Slacks-based Measure Of Efficiency Research Articles

Maximum slacks-based measure of efficiency in network data envelopment analysis: A case of garment manufacturing

The conventional slacks-based measure (SBM) model is widely applied to measure the relative efficiency of a set of decision making units (DMUs) because the measured efficiency is not affected by weakly efficient frontiers. This model seeks the target point on the production frontier that is farthest to the assessed DMU to calculate efficiency, which requires more effort for the DMU to reach to become efficient. This paper develops a model to calculate the maximum SBM efficiency for general network production systems. Different from the conventional minimum SBM efficiency that is always less than the radial efficiency for inefficient DMUs, the maximum SBM efficiency can be greater than the radial efficiency. The measured efficiency satisfies the monotonicity property. The efficiencies of the component divisions of the network system can also be calculated at the same time. A garment manufacturing company whose major operations comprise cutting and sewing is studied using the developed model. The results show that the average maximum SBM efficiency is 35 % higher than the average minimum SBM efficiency and the sewing operation contributes more to the system efficiency than the cutting operation does.

A SLACKS-BASED MEASURE OF EFFICIENCY IN DATA ENVELOPMENT ANALYSIS TO ASSESS EFFICIENCY OF INDONESIAN SHARIA BANKS

With the development of sharia banks, one of the effects that occurs is the existence of competition among sharia banks. The objective of this study is then to analyze the efficiency of sharia banks in Indonesia. Understanding the efficiency is important because if banks perform consistently with full efficiency, the less inputs they use, the larger output they achieve. The output is measured by total earning asset, while the inputs used are total deposit and total operating costs. A slacks-based measure of efficiency in data envelopment analysis is used to accomplish the objective of the research. Result shows that among twelve sharia banks under-investigated, four of them are considered as the most efficient.

Influence Mechanism of Different Environmental Regulations on Carbon Emission Efficiency.

The rational use of environmental regulation tools has become an important means by which to improve the efficiency of carbon emissions. Different types of environmental regulations and their combinations have different impacts on carbon emission efficiency. In order to determine the environmental regulation configurations that may achieve high carbon emission efficiency or lead to low carbon emission efficiency, we constructed an analytical framework of connections between environmental regulation configurations and carbon emission efficiency. Moreover, 30 Chinese provinces from the period covering 2016 to 2019 were selected as research cases. In addition, the super slacks-based measure of efficiency (SE-SBM) model was applied to evaluate carbon emission efficiency. Finally, the fuzzy-set qualitative comparative analysis (fsQCA) method was employed to analyze the impact of different environmental regulation configurations on carbon emission efficiency. The results showed that the carbon emission efficiency of various regions of China is generally low (with most regions not having reached an effective level) and that there are large regional differences. We found that there are four environmental regulation configurations that can achieve high carbon emission efficiency and two environmental regulation configurations that lead to low carbon emission efficiency. Based on these configurations, we draw three conclusions: (1) There are three paths to achieving high carbon emission efficiency: one that values command-and-control environmental regulation but disfavors market-incentive environmental regulation, another that combines command-and-control environmental regulation with market-incentive environmental regulation, and a third that couples command-and-control environmental regulation with voluntary environmental regulation. (2) Two paths that may lead to low carbon emission efficiency were established: excessive penalties and the lack of specific measures. (3) In some conditions, environmental governance investment and fiscal expenditure could be substituted for each other; environmental protection administrative penalties and pollution charges are synchronized; environmental governance investment in the promotion of carbon emission efficiency is indispensable. Policies and suggestions on how the government can use environmental regulation tools to improve carbon emission efficiency are proposed from a general coordinative perspective in the final section of this paper.

Continuous models combining slacks-based measures of efficiency and super-efficiency

In the framework of data envelopment analysis (DEA), Tone (Eur J Oper Res 130(3):498–509, 2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of the evaluated decision-making units (DMUs) into their efficiency scores, unlike classical radial efficiency models. Next, Tone (Eur J Oper Res 143(1):32–41, 2002) developed the SBM super-efficiency model in order to differentiate and rank efficient DMUs, whose SBM efficiency scores are always 1. However, as pointed out by Chen (Eur J Oper Res 226(2):258–267, 2013), some interpretation problems arise when the so-called super-efficiency projections are weakly efficient, leading to an overestimation of the SBM super-efficiency score. Moreover, this overestimation is closely related to discontinuity issues when implementing SBM super-efficiency in conjunction with SBM efficiency. Chen (Eur J Oper Res 226(2):258–267, 2013) and Chen et al. (Ann Oper Res 278(1):101–121, 2019) treated these problems, but they did not arrive to a fully satisfactory solution. In this paper, we review these papers and propose a new complementary score, called composite SBM, that actually fixes the discontinuity problems by counteracting the overestimation of the SBM super-efficiency score. Moreover, we extend the composite SBM model to different orientations and variable returns to scale, and propose additive versions. Finally, we give examples and state some open problems.

Integrated one-stage models considering undesirable outputs and weighting preference in slacks-based measure of efficiency and superefficiency

In the evaluation scenario with undesirable outputs, the SBM-Undesirable model is usually used together with the SuperSBM-Undesirable model to fully differentiate efficient and inefficient decision-making units (DMUs). The existing SuperSBM-Undesirable model has two main forms, but both have problems in implementation. One form may be infeasible under the variable returns to scale (VRS); Another form has an inappropriate definition for undesirable output efficiency. These two problems are seriously ignored in the existing applications. In this paper, we first propose an improved SuperSBM-Undesirable model with strongly efficient projections, which is feasible under the constant returns to scale (CRS) or VRS technology. Then, by integrating the SBM-Undesirable and the improved SuperSBM-Undesirable models, we focus on proposing a concise, precise and practical one-stage model considering undesirable outputs to differentiate all DMUs and determine their strongly efficient projections simultaneously. The proposed one-stage model only contains essential decision variables and constraints, thereby effectively conserving computational time for large-scale practical applications. Further, by introducing the weighting preference of inputs and outputs, we construct the one-stage model with weighting preference to differentiate the importance of different indicators. Finally, through several data experiments, the superiority of our models in computational results and computational scale are verified.

A fuzzy stochastic slacks-based data envelopment analysis model with application to healthcare efficiency

Performance assessment can play an effective role in providing quality services in healthcare organizations. To develop and compete, hospitals need a performance evaluation system to measure the effectiveness and efficiency of their programs, processes, and workforce. However, hospital data are often uncertain, imprecise, or unknown. In this paper, a fuzzy stochastic data envelopment analysis (DEA) method based on the slacks-based measure of efficiency (SBM) is presented and employed to evaluate the performance of 11 hospitals in an urban setting. Due to the multiplicity of the initially identified criteria, an integrated algorithm based on Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Network Process (ANP) is used to determine the main and effective criteria. The result of the algorithm shows that the criterion “total inpatient visits” is the most important criterion in this evaluation. Finally, the proposed model is implemented based on different levels of significance, and the performance of each unit is determined in uncertain conditions.

Productivity improvement to sustain small-scale fish production in developing countries: The case of Bhutan

Would productivity improvement in small-scale aquaculture “kill two birds with one stone” by simultaneously reducing the tendency to exit production and increasing output? While resource limitations restrict smallholders' involvement in aquaculture, their exit from production is among the factors threatening the sustainability of the aquaculture industry in developing countries. Against this backdrop, the productivity of small-scale aquaculture producers and the ways in which productivity improvement influences their behavior remains insufficiently understood. Based on survey data of 202 fish farmers in Bhutan, this study examined how productivity improvement impacts likelihood of exiting small-scale fish production. Data envelopment analysis was used to compute a slacks-based measure of efficiency as an estimate of productivity. The effect of the resultant estimate of productivity on likelihood of exiting fish production was examined using regression analysis. Results showed that a 10-percentage point increase in productivity among small-scale fish farmers in Bhutan reduced the likelihood of them exiting fish production by 2 percentage points. It is likely that surplus output from productivity improvement and the resultant revenue in the lucrative domestic market motivate Bhutanese farmers to continue fish production. We also found that Bhutan's current aggregate output of farmed fish could be increased by 63% by enabling farmers to produce more efficiently using existing pond sizes and production technologies. Further, it became clear that while subsistence-oriented fish farmers in Bhutan are likely to transition to commercial production, the use of non-cash inputs may be a deterrent. Our findings suggest that productivity improvement has substantial potential to be employed as a policy instrument to reduce the likelihood of farmers exiting small-scale aquaculture and simultaneously increase the aggregate output of farmed fish.

Evolution Characters and Influencing Factors of Regional Eco-Efficiency in a Developing Country: Evidence from Mongolia.

The sandstorm in 2021 in East Asia demonstrated the ecological issues that culminated for decades in Mongolia. Mongolia is facing challenges to realize green and sustainable development. This article aims to increase the understanding of eco-efficiency and its influencing factors in Mongolia and to provide a reference for similar developing countries and regions to achieve green and sustainable development. This article used the Slacks-Based Measure of Efficiency (SBM) model with advantages of dimension freedom and unit variable to estimate the economic efficiency and eco-efficiency of 22 provinces in Mongolia from 2007 to 2016; energy consumption and undesirable environmental outputs were taken as ecological/environmental indicators in the input and output system of regional eco-efficiency in Mongolia, combining traditional indicators of economic efficiency to build Mongolia’s eco-efficiency input–output framework. This article applied hot spot analysis and gravity center analysis to reveal the temporal and spatial evolution characters of eco-efficiency in Mongolia. Finally, the article applied panel Tobit regression to analyze the influencing factors of eco-efficiency. We were found that Mongolia’s eco-efficiency slightly improved from 0.7379 in 2007 to 0.7673 in 2016, lower than the economic efficiency. The high eco-efficiency provinces appeared in the capital Ulaanbaatar and its surrounding areas, showing an obvious spatial spillover effect. The low eco-efficiency provinces were mainly in the undeveloped western region. The relationship between per capita GDP and eco-efficiency was U-shaped and consistent with environmental Kuznets theory. Accelerating economic growth, optimizing population distribution, and improving energy structure and green technology can improve Mongolia’s eco-efficiency.

Assessing the efficiency of the Covid-19 control measures and public health policy in OECD countries from cultural perspectives

PurposeTo identify sources of the success and failure of COVID-19 control measures and develop best-practice public health policy in mitigating the spread of COVID-19, this paper aims to evaluate the efficiency of various combinations of government COVID-19 control measures among OECD countries. This paper also identifies which factors critically influence the efficiency of COVID-19 control measures.Design/methodology/approachThis paper employed two-stage network SBM (slacks-based measure of efficiency) models with variable returns-to-scale and constant returns-to-scale, respectively, among various forms of data envelopment analysis (DEA) models. As a post hoc analysis, the authors used Tobit regression for examining the causal relationship between a nation's cultural dimensions and its COVID-19 control measure's efficiency scores.FindingsThe authors found that the pervasive less individualistic and higher uncertainty avoiding culture positively influenced the efficient control of COVID-19 outbreaks since such a culture helped the government impose its mandatory COVID-19 control measures without people's strong resistance to those measures.Originality/valueMany public health policymakers are wondering why COVID-19 control measures are not effective in coping with the COVID-19 outbreaks. This paper helps the government find the most efficient combination of COVID-19 controls measures for curbing the spread of the stubborn coronavirus. This paper is one of the first attempts to identify pandemic risk mitigation factors from a cultural perspective.

A maximum slacks-based measure of efficiency for closed series production systems

The conventional slacks-based measure (SBM) model measures efficiency based on the target point that is farthest to the decision making unit (DMU) being assessed. The result is that the efficiencies for inefficient DMUs are relatively low, and more effort is required for the DMUs to become efficient. In this research, a model is developed to calculate the SBM efficiency based on the target that is closest to the assessed DMU for a closed series production system, where the outputs of a division are the only inputs for the succeeding division. The efficiency measured from this model satisfies the monotonicity property. It is greater than that measured from the radial model. Since the target is closest to the assessed DMU, less effort is required for inefficient DMUs to become efficient. Furthermore, the efficiency of the system can be decomposed into the product of the efficiencies of the component divisions. The divisions that cause unsatisfactory system performance can thus be detected. Making improvements to these divisions can effectively increase the efficiency of the system. A case of non-life insurance companies in Taiwan with a two-division series structure is studied for illustrative purposes.

Variations on the theme of slacks-based measure of efficiency: Convex hull-based algorithms

Non-radial data envelopment analysis (DEA) models, such as the slacks-based measure (SBM) model, exert an important role in theoretical research and real applications on efficiency evaluation and improvement. However, those models maximize input and output slacks and may therefore find a rather far projection for each inefficient decision-making unit (DMU). This results in varying performance measures and inconveniences in improving the performance of inefficient DMUs. Tone (2016) proposed a new non-oriented SBM-Max model and several algorithms to overcome such limitations. However, those algorithms were computationally expensive and complicated, limiting their applications to different problems.In the present study, algorithms are proposed based on two convex hull algorithms to make a novel variation of (Tone, 2016) that is easily applicable to different problems. The proposal is based on the constant returns-to-scale (CRS) assumption. The algorithms can be further extended based on other assumptions of returns to scale. The used two convex hull algorithms were the Quickhull (Qhull) algorithm and the C++ (ANSI C) implementation of the double description (CDD) algorithm. The proposed algorithms were tested on a dataset from prior literature and a real dataset of Hong Kong hospitals. The results demonstrate that the proposed algorithms are effective for finding a close projection on efficiency evaluation, resulting in improvements in DMUs.

Closest targets in the slacks-based measure of efficiency for production units with multi-period data

The efficiency calculated from the conventional slacks-based measure (SBM) model is the minimum in terms of efficiency scores, and the corresponding target point requires more effort for an inefficient decision making unit (DMU) to become efficient. To find the closest target point to the assessed DMU, several models have been proposed via calculating the maximum efficiency. This paper proposes a set of models to measure the maximum SBM efficiency for DMUs with multi-period data. It is found that, when the non-Archimedean number is not in effective in claculating the radial efficiency, the maximum SBM efficiency is greater than or equal to the radial efficiency. The corresponding target point is easier for an inefficient DMU to reach. This efficiency is more reliable than radial efficiencies because the latter may be affected by the non-Archimedean number. Furthermore, the SBM efficiency can be decomposed into the product of the input and output efficiencies. Under the different-multiplier models, the DMU efficiency can also be decomposed into a weighted average of the individual year efficiencies. The factor and year that cause the unsatisfactory performance can thus be detected. A case of Taiwanese commercial banks is used as an illustration.

Sustainable efficiency and CO2 reduction potential of China’s construction industry: application of a three-stage virtual frontier SBM-DEA model

ABSTRACT In this paper, a new three-stage virtual frontier SBM-DEA (Slacks-Based Measure of Efficiency in Data Envelopment Analysis) model is proposed to evaluate the sustainable efficiency of the construction industry. The relevant construction industry data of 30 Chinese PARs (provincial administrative regions) from 2011 to 2016 are brought into the model to calculate the sustainable efficiency of each administrative region and verify the rationality of the model. In order to solve the problem that the efficiency values of multiple effective decision units cannot be differentiated in traditional DEA model evaluation, the reference decision unit set and the evaluation decision unit set are respectively different sets in the virtual frontier SBM-DEA model. In the three-stage virtual frontier SBM-DEA, the reference decision unit set and evaluation decision unit set are two different sets that can distinguish among the effective decision units of DEA. The analysis results show that the average sustainable efficiency values of the construction industry in eastern, middle and western China exhibit a decreasing trend, at 0.643, 0.586 and 0.4830, respectively. Moreover, the technical equipment rate and external environmental factors play an important role in the sustainable efficiency of the construction industry and the CO2 emission reduction potential of most PARs shows a downward trend.

A modified slacks-based measure of efficiency in data envelopment analysis

The slacks-based measure (SBM) model can divide the set of observations into two mutually exclusive and collectively exhaustive sets: efficient and inefficient. However, it fails to provide more details about efficient DMUs, which reveals the lack of discrimination power in the SBM model. With the aim of addressing this issue, the super SBM (SupSBM) model has been suggested which can rank the SBM-efficient DMUs without providing any useful information about SBM-inefficient DMUs. As a result, in order to fully rank both efficient and inefficient DMUs, one needs to run both SBM and SupSBM models which leads to a significant increase in the number of required computations. This paper tackles this problem and modifies the SBM model which measures SBM-efficiency score for inefficient DMUs and SupSBM-efficiency score for strong efficient DMUs, simultaneously. Finally, a simulation study is presented to illustrate the superiority of our proposed model over the existing models with various problem sizes.

Efficiency data analysis in EU aquaculture production

This paper analyses the operational efficiency of fish farming across EU Member States using a two-stage Data Envelopment Analysis (DEA) approach. In the first stage, a non-oriented Slacks-Based Measure of efficiency (SBM) DEA model is used to compute efficiency scores in marine and freshwater finfish and shellfish aquaculture subsectors for different EU countries during the period 2014–2016. In a second stage, these scores are processed by standard, censored and fractional regression models to test the effects of some exogenous variables. Between 57% and 74% of the observations, depending on the subsector considered, were efficient. The average technical efficiency was 0.918 for freshwater finfish, 0.885 for marine finfish and 0.802 for shellfish. Extending the best practices to the inefficient countries would involve a reduction of feed costs (2.9% - 4.3%), livestock costs (9.0% - 11.8%), energy costs (2.4% - 25.3%), repairing costs (3.7% - 13.8%) and other operating costs (4.3% - 13.8%)at the same time that an improvement in production value totalling 0.03% for freshwater finfish, 2.13% for marine finfish and 0.37% for shellfish. As regards productivity change in the period under study, there has been a productivity regress in the case of freshwater finfish, productivity increase in the case of marine finfish and an initial productivity increase between 2014 and 2015 followed by a slight decrease between 2015 and 2016 in the case of shellfish. Results also indicate that countries specializing in cultivating freshwater and marine populations are more likely to be on the efficient frontier and that technical efficiency seems to be influenced by the size of the country's gross domestic product and capture fisheries.

Decomposition of slacks-based efficiency measures in network data envelopment analysis

One objective of the efficiency measurement of multi-division systems is to find the least efficient divisions such that making improvements to them will increase the efficiency of the system most effectively. To accomplish this task, it is desirable to find the relationship between the system and division efficiencies. This issue has been addressed for the radial efficiency measures. This paper explores the relationship for a non-radial efficiency measure known as the slacks-based measure. The idea is to transform the network system into an equivalent one that is composed of a series of subsystems with parallel structures. Based on the property that the system efficiency is the product of the division efficiencies adjusted by the linkage efficiencies for series systems and is a linear combination of the division efficiencies for parallel systems, the system efficiency can be decomposed into a function of the division and linkage efficiencies. The decomposition of the slacks-based efficiency measure works not only for the technology of constant returns to scale, but also for the case of variable returns to scale. In addition, the proposed model produces suitable efficiency scores for weakly efficient units and for those using weakly efficient units as the target to calculate efficiencies, which makes it possible to obtain reliable rankings for the assessed units.

Application of Multi-Criteria Decision-Making Model and GM (1,1) Theory for Evaluating Efficiency of FDI on Economic Growth: A Case Study in Developing Countries

Foreign direct investment (FDI) and corporate social responsibility (CSR) spending are one of the major factors in improving sustainable economic development of a country. Therefore, this study focuses on the multi criteria application of FDI and sustainability factors (CSR spending) in various developing countries to explore its impact and decision making for sustainable economic growth. The study uses a case study methodology whereby FDI, exchange rate, and CSR expenditure data from 20 countries were used to assess the efficiency in sustainable economic growth. Data were collected from the World Bank for 20 Asian and African developing countries during 2012–2017 and analyzed using GM (1,1), mean absolute percentage error (MAPE), Malmquist productivity index (MPI)-data envelopment analysis (DEA), and the slacks-based measure of efficiency (SBM) model. Correlation analysis is used to find the relationship for FDI, CSR, exchange rate, gross domestic product (GDP), and GDP per capita (GDPPC). The results of the Malmquist productivity index and the frontier effect clearly highlight that a few countries have witnessed a great improvement in terms of productivity and technological progression. Therefore, the decision makers must adopt the model of those countries with respect to sustainable development of the nation. This study helps developing nations as well as researchers to benchmark efficient countries and follow their strategies to develop a new one for utilizing FDI and CSR spending in sustainable economic development. The study also helps policy makers in multi criterion application of FDI and CSR for decision making in economic development.

Measuring Eco-Efficiency of State-Owned Forestry Enterprises in Northeast China

State-owned forestry enterprises (SOFEs) play an important role in the forestry economy in China. Understanding the eco-efficiency of their production is beneficial for the development of sustainable forestry and for achieving Goal 8 of the United Nations’ Sustainable Development Goals (SDGs): Decent Work and Economic Growth. This paper assesses SOFEs’ overall eco-efficiency by analyzing various undesirable outputs using the Slacks-Based Measure of efficiency in Data Envelopment Analysis (SBM-DEA) model. Using basic data from 87 SOFEs in Northeast China from 2003 to 2016, this paper evaluated the eco-efficiency development level and spatial patterns of that region. The results show that SOFEs’ low eco-efficiency was caused by low pure-technical efficiency. Regional differences in eco-efficiency were very significant and became larger, but a market-oriented reform might help to improve such efficiency. The eco-efficiency of SOFEs was in decline from 2003 to 2016 due to the implementation of the Natural Forest Protection Project (NFPP). However, due to a relative lack of production factor inputs, most SOFEs’ scale returns are now increasing. In the future, efforts should be made to promote market-oriented reforms and take the path of large-scale 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.

A classification of slacks-based efficiency measures in network data envelopment analysis with an analysis of the properties possessed

The slacks-based measure (SBM) is a data envelopment analysis (DEA) technique that has been widely used in measuring the efficiency of a system treated as a whole unit. When the internal structure of a system is considered, different ways of modeling the intermediate products that link the component divisions based on the production possibility set (PPS) have been proposed. The types of PPSs can be classified as independent, relational, and cooperative, and the efficiency of the system can be measured from the viewpoint of either outside peers or inside managers for different purposes. This paper shows that models corresponding to the independent type do not properly describe the relationships between the divisions, and are not suitable for measuring the efficiency of network systems. Models corresponding to the relational type may cause a waste of the intermediate products in the system, and are not suitable for internal evaluations, while they are more persuasive for external evaluations. Those corresponding to the cooperative type are appropriate for both external and internal evaluations, and are able to obtain comparable results. An example is used to illustrate the characteristics of the efficiencies measured from the models corresponding to different types of PPSs.