Super-efficiency Approach Research Articles

A two-stage improved Base Point Slacks-Based Measure of super-efficiency for negative data handling

For most of the Slacks-Based Measure (SBM)-type models in Data Envelopment Analysis, the variable returns-to-scale (VRS) condition is required to become feasible and translation invariant while applied on negative data. Unlike them, the “Base Point SBM (BP-SBM)” and “Super BP-SBM” models accept negative values under four returns-to-scale (RTS) conditions; however, (i) they are not translation invariant, (ii) they are sensitive to some perturbation terms which help to translate negative data to positive data by avoiding division-by-zero irrationality, and (iii) the Super BP-SBM model suffers from infeasibility issue. To address the above limitations, this study improves the existing BP-SBM and Super BP-SBM models. The Improved BP-SBM (IBP-SBM) and Improved Super BP-SBM (ISBP-SBM) models are translation invariant under four different RTS conditions, and do not involve any perturbation terms. Although the proposed ISBP-SBM model is feasible under the four RTS conditions, it fails to provide Pareto efficient projections. Therefore, we propose a two-stage super-efficiency approach, where the ISBP-SBM model is applied on the first stage to obtain the input savings and output surpluses, which are incorporated in the IBP-SBM model to be applied on the second stage. To validate the proposed models, their results are compared with some state-of-the-art models using a benchmark dataset. Experimental findings indicate that the proposed models have overcome the limitations of the existing models while applied on negative data. Further, three real-life case studies of supplier selection, financial performance evaluation, and airline performance evaluation are used to discuss the applicability of the proposed approach.

Performance Evaluation of Utility Exchange-Traded Funds: A Super-Efficiency Approach

Choosing funds is a general issue for investors, with the aim of balancing potential risks and returns. The aim of this article is to use a super-efficiency approach to analyze and rank exchange-traded funds (ETFs) in order to find the best utility ETFs. The range-adjusted measure (RAM)-based data envelopment analysis (DEA) model is used in this work to evaluate a set of utility ETFs and rank inefficient funds, while the super-efficiency RAM model is used to fully rank RAM-based efficient funds. Other slack-based selected DEA models are also used to analyze the ETFs. The results show that the suggested approach delivers the same efficient funds as other slack-based selected DEA models; hence, it appears to be useful as a fund selection tool.

Random Forests and the measurement of super-efficiency in the context of Free Disposal Hull

In the technical efficiency evaluation area, it may happen that many observations obtain a similar relative technical efficiency status, making it difficult to discriminate between them. The determination of super-efficiency has been a way of solving this problem by providing a method to differentiate between the performance of observations. Despite the existence of some approaches dealing with the notion of super-efficiency in the literature, there have been few attempts to address this problem from the standpoint of machine learning techniques. In this paper, we fill this gap by adapting Random Forest to determine super-efficiency in the context of the Free Disposal Hull (FDH) technique. The new super-efficiency approach is robust to resampling on inputs and data. Additionally, we show how the new approach could be a possible solution for dealing with the curse of dimensionality problem; typically associated with FDH. Furthermore, exploiting the adaptation of Random Forest, a new method for assessing the importance of input variables is introduced. Finally, the advantages of the proposed approach are illustrated through a real example.

A Novel Decision Support System Based on Fuzzy Multi Criteria Decision Making for Optimizing Machining Parameters

The aim of this study is to develop a novel decision support system, which has never been developed yet, in order to optimize machining parameters. We combine the three distinct methods: experimental design and analysis, fuzzy data envelopment analysis (DEA) and fuzzy analytical hierarchy process (AHP). Firstly, a full factorial experiment including four factors and three levels is carried out. We take into account cutting speed, feed rate, depth of cut and number of cutting tool inserts as factors. The following three outputs are selected: Material Removal Rate, Machining Time and Surface Roughness. Secondly, a total of 23 experiments are determined as efficient decision-making units using fuzzy DEA with super efficiency method. Finally, a fuzzy AHP approach is conducted to rank the efficient experiments among each other. In conclusion, the results show that the Fuzzy DEA-Fuzzy AHP and the Fuzzy DEA with Super Efficiency generate clearly different rankings of experiments and Fuzzy DEA-Fuzzy AHP Approach has outperformed Fuzzy DEA with Super Efficiency Approach. The results highlight the importance of taking into account the expert opinions in the decision-making processes.

Efficiency Analysis of Malaysian General Insurance Companies Using Data Envelopment and Super-efficiency Approach

Due to the phenomenal growth of the insurance sector, extensive research has been conducted to evaluate the insurers' efficiency at both domestic and international levels. Thus, this paper illustrates the applications of Data Envelopment Analysis (DEA) to measure the relative efficiency of 18 general insurance companies that were operating in Malaysia in the year 2018. The inputs included in this study are fees, commission, and management expenses while the outputs are net premium and generated investment income. The results reveal that the four general insurance companies can be identified as efficient units. The standard DEA method cannot discriminate efficient units. This study employs the super-efficiency DEA model to select the most efficient unit among them. This study makes a significant contribution to the financial industry especially for matters concerning insurance, as there is a lack of studies on exclusive efficiency analysis of general insurance companies in Malaysia. In addition, it has major implications for insurance decision makers, government agencies and emerging insurance markets. The information obtained from this study will benefit the insurance company’s top management in devising viable strategies to enhance the efficiency of the company.

Efficiency Analysis of Malaysian General Insurance Companies Using Data Envelopment and Super-efficiency Approach

Efficiency Analysis of Malaysian General Insurance Companies Using Data Envelopment and Super-efficiency Approach

A Distance-Based AHP-DEA Super-Efficiency Approach for Selecting an Electric Bike Sharing System Provider: One Step Closer to Sustainability and a Win–Win Effect for All Target Groups

Existing research on electric bike sharing systems (e-BSS) emphasises the importance of the sustainability of the systems and the need to respect the views of all stakeholders when planning e-BSS. However, this research overlooks the fact that the sustainability of e-BSS depends to a large extent on the skills and knowledge of the parties who select an electric bike provider, which in most cases is the investor in the e-BSS. There is no previous paper that provides support for investors in (1) defining a set of criteria for selecting a provider that takes into account all of the three domains of sustainability (economic, social, and environmental) and (2) developing a tool that best meets sustainability standards on the one hand and the needs and requirements of all stakeholders (including e-bike users and investors) on the other hand. A distance-based analytic hierarchy process/data envelopment analysis (AHP-DEA) super-efficiency approach was proposed and applied to adapt DEA to the needs of predefined groups by using slack variables. The approach takes into account the fact that not all outputs have a positive impact on the final outcome; the approach also allows decision-makers to define the hierarchical structure of the importance of the criteria directly based on the responses of the selected group. A case study in Slovenia illustrated the application of the approach.

Identifying production units with outstanding performance

In many applications of data envelopment analysis, there are situations in which a central body manages a large set of similar units delivering some services. In such multi-unit organizations, the central management desires a mechanism by which the local management of each unit is incentivized to perform towards the improvement of the performance of the organization as a whole. In a recent paper, Afsharian et al. (2017) have proposed a system of incentives under these circumstances. In their approach, – which relies on the original concept of super-efficiency – units with outstanding performance are identified and incentivized by some reward compatible with the level of their impact on the overall performance of the organization. We discuss why the conventional super-efficiency approach may not be optimal in such situations. We revisit the definition of the collective impact and propose a new method, which can identify – in a controlled manner – a subset of k outstanding DMUs among n existing units in the system. The proposed approach is illustrated using data from a German retail bank.

An analysis of the energy production efficiency of countries

ABSTRACT Since energy resources are nonrenewable and may lead to dependence on other countries in time, any country needs to ensure efficient energy production and consumption by taking into account issues such as environmental impacts and climate change. In the light of this, the aim of this study was to analyze the energy production efficiency of 35 countries around the world and to come up with recommendations to determine their positions among other countries and to take required precautions for the future. As the first step in the analysis, each country’s efficiency was obtained by using Data Envelopment Analysis (DEA), and then Super-Efficiency approach was used to rank the efficient countries.

A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system

Conventional data envelopment analysis (DEA) may generate the non-integer targets for integer-valued inputs and outputs of decision-making units (DMUs). To derive the convincing projections, integer-valued DEA has attracted much attention. Given the integrality restriction, Du et al. (Eur J Oper Res 218(1):186–192, 2012) proposed the super-efficiency approach consisting of additive integer-valued and additive super-efficiency integer-valued models for the differentiation of efficient DMUs, thereby raising the discriminatory power. This paper extends their approach to develop a simpler but stricter version, which we refer to as the unified additive super-efficiency model. The newly-developed model has three advantages. First, the slacks of input excess, input saving, output shortage and output surplus can be directly computed in a single program to obtain the efficiencies of inefficient DMUs and super-efficiencies of efficient DMUs. Secondly, it suggests the strongly Pareto-efficient projections for efficient DMUs. Finally, the identified super-efficiencies allow for the property of continuity. A comparison of the proposed model, with Du et al.’s (2012) and standard additive super-efficiency approaches is discussed using a numerical example. In addition, the applicability of the proposed model is illustrated by a data set covering 13 bus companies operating in the municipal bus system of Taichung. Our work not only provides managerial insights into the primary sources of inefficiency and super-efficiency but also contributes to the current understanding of how super-efficiency would be effectively and accurately measured in the presence of integer-valued data.

Efficiency of banks in Malaysia: A super efficiency approach

The stability of the economic system of a country very much depends on its banking industry. Data Envelopment Analysis (DEA) has been applied widely for measuring efficiency of banks. Limited studies, however, have employed the radial and non-radial DEA models to evaluate efficiency of banks without considering the ranking of the fully efficient banks since those banks have the same efficiency score. Considering the weakness of the radial and non-radial DEA, this paper aims to calculate the banks efficiency of nine commercial banks in Malaysia from 2004 to 2013 by adopting the two-stage of super efficiency slack-based measure (SE-SBM) model. This model can discriminate between the efficient banks and recalculate their efficiency scores. Then, the selected banks were able to be ranked according to their final efficiency scores. Moreover, comparative analyses of the efficiency of the banks and the year-wise efficiency of the selected banks were also conducted. The methodology consists of two stages. In the first stage the SBM model is run to classify efficient and inefficient banks. In the second stage the super efficiency model is run to rank the efficient banks obtained from the first stage by calculating their super efficiency scores. Our empirical results show that: (1) the efficiency status of the banks fluctuated over the examined period, the high number of the efficient banks is achieved in the years 2006 and 2008, while the year 2012 has the lowest number of the efficient banks. (2) the ranking of the banks fluctuated in the studied period. (3) most of the banks are inefficient in terms of their average efficiency scores. This paper has two limitations. First, the paper did not integrate undesirable output, despite it deals with non-interest income. Second, performance evaluation of Malaysian commercial banks was only compared among the Malaysian banks.

Ranking Chinese commercial banks based on their expected impact on structural efficiency

This paper examines the performance of 16 major Chinese commercial banks. In particular, we employ a new way of ranking the banks based on their average marginal impact on structural efficiency. We find important differences between our ranking results and that of the conventional super-efficiency approach. We argue that in case of Chinese commercial banks the new way of ranking the banks is more in line with expectations based on various key performance indicators. The findings further reconfirm that the performance of the large commercial banks surpass that of the small to medium sized commercial banks.

Measuring the efficiency of community colleges using super efficiency approach for the case of non-discretionary factors in data envelopment analysis with sensitivity analysis

Measuring the efficiency of community colleges using super efficiency approach for the case of non-discretionary factors in data envelopment analysis with sensitivity analysis

Measuring the Efficiency of Community Colleges Using Super Efficiency Approach for the Case of Non-discretionary Factors in Data Envelopment Analysis with Sensitivity Analysis

Malaysian community colleges play a significant role in achieving Malaysia's vision to be a developed country in 2020. For this reason, their efficiency should appropriately be measured. However, their efficiency measurement using a conventional data envelopment analysis (DEA) model is not appropriate since some of their inputs; e.g., entrant and enrolment students are non-discretionary while a part of output of their graduate employability is discretionary. This paper thus proposes an alternative approach of super efficiency slack-based measure for the case of non-discretionary factors in DEA. The proposed approach was used to evaluate the efficiency of 25 main campuses of Malaysian community colleges from 2012 to 2013. The results support the decision maker of Malaysian community colleges to discriminate and rank efficient and inefficient community colleges in the presence of both super efficiency and non-discretionary factors. The significance of inputs-outputs on efficiency status was tested by sensitivity analysis.

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 additive super-efficiency DEA approach to measuring regional environmental performance in China

ABSTRACTIt is one of the issues of current concern for international research engaged in data envelopment analysis (DEA) that how to achieve more accurate results of environmental and energy efficiency evaluation. Past studies about the application of DEA to environmental performance measurement often follow the concept of undesirable factors. In the context, slacks-based measure of super-efficiency, a non-radial super-efficiency model compared to the traditional radial super-efficiency DEA models, offers a remarkable alternative, largely due to their ability to deal with ranking the performance of efficient decision-making units (DMUs). This paper extends super-efficiency approach to the additive super-efficiency DEA approach with undesirable outputs to measuring environmental performance. Unlike the traditional radial super-efficiency DEA suffering from infeasibility, the additive super-efficiency models in the context of undesirable factors are always feasible. A case study of regional environmental performance in China is also presented by applying the proposed the additive super-efficiency DEA approach. The results show that the environmental efficiency scores of inefficient provinces were slightly lowered in China, and identified regions where these provinces have the capacity to develop without damaging overall performance.

A new super-efficiency dual-role FDH procedure: an application in dairy cold chain for vehicle selection

Cold chain management (CCM) is a system in which perishable products are managed. For the success of transportation system of CCM, optimal selection of vehicle is a significant subject. Data envelopment analysis (DEA) can be used for vehicle selection problems. However, in this particular area, conventional DEA models are faced with difficulties. The problem are: 1) dual-role factors which classical DEA models cannot deal with them; 2) comparing decision making units (DMUs) with virtual DMUs (not with actual DMUs); 3) tie between DMUs (i.e., many DMUs are recognised efficient; 4) infeasibility of DEA ranking model for certain data. In this paper, a new procedure is developed to rectify the mentioned shortcomings. The proposed procedure, which utilises free disposal hull (FDH) technology, is a super-efficiency approach to provide a full ranking of efficient DMUs in the presence of dual-role factors. A case study illustrates application of the proposed procedure.

Nonparametric measures of returns to scale: an application to German water supply

The evaluation of market structures and the quantification of returns to scale in network industries usually are of high interest for researchers and policy makers. Regarding the debate on optimal market structures in German potable water supply, we use a cross-sectional sample of 364 German water utilities observed in 2006 to derive a nonparametric measure of scale elasticity for the water industry. The data sample is validated by applying a super-efficiency approach and a statistical testing procedure for outlier detection. Besides using a standard data envelopment analysis approach, a conditional efficiency approach is applied to account for the water utilities’ operating environments. The results indicate non-decreasing returns to scale for the majority of water utilities and constant or non-increasing returns for larger utilities. Optimal firm size is found to be generally larger than the current sample median firm size. Efficiency improvements could be realized by increases in firm sizes and through a consolidation of the industry.

A NEW RANKING APPROACH WITH A MODIFIED CROSS EVALUATION MATRIX

Cross evaluation matrix was suggested to resolve a ranking problem in the data envelopment analysis (DEA) context. The cross evaluation matrix is composed of simple efficiency and cross-efficiency (CE) values of decision making units (DMUs). However, simple efficiency cannot discriminate efficient DMUs because of the nature of basic DEA models. To make complete use of the efficiency information of DMUs, a modified cross evaluation matrix is proposed. The modified matrix consists of super-efficiency (SE) values for diagonal elements and CE values for nondiagonal elements. As the efficiency values are not limited to "1" in SE approach, the proposed matrix can explain the difference of efficiency of efficient DMUs. The proposed matrix can be more accurate than the original cross evaluation matrix. Consequently, the rank order of DMUs generated by the suggested matrix reflects differences in relative efficiency of DMUs. A numerical example is given to show the superiority of the proposed approach. This is done by comparing with other available ranking methods in the DEA context. Several distance measures are utilized to compare rank consistency of the ranking methods. Finally, a case study is presented to explain how our approach is applied to real ranking problems.

Ranking non-extreme efficient units based on super efficiency method in the presence of undesirable outputs: a DEA approach

Data envelopment analysis (DEA) is a non-parametric method for analysing the performance of a set of decision-making units (DMUs). Computing the efficiency scores and ranking each organisation are two important parts of analysing performance. A large number of DEA models have been proposed for ranking DMUs, but most of them are unable to rank non-extreme efficient units. In this paper, a method is proposed based on super efficiency approach for ranking all DMUs, including extreme efficient, non-extreme efficient and inefficient units. Then, the suggested method is applied for ranking DMUs in which undesirable outputs are also produced in the production process. Finally, numerical examples are provided to illustrate the proposed approach.