid growth of economic aggregate output in the country. Additionally, the CO2 emitted in China also constantly increases. Based on panel data pertaining to 30 provinces from 1998 to 2015 in China, the CO2 emission efficiency and marketisation level of China were separately measured using a super Slacks-based measure approach and generalised principal component analysis. On this basis, by utilising a dynamic panel regression model and a panel smooth transition regression model, the influence of market reform on CO2 emission efficiency was explored. The results show that the marketisation level exerts a significantly positive effect on CO2 emission efficiency in both models and the results are robust. On the condition of taking energy price as a threshold variable, the influence of process of marketisation is significantly greater than that when taking technological progress as a threshold variable. It implied that although energy price and technological progress both significantly promote the marginal effect of market reform on CO2 emission efficiency, the energy price shows a greater influence than technological progress. Infrastructure construction and urbanisation can inhibit the improvement of CO2 emission efficiency. Additionally, the proportion of secondary industries can delay the improvement of CO2 emission efficiency.

Application in International Market Selection for the Export of Goods: A Case Study in Vietnam

International market selection for conducting exports is based on various trade and economic factors. It is very important to understand how to efficiently trade with another country and to maintain consistency. However, such a consistency is not possible in the case of economics. Therefore, using an efficiency measure helps us to explore and benchmark a country’s exportation businesses. The main goal of this study is to develop an integrated data envelopment analysis (DEA) model to explore the most productive manner through which Vietnam exports goods to other countries. Exploring the most productive export business will help us achieve another goal of this study, which is the selection of international market efficiencies. The variables used for this analysis include the exports, total exports, import tariff, dollar exchange, and the ease of doing business. Based on the data collected from an international organization, on the 15 leading export markets in Vietnam, this study applied integrated DEA, which combines the super slack-based measure (Super SBM) and Malmquist Productivity Index (MPI) analysis to evaluate the export market efficiency. The findings show that for the selection of the export market, the three countries that were the most consistently efficient during 2014–2017 were Malaysia, Singapore, and the United States. This study indicates that the selection of international markets for developing countries should comply with low tariff rates, low exchange rates, and a higher ease of doing business in order to improve the gross domestic product (GDP) and economy of the country.

Technological innovation, environmental regulation, and green total factor efficiency of industrial water resources

The aim of this study based on the panel data of 30 Chinese provinces obtained from 2000 to 2016 was to calculate the green total factor efficiency (GTFE) of industrial water resources by applying the Super-Slack Based Measure (SBM) model of non-expected output, and to analyze the effect of core variables (technological innovation, environmental regulation, and the interaction of these two factors) and control variables (education level, industrial development and the degree of openness) on the GTFE of industrial water resources by making use of Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) model and the dynamic panel system Generalized Method of Moments (GMM). The results show that technological innovation had no significant impact on the GTFE of industrial water resources in China and the eastern region. It had a restraining impact on the central region, while a positive effect on the western region. Environmental regulation was not conducive to the improvement of China's GTFE of industrial water resources, and the promotion of efficiency in the eastern, central, and western regions was not significant. The interaction between technological innovation and environmental regulation positively affected the GTFE of industrial water resources of China, whereas it had a negative impact on the central region and an insignificant impact on the eastern and central regions. This showed that there were regional, economic, and industrial structure differences in the effect of technological innovation and environmental regulation on the GTFE of industrial water resources. In addition, the first-phase lag of GTFE of industrial water resources in China and the central region, the degree of openness of China and eastern, central, and western regions, the education level of central residents, and the industrial development degree of western region effectively improved the GTFE of industrial water resources, whereas the education level of western residents had an inhibitory impact. Therefore, China needs to formulate a differentiated and diversified technological innovation system and environmental protection policy, improve the green research and development investment of industrial enterprises, and form a green development model; at the same time, China needs to guide rational consumption, develop high-tech industries, and adhere to opening up.

Comprehensive Evaluation of Regional Sustainable Development Based on Data Envelopment Analysis

In the light of the shortcomings of the analytic hierarchy process and other common regional sustainable development evaluation methods, this paper proposes the use of a combination of subjective and objective weights to generate input/output indicators using the Data Envelopment Analysis (DEA) method. Using this methodology, we construct a comprehensive evaluation index which is useful in expanding the application of Data Envelopment Analysis (DEA) in the comprehensive evaluation of sustainable development. Moreover, this paper addresses the shortfalls of the traditional DEA evaluation model and uses the Super-Slack Based Measure (SBM)-Undesirable and DEA-Malmquist evaluation models, which are based on traditional DEA model optimization, to analyze the spatio-temporal characteristics of sustainable development on regional scales. Using China’s Yangzte River Economic Belt as an example, an empirical analysis is carried out. We show that analysis results are virtually identical to the extant situation and can objectively reflect the status and abilities of sustainable development in each subregion. Additionally, from the angles of input, output and technological progress, this paper uses the DEA evaluation method to analyze the reasons behind the slow development in several provinces and municipalities along the Yangzte River Economic Belt (YERB). The regional characteristics of each province and city within our study are combined to explore the optimal mechanisms for sustainable development.

Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis

In this paper, we develop an integrated model for slacks-based measure (SBM) simultaneously of both the efficiency and the super-efficiency for decision-making units (DMUs) in data envelopment analysis (DEA). Unlike the traditional solution approaches in which we need to identify the efficient DMUs by the SBM model of Tone (2001) [20] before applying the super SBM model of Tone (2002) [21] for the DMUs to achieve their super-efficiency scores, our integration can obtain the efficiency scores of the inefficient DMUs and the super-efficiency scores of the efficient DMUs by solving simultaneously these two models by an one-stage approach. Therefore, it may save computational time for large-scale practical applications. Due to the non-linearity in the objective function of this integrated model, we develop a linearisation technique to deal with the non-linear model. The numerical experiments, carried out on several examples in the literature and a case study, have demonstrated the accuracy and the computational time effectiveness of our proposed model as compared with the traditional solution approaches.

Investigating the energy efficiencies of European countries with super efficiency model and super SBM approaches

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.

An Integrated Approach for Estimating the Energy Efficiency of Seventeen Countries

Increased energy efficiency is one of the most effective ways to achieve climate change mitigation. This study aims to evaluate the energy efficiency of seventeen countries. The evaluation is based on an integrated method that combines the super slack-based (super SBM) model and the Malmquist productivity index (MPI) to investigate the energy efficiency of seventeen countries during the period of 2010–2015. The results in this study are that the United States, Columbia, Japan, China, and Saudi Arabia perform the best in energy efficiency, whereas Brazil, Russia, Indonesia, and India perform the worst during the entire sample period. The energy efficiency of these countries arrived mainly from technological improvement. The study provides suggestions for the seventeen countries’ government to control the energy consumption and contribute to environmental protection.

An extension on super slacks-based measure DEA approach

In order to break the tie of efficient decision-making units, super-efficiency data envelopment analysis is proposed to fully discriminate them. Recently, a slacks-based version of the super slacks-based measure (S-SBM) is developed and a novel two-stage approach is proposed to calculate both super-efficiency score by the S-SBM model and efficiency score by the slacks-based measure model. In this paper, we extend the approach to consider continuity of efficiency scores. We illustrate the discontinuity of efficiency measure, and define a continuous slacks-based measure which is proved continuous and directly calculated. An interesting efficiency zone category is also provided. In addition, this paper investigates the relationship among the super-efficiency measures of the proposed approach and some existing approaches under variable returns to scale.

An integrated model for slack-based measure of super-efficiency in additive DEA

As a non-radial approach, a super-efficiency model, Super SBM, was proposed by Tone [15] to rank efficient DMUs. Du et al. [7] extends the Super SBM model to the additive (slacks-based) DEA model. To obtain the super-efficiencies of the DMUs, one needs to identify the efficient DMUs first and then apply the additive super-efficiency model to those efficient DMUs. In this paper, we propose an integrated model so that the efficiencies of the inefficient DMUs and the super-efficiencies of the efficient DMUs can be obtained by a single model. The efficiency scores obtained by our integrated model are the same as those obtained by Du et al. [7] and the additive DEA model.

Does international trade improve environmental efficiency? An application of a super slacks-based measure of efficiency

This study analyzes the impact of international trade on environmental efficiency. Using a data envelopment analysis (DEA) model that allows us to treat undesirable outputs and super-efficiency beyond unity, we measure the environmental efficiency of four typical air pollutants—SO2, NOx, particulate matter 10 μm or less in diameter, and CO2—for 98 countries for the period 1970–2008. The resulting environmental efficiency is regressed on income, capital-labor ratio, and trade openness. The panel regression results reveal that trade openness is positively correlated to the environmental efficiency. However, the impact of trade openness on environmental efficiency varies across countries depending on their relative per capita income. The estimated results show that the higher the relative income per capita, the more the benefit of trade on the environmental efficiency.

Is China's e-governance sustainable? Testing Solow IT productivity paradox in China's context

The role of technology in economic development and productivity change has always been an important issue, and it is also a debated topic that whether the ICT (information and communication technology) succeeded in promoting the productivity or not, thus proposing a famous notion of “Solow paradox”. If the ICT could drive the productivity, we could state that the e-governance management of Chinese government is sustainable. By using the SBM and super SBM method, this article measures the regional efficiency and productivity in China, and then conducts an empirical investigation to examine whether the Solow paradox applies in China or not. We found that in recent two decades, the regional disparity of productivity has been widening accompanied with the bigger wealth gap between the east and the central, west regions. ICT may contribute to the widen discrepancy of productivity in part, and the west region has outperformed the central region in both catch up effect and frontier shift, which means that the productivity gap between central and west region has been narrowed. The empirical results also show that the ICT has a negative impact on the regional productivity in China, while for the east region, the negative impact can be basically ignored, while the central and the west region are negatively affected. This result may indicate that with a higher development level, the current period negative impact of ICT on productivity will be lessened and maybe converted to positive impact in the future.

A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach

The current paper proposes a slack-based version of the Super SBM, which is an alternative super-efficiency model for the SBM proposed by Tone. Our two-stage approach provides the same super-efficiency score as that obtained by the Super SBM model when the evaluated DMU is efficient and yields the same efficiency score as that obtained by the SBM model when the evaluated DMU is inefficient. The projection identified by the Super SBM model may not be strongly Pareto efficient; however, the projection identified from our approach is strongly Pareto efficient.

Developing an Output-Oriented Super Slacks-Based Measure Model with an Application to Third-Party Reverse Logistics Providers

Outsourcing is an increasingly significant topic pursued via corporations seeking enhanced efficiency. Third-party reverse logistics involves the employ of external firms to carry out some or all of the firm's logistics activities. Output-oriented super slacks-based measure (SBM) model is one of the models in data envelopment analysis (DEA). In many real-world applications, data are often stochastic. A successful approach to address uncertainty in data is to replace deterministic data via random variables, leading to chance-constrained DEA. In this paper, a chance-constrained output-oriented super SBM model is developed and also its deterministic equivalent, which is a nonlinear program, is derived. Furthermore, it is shown that the deterministic equivalent of the stochastic output-oriented super SBM model can be converted into a quadratic program. In addition, sensitivity analysis of the stochastic output-oriented super SBM model is discussed with respect to changes on parameters. Finally, a numerical example demonstrates the application of the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

Using fuzzy super-efficiency slack-based measure data envelopment analysis to evaluate Taiwan’s commercial bank efficiency

Data envelopment analysis (DEA) mainly utilizes envelopment technology to replace production function in microeconomics. The input and output of decision making units (DMUs) are projected into the attributes to evaluate or measure their performance. However, if the inputs and outputs are linguistically termed or are fuzzy-numbered, conventional DEA can not easily measure the performance. Therefore, we propose the use of a fuzzy super-efficiency slack-based measure DEA to analyze the operational performance of 24 commercial banks facing problems on loan and investment parameters with vague characteristics. After our analysis, we find that the fuzzy slack-based measure of efficiency (Fuzzy SBM)/fuzzy super-efficiency slack-based measure of efficiency (Fuzzy Super SBM) can not only effectively characterize uncertainty, but also have a higher capability to evaluate bank efficiency than the conventional Fuzzy DEA approach.

Efficiency analysis on private universities: the case of Taiwan

Because Taiwan's population of children has decreased and the number of university is too many, all universities in the country are facing fierce competition. This study uses the Super Slacks-based Measure (SBM) model and Malmquist productivity index to evaluate the performance of Taiwan's 20 private universities. Some conclusions are found as follows: (1) If academic research is emphasized in universities, then the efficiency values of them will increase. (2) If a university is far from downtown, then it can set up a continuing and cooperative education center downtown so as to upgrade its average productivity. (3) The universities in Taiwan with high average productivity have high efficiency. (4) A traditional private university in Taiwan will be caught up by newlyestablished private universities if the traditional private university has not made any progress. Under the structure of the World Trade Organization (WTO), all countries will open up their education market in the future, and Taiwan is not an exception. We hope that Taiwan's education experience can provide a reference for all the countries in the world

The analysis of Taiwanese bank efficiency: Incorporating both external environment risk and internal risk

This study adopts a three-stage approach to estimate bank efficiency based on information obtained from 29 banks in Taiwan for the period from 2002 to 2004. In the first stage we employ super SBM (super slacks-based measure) to estimate the scores relating bank efficiency including internal risk. In the second stage a stochastic frontier regression model is then employed to estimate the external environment risk effects. In the third stage we employ the DEA method again to estimate the scores relating bank efficiency including the internal risk and excluding the external risk. Our empirical results from the three-stage approach are summarized as follows: (1) the mean efficiency score of public-owned banks is higher than that in mixed banks and private-owned banks under the first and third stages. (2) The super-efficiency of domestic banks adjusted by three stages of risk is less than that of internal risk adjusted in one stage. (3) External environmental variables do influence the efficiency of the domestic banks. (4) The influence of external environmental adjustment toward the efficiency of the privately-owned banks is largest when comparing mixed and publicly-owned banks.