Radial Data Envelopment Analysis Models Research Articles

Evaluation of undergraduate academic programs through data envelopment analysis and time-to-degree estimates at Spanish public universities

This article proposes nonparametric and parametric methods for conducting meaningful evaluations of academic programs. In particular, it proposes the use of data envelopment analysis (DEA) along with regression analysis for the evaluation of Spanish public universities' undergraduate curricula. Unlike the radial DEA models, which assume an equiproportional expansion of all outputs to achieve efficiency, the current study also relies on the use of non-radial DEA models for assessing the efficiency of Spanish public universities. A non-radial DEA measure (the so-called Russell measure) allows for unlike proportional augmentations in each positive output. In this study, non-radial DEA measures allow us to identify different levels of inefficiency for each output considered (social sciences and non-social sciences degrees). Specifically, the results show that the inefficiency in the production of scientific and technical degrees is greater than that in the production of humanities and social sciences degrees, although there are differences among institutions. Bachelor's degree production time is also estimated, and a duration analysis explains the time to degree. A worrying result is the "excessive" time it takes for a university to produce four-year undergraduate degree programs. The mean graduation time is 5.7 years. The Cox proportional hazards regression shows that a shorter time to graduation is associated with higher teaching quality as well as a higher faculty-to-student ratio. Parametric survival analysis using a lognormal distribution with gamma frailty also verifies these latter results.

Integrating group frontier and metafrontier directional distance functions to evaluate the efficiency of production units

Over the last decade, many studies have adopted the data envelopment analysis (DEA)-type metafrontier framework to relax the constraint of technological heterogeneity. In conventional metafrontier analyzes, either radial or nonradial DEA models are used in two separate DEA efficiency analyzes. The results of a metafrontier analysis may be biased if this approach is adopted in a nonradial DEA model. One possible problem is that the value of the technology gap ratio is greater than one because the technology gaps to be estimated for decision-making units (DMUs) under different technology groups relative to the metatechnology have no connection between group frontiers and metafrontiers. Furthermore, the direction of projection of each DMU onto the metafrontier is totally independent of the direction to the efficiency frontier of the respective group frontier. Our proposed integration of group technology and metatechnology constraints into a union model offers a possible solution to the existing metafrontier problem and provides more robust metafrontier results regardless of whether radial or nonradial DEA models are used. Four numerical examples and one empirical application are demonstrated, and the results appear to support the use of our proposed model.

Eco-efficiency and Eco-productivity assessments of the states in the United States: A two-stage Non-parametric analysis

This study implements radial and non-radial Data Envelopment Analysis (DEA) models to assess eco-efficiency and eco-productivity of the 50 states in the United States in 2018. The models are based on three inputs (capital stock, employment, and energy consumption), a single desirable output (real gross domestic product) and a single undesirable output variable (CO2 emissions). The radial DEA models reveal that at least 32 states are operated efficiently. Five states perform at the most optimal scale size, whereas 17 states have considerable potential to boost their productive efficiencies by enlarging available resources, and 28 states are overinvested in their input variables given their current output levels. The non-radial DEA models show that, overall, the states’ capital efficiency is very high, whereas energy and emission efficiencies are very low. The states’ eco-productivity is relatively higher than the eco-efficiency levels. In the second stage of the analysis, non-parametric statistical tests and Tobit regressions are conducted for further investigation. According to the non-parametric statistical test, high capital stock, labor force, and energy usage do not affect the states’ productive efficiency. However, states with low carbon dioxide emissions have significantly higher eco-efficiency and eco-productivity levels. The Tobit regression results illustrate that nuclear power and renewable energy consumption significantly affect the states’ relative efficiencies.

Improving information reliability of non-radial value efficiency analysis: An additive slacks based measure approach

The value efficiency approach is one possible way of incorporating information preferences into performance analysis of Decision-Making Units (DMUs). In this paper, we propose a novel geometric interpretation of value efficiency while plugging it into radial and non-radial DEA (Data Envelopment Analysis) models under the assumption of variable returns to scale. In addition, this novel geometric interpretation of value efficiency is extended to Additive Slacks-Based Measure (ASBM) modeling. This is achieved by linearization of non-radial DEA models using multi-objective programming. Performance of such proposed approaches in terms of reliability and discriminatory power are compared through a case study involving Finish bank branches. Research implications are then derived and conclusions are drawn.

A Review of Data Envelopment Analysis in Airline Efficiency: State of the Art and Prospects

The rapid development of the aviation industry has brought about the deterioration of the climate, which makes airline efficiency become a hot issue of social concern. As an important nonparametric method, Data Envelopment Analysis (DEA), has been widely applied in efficiency evaluation. This paper examines 130 papers published in the period of 1993–2020 to summarize the literature involving the special application of DEA models in airline efficiency. The paper begins with an overall review of the existing literature, and then the radial DEA, nonradial DEA, network DEA, dynamic DEA, and DEA models with undesirable outputs applied in airline efficiency are introduced. The main advantages and disadvantages of the above models are summarized, and the drivers of airline efficiency are analyzed. Finally, the literature review ends up with future research directions and conclusions.

Being a state-owned bank is not a fatality: an Algerian case study

The Algerian banking industry is clearly dominated by the six state-owned banks (SOBs) which represent more than 85% of total banking asset. While it is widely admitted that public ownership in developing countries is often correlated with inefficiency and waste of resources, performance management in SOBs branches is mostly operated using basic accounting ratios. The data envelopment analysis (DEA) is a more sophisticated approach which if designed properly may enhance significantly SOBs branches' performance by creating the competitive pressure that is generally unattainable in public sectors. This research demonstrates all the potential of the DEA technique as a comparative performance measure in enhancing the efficiency of public bank branches. To that aim, the radial and super-efficiency DEA models are conjointly applied.

Chinese liquor company management efficiency from a social responsibility perspective: a two stage dynamic directional distance function

Because the liquor industry is an important industry in China, alcohol companies have greater social responsibilities when upgrading their production processes to improve efficiencies. Two main data envelopment analysis (DEA) methods have been used for efficiency analyses: radial models, such as CCR (Charnes, Cooper, Rhodes) and BCC (Banker, Charnes, Cooper) and non-radial methods such as SBM (slacks-based model); however, both have disadvantages. The radial DEA model ignores the non-radial slacks and the non-radial DEA model ignores the characteristics of the same proportion in the radial DEA model. Therefore, this research used a dynamic two-stage directional distance function (DDF) model to analyse the production efficiencies of Chinese listed liquor companies from 2016 to 2018 by evaluating each company’s poverty alleviation input efficiencies, business operations efficiencies, and their social responsibility efficiencies, which was based on their wastewater treatment efficiencies. To overcome the disadvantages in traditional data envelopment models, the DDF model consisted of both input and output direction vectors, the indicator values for which indicated their relative importance or priorities. The analyses found that the indicator efficiencies at most liquor companies had declined, with the poverty alleviation indicator efficiencies being generally lower than the wastewater treatment indicator efficiencies. Several policy and management recommendations are given to improve the overall corporate efficiency and social responsibility in the Chinese liquor industry.

A relatív hatékonyságvizsgálat (DEA) alkalmazása üzleti szimulációs játékban nyújtott teljesítmény értékelésére

Az üzleti szimulációs játékokban résztvevők teljesítményének értékelése nehéz feladat a szubjektív értékelési szempontok és a nehezen aggregálható kvantitatív információk miatt. A cikk célja annak bemutatása, hogyan alkalmazható a relatív hatékonyságvizsgálat (DEA) a szimulációs játékokban résztvevők teljesítményének átfogó értékelésére. A cikk áttekinti a szimulációs játékok jelentőségét az oktatásban, valamint az eredmények kiértékelésének problémáit és gyakorlatát. A tanulmányban állandó skálahatékonyságú, inputorientált, radiális DEA-modell segítségével elemzik a szerzők egy termelésszimulációs játékban részt vevő hallgatók teljesítményét. Az értékelés sajátos szempontjait figyelembe véve súlyszámkorlátok alkalmazásával oldják meg, hogy valamennyi fontos értékelési kritérium szerepeljen a vizsgálatban. Az ismertetett módszer egyrészt új utat nyithat a szimulációs játékok résztvevőinek teljesítményértékeléséhez, továbbá a DEA egy eddig fel nem tárt új alkalmazási lehetőségére is rámutat. A teljesítményt átfogóan jellemző hatékonysági mutatón túl, a nem hatékony működés okai, és a mintaként szolgáló döntési stratégiák is azonosíthatók, továbbá a teljesítményjavítás útjai feltárhatók.

Being a state-owned bank is not a fatality: an Algerian case study

The Algerian banking industry is clearly dominated by the six state-owned banks (SOBs) which represent more than 85% of total banking asset. While it is widely admitted that public ownership in developing countries is often correlated with inefficiency and waste of resources, performance management in SOBs branches is mostly operated using basic accounting ratios. The data envelopment analysis (DEA) is a more sophisticated approach which if designed properly may enhance significantly SOBs branches' performance by creating the competitive pressure that is generally unattainable in public sectors. This research demonstrates all the potential of the DEA technique as a comparative performance measure in enhancing the efficiency of public bank branches. To that aim, the radial and super-efficiency DEA models are conjointly applied.

Efficiency in the Holiday and Other Short-Stay Accommodation Industry

This study extends previous empirical efficiency research by focusing on a tourism sector which has limited evidence to date: the holiday and other short-stay accommodation industry (tourist apartments and hostels). The sample comprises 12,864 firm-level observations during the period 2005–2016. First, we calculate the efficiency index using a non-radial Data Envelopment Analysis (DEA). Second, we test the association between efficiency index and contextual factors using both Tobit and bootstrapped regression. Another major contribution is the use of a radial DEA model to confirm the results of the study. The current study offers new insights by focusing on an industry with scarce evidence, using radial and non-radial DEA approaches, and examining a wide variety of efficiency drivers. The efficiency results are examined by year, region and tourist destination type (including tourism dimensions such as rural, cultural and wine tourism). This is an important novelty of the study. The main findings reveal that the most efficient tourism destinations correspond to mixed or diversified destinations: those that combine some dimensions such as cultural, rural and wine tourism. The regressions models show that environmental, macroeconomic and business variables are drivers of tourism competitiveness. Taken together, the study goes a step further in the efficiency field.

Carbon Emissions Abatement (CEA) Allocation Based on Inverse Slack-Based Model (SBM)

Carbon emissions abatement (CEA) is an important issue that draws attention from both academicians and policymakers. Data envelopment analysis (DEA) has been a popular tool to allocate the CEA, and most previous works are based on radial DEA models. However, as shown in our paper, these models may give biased results due to their ignorance of slackness. To avoid such problems, we propose an allocation model based on the slack-based model and multiple-objective nonlinear programming to find the CEA allocation plan, which can minimize the GDP loss. The property of nonconvexity makes the model difficult to solve. Thus, we construct an approximation algorithm to solve this model with guaranteed error bounds and complexity. In the empirical application, we take regions of china as an illustrative example and find there is a significant region gap in China. Hence, we group the regions into eastern, central, and western, and give the main results, as well as the superiority of our allocation models compared with radial models.

Supporting better practice benchmarking: A DEA-ANN approach to bank branch performance assessment

The quest for best practices may lead to an increased risk of poor decision-making, especially when aiming to attain best practice levels reveals that efforts are beyond the organization’s present capabilities. This situation is commonly known as the “best practice trap”. Motivated by such observation, the purpose of the present paper is to develop a practical methodology to support better practice benchmarking, with an application to the banking sector. In this sense, we develop a two-stage hybrid model that employs Artificial Neural Network (ANN) via integration with Data Envelopment Analysis (DEA), which is used as a preprocessor, to investigate the ability of the DEA-ANN approach to classify the sampled branches of a Greek bank into predefined efficiency classes. ANN is integrated with a family of radial and non-radial DEA models. This combined approach effectively captures the information contained in the characteristics of the sampled branches, and subsequently demonstrates a satisfactory classification ability especially for the efficient branches. Our prediction results are presented using four performance measures (hit rates): percent success rate of classifying a bank branch’s performance exactly or within one class of its actual performance, as well as just one class above the actual class and just one class below the actual class. The proposed modeling approach integrates the DEA context with ANN and advances benchmarking practices to enhance the decision-making process for efficiency improvement.

A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model.

Additive Integer-Valued DEA Models With Fuzzy Undesirable Outputs: Closest Benchmarking Targets and Super-Efficiency

Many production activities generate undesirable outputs apart from desirable outputs. In addition, the data related to undesirable outputs may be fuzzy (imprecise) in some cases. Based on the fuzzy data theory, we propose a group of additive integer-valued data envelopment analysis (DEA) models with fuzzy undesirable outputs. The advantages of the proposed models are as follows: (1) they enable decision-makers to evaluate the efficiency of decision making units (DMUs) with integer-valued variables and fuzzy undesirable outputs; (2) they can be easily solved without any transformation because they are linear programming models; (3) they are better than radial DEA models as they can identify inefficiencies in all the selected inputs and outputs. Particularly, minimum distance-based additive integer-valued DEA models with fuzzy undesirable outputs are developed in this paper to find the closest benchmarking targets for inefficient DMUs, and additive super-efficiency integer-valued DEA models with fuzzy undesirable outputs are presented to differentiate and rank efficient DMUs. The validity of the proposed models is examined by an empirical application in the pallet rental industry.

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.

New Energy Development and Pollution Emissions in China.

China’s rapid economic growth is accompanied by increasing energy consumption and severe environmental problems. As sustainable development can only be achieved by reducing energy intensity, new energy and renewable energy investment, as well as improving traditional energy efficiency, is becoming increasingly important. However, past energy efficiency assessments using data envelopment analysis (DEA) models mostly focused on radial and non-radial DEA model analyses. However, traditional radial DEA models ignore non-radial slacks when evaluating efficiency values, and non-radial DEA models ignore the same proportionality as radial DEA when evaluating efficiency value slacks. To balance the radial and non-radial model characteristics and consider undesirable output, this study combines a modified Epsilou-based measure (EBM) DEA and undesirable output and proposes a modified undesirable EBM DEA model to analyze the efficiency of China’s new and traditional energy sources. The empirical results found that (1) most new energy investment in most municipalities/provinces rapidly grew from 2013 to 2016; (2) as the annual efficiency score was only 1 in Beijing, Inner Mongolia, Shanghai, and Tianjin, the other 26 municipalities/provinces need significant improvements; (3) traditional energy efficiency scores were higher than new energy efficiency; and (4) NO2 efficiencies are slightly better than CO2 and SO2 efficiencies.

An alternative metafrontier framework for measuring the heterogeneity of technology

AbstractThe metafrontier framework proposed by O'Donnell et al. enables the evaluation of relative efficiencies for decision‐making units (DMUs) operating under heterogeneous technologies. The metatechnology ratio (MTR) constructed under the metafrontier framework helps estimate the gap between group frontiers and the metafrontier, with its score between 0 and 1. However, an unreasonable MTR value (ie, greater than 1) may appear when the traditional metafrontier framework is applied in the nonradial data envelopment analysis (DEA) models. This article proposes an alternative metafrontier framework for addressing this issue. The newly constructed technology gap measurement (TGM) can avoid unreasonable technology gap ratio values in nonradial DEA models and substitute for MTR in radial DEA models. To demonstrate how this alternative metafrontier approach works, this article applies it to the efficiency evaluation of regional transportation sectors in China.

Closest target for the orientation-free context-dependent DEA under variable returns to scale

An important branch of data envelopment analysis (DEA) is context-dependent DEA, which evaluates efficiency by combining the attractiveness and progress for a particular decision-making unit (DMU). Traditionally, context-dependent DEA models are based on the assumption of constant returns to scale. Two limitations are found when directly extending original radial context-dependent DEA (ORCD-DEA) models into variable returns to scale versions. One is that it may not be possible to determine the attractiveness of a DMU that logically must be attractive in that context. The other problem is that the progress measure cannot ensure an inefficient DMU projects to a Pareto-efficient frontier. A small numerical example is used to illustrate these two issues. In order to overcome these deficiencies, the concept of closest target is introduced to determine the attractiveness and progress for each DMU. The closest target method can further improve DMUs’ performance with less wastes in inputs or underproduction in outputs. Finally, a practical application involving computer printers is presented.

Supply chains performance with undesirable factors and reverse flows: A DEA-based approach

Supply chain performance evaluation is an essential aspect for decision-makers in order to make better and profitable decisions and survive in the competitive environment. Furthermore, considering desirable and undesirable outputs that are usually produced in supply chain processes simultaneously is significant and effective for obtaining rational results. This study proposes an approach based on data envelopment analysis (DEA) to evaluate the relative efficiency of supply chains with reverse flows in the presence of undesirable factors. The weak disposability assumption is used to handle undesirable factors. To illustrate, a radial DEA model is introduced to determine the efficiency of reverse supply chains while undesirable outputs are present as external factors and reverse flows. The proposed approach herein is illustrated using a data-set.

Integrated Analysis of Healthcare Efficiency: A Systematic Review.

Data Envelopment Analysis (DEA) has been used as a performance measurement tool in efficiency assessment of healthcare systems. However, over the years, researchers and health practitioners presented the theoretical and methodological limitations of DEA that limits the full view of healthcare efficiency. To address these limitations, a commonly used strategy is to integrate other statistical methods and techniques with DEA to provide better efficiency evaluation. This paper reviews 57 studies with DEA applications in the healthcare industry to illustrate the integrated analysis of healthcare efficiency. With DEA as the central method, regression models in conjunction with statistical tests are commonly used. Input-oriented radial DEA models using predominantly capacity-related inputs and activity-related outputs and following either constant return to scale or variable return to scale assumptions are mostly applied to measure healthcare efficiency.