A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann–Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal–Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann–Whitney and Kruskal–Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework.      

A Simulation Study of Joint Uses of Data Envelopment Analysis and Statistical Regressions for Production Function Estimation and Efficiency Evaluation

A previous paper by Arnold, Bardhan, Cooper and Kumbhakar (1996) introduced a very simple method to estimate a production frontier by proceeding in two stages as follows: Data Envelopment Analysis (DEA) is used in the first stage to identify efficient and inefficient decision-making units (DMUs). In the second stage the thus identified DMUs are incorporated as dummy variables in OLS (ordinary least squares) regressions. This gave very satisfactory results for both the efficient and inefficient DMUs. Here a simulation study provides additional evidence. Using this same two-stage approach with Cobb-Douglas and CES (constant elasticity-of-substitution) production functions, the estimated values for the coefficients associated with efficient DMUs are found to be not significantly different from the true parameter values for the (known) production functions whereas the parameter estimates for the inefficient DMUs are significantly different. A separate section of the present paper is devoted to explanations of these results. Other sections describe methods for estimating input-specific inefficiencies from the first stage use of DEA in the two-stage approaches. A concluding section provides further directions for research and use.     

The benefits of non-radial vs. radial super-efficiency DEA: an application to burden-sharing amongst NATO member nations

Using radial super-efficiency data envelopment analysis (DEA) has improved the discriminating performance across efficient decision-making units (DMUs). This paper extends the super-efficiency approach to a non-radial super-efficiency DEA (NRSE-DEA) index. NRSE-DEA is shown to be invariant to units of input (output) measurement. NRSE-DEA is illustrated here via an application to NATO burden-sharing assessment in which the DMUs are the member nations of NATO. The NRSE-DEA provides additional insights into the ranking of efficient countries, suggesting which are absorbing a particularly large share of NATO responsibilities. The NRSE-DEA generates a smaller set of efficient DMUs. This, in turn, provides more discriminatory power, a more accurate measure of super-efficiency, a more meaningful ranking of the efficient burden sharing countries, and a more reliable assessment of contributions by NATO members, amongst other policy issues.     

交叉效率评价方法中一种改进的新单元导入保序性方法

针对交叉效率方法在评估排序时所存在的局限性,即在导入新的决策单元时,可能会使原先的决策单元(DMU)排序发生变化,本文通过建立二次权重集结交叉效率保序性模型对各DMU的权重进行二次分配,进而对交叉效率矩阵进行集结以得到最终的均衡交叉效率值。利用该均衡交叉效率值进行排序时可以消除导入新DMU时所产生的逆序现象。算例说明了该方法有效,计算结果较纳什讨价还价交叉效率保序性模型有所改进,综合计算量更小,各DMU权重更加合理,与一般交叉效率模型的效率值差异更小。     

A novel method for computing single output for DEA with application in hospital efficiency

There are two main methods for measuring the efficiency of decision-making units (DMUs): data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Each of these methods has advantages and disadvantages. DEA is more popular in the literature due to its simplicity, as it does not require any pre-assumption and can be used for measuring the efficiency of DMUs with multiple inputs and multiple outputs, whereas SFA is a parametric approach that is applicable to multiple inputs and a single output. Since many applied studies feature multiple output variables, SFA cannot be used in such cases. In this research, a unique method to transform multiple outputs to a virtual single output is proposed. We are thus able to obtain efficiency scores from calculated virtual single output by the proposed method that are close (or even the same depending on targeted parameters at the expense of computation time and resources) to the efficiency scores obtained from multiple outputs of DEA. This will enable us to use SFA with a virtual single output. The proposed method is validated using a simulation study, and its usefulness is demonstrated with real application by using a hospital dataset from Turkey.     

Using DEA and Worst Practice DEA in Credit Risk Evaluation

The purpose of this paper is to introduce the concept of worst practice DEA, which aims at identifying worst performers by placing them on the frontier. This is particularly relevant for our application to credit risk evaluation, but this also has general relevance since the worst performers are where the largest improvement potential can be found. The paper also proposes to use a layering technique instead of the traditional cut-off point approach, since this enables incorporation of risk attitudes and risk-based pricing. Finally, it is shown how the use of a combination of normal and worst practice DEA models enable detection of self-identifiers. The results of the empirical application on credit risk evaluation validate the method. The best combination of layered normal and worst practice DEA models yields an impressive 100% bankruptcy and 78% non-bankruptcy prediction accuracy in the calibration data set, and equally convincing 100% and 67% out-of-sample classification accuracies.     

Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammons mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.JEL Classification: C14, C61, D24, M2     

Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. This paper extends this methodology in two substantive ways. First, a method is developed that determines the least-norm projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the observable frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions.     

Multiple Objective Approach as an Alternative to Radial Projection in DEA

Radial projection is a standard technique applied in data envelopment analysis (DEA) to calculate efficiency scores for input and/or output variables. In this paper, we have studied the appropriateness of radial projection for target setting. We have created a situation where the decision making units (DMUs) are free to choose their own target values on the efficient frontier and then compared the results to those of radial projection. In practice, target values are primarily used for future goal attainment; hence, not only preferences but also, and on the whole, change in time frame, affect the choice of target values. Based on that, we conducted an empirical experiment with an aim to study how the DMUs choose their most preferred target values on the efficient frontier. The subjects, who all were students of the Helsinki School of Economics, were given the freedom to explore their personalized efficient frontiers by using a multiple objective linear programming (MOLP) approach. To study various and relevant scenarios, the personalized efficient frontiers for all students were constructed in such a way that the current position of each student in relation to the frontier made him/her inefficient, efficient, or super-efficient. The results show that the use of radial projection for target setting is too restrictive.     

Integration of network data envelopment analysis and decision-making trial and evaluation laboratory for the performance evaluation of the financial holding companies in Taiwan

Data envelopment analysis (DEA) has been constantly used to measure the technical efficiency of decision-making units (DMUs). However, the major problem of traditional DEA methods is that they do not consider the possible intermediate effects. Recently, many papers have applied network DEA models to evaluate the efficiency scores. However, the linking activity of DMUs is still hard to be recognized. Hence, we employ DEMATEL to obtain the linking activity of DMUs. Our empirical research shows that the proposed method can soundly deal with the purpose of identifying the relationship between variables and derive the reasonable result in network DEA.     

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.     

Research efficiency analysis of China's university faculty members: A modified meta-frontier DEA approach

Traditionally, data envelopment analysis (DEA) requires all decision-making units (DMUs) to have similar characteristics and experiences within the same external conditions. In many cases, this assumption fails to hold, and thus, difficulties will be encountered to some extent when measuring efficiency with a standard DEA model. Ideally, the performance of DMUs with different characteristics could be examined using the DEA meta-frontier framework. However, some of these DMUs are mixed-type DMUs that may affiliate with more than one group. Furthermore, the total number of observations of these mixed-type DMUs is limited. This is one of the common problems when studies focus on faculty research performance in higher education institutions. In general, a faculty member is affiliated with a certain department, and if the departmental assessment policy is not suitable for faculty members who are involved in interdisciplinary research, their performance could be underestimated. Therefore, the proposed model is an extension of the DEA meta-frontier framework that can assess the performance of mixed-type DMUs by constructing the reference set without the same type of DMUs. In this paper, the scientific research efficiency of faculty members at the Inner Mongolia University is used as an example to provide a better understanding of the proposed model. The proposed model is intended to provide a fair and balanced performance assessment method that reflects actual performance, especially for mixed-type DMUs.     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.     

Research performance evaluation of Chinese university: A non-homogeneous network DEA approach

Performance evaluation for universities or research institutions has become a hot topic in recent years. However, the previous works rarely investigate the multiple departments’ performance of a university, and especially, none of them consider the non-homogeneity among the universities’ departments. In this paper, we develop data envelopment analysis (DEA) models to evaluate the performance of general non-homogeneous decision making units (DMUs) with two-stage network structures and then apply them to a university in China. Specifically, the first stage is faculty research process, and the second stage is student research process. We first spit each DMU (i.e. department) into a combination of several mutually exclusive maximal input subgroups and output subgroups in terms of their homogeneity in both stages. Then an additive DEA model is proposed to evaluate the performance of the overall efficiency of the non-homogeneous DMUs with two-stage network structure. By analyzing the empirical results, some implications are provided to support the university to promote the research performance of each department as well as the whole university.     

银行效率DEA分析的可信度检验

近年来涌现出大量基于DEA方法的银行效率这一热点问题的研究成果,但是由于DEA方法自身的局限性,诸如对效率值的估计偏低且离散程度较大,以及不能方便地检验结果的显著性等等问题,使其研究的结果受到影响;而Bootstrap技术是基于对经验数据及其相关估计的重复抽样来提高估计置信区间和临界值精度的统计技术,可有效地克服DEA方法结果可信度的这种内在依赖性。本文给出了基于Boot-strap技术的DEA方法来计量银行效率的手段,提高了效率分析结果的可信度,并对我国四大国有商业银行的效率进行了对比性实证分析。     

Hierarchies and Groups in DEA

Conventional applications of data envelopment analysis (DEA) presume the existence of a set of similar decision making units, wherein each unit is evaluated relative to other members of the set. Often, however, the DMUs fall naturally into groupings, giving rise first to the problem of how to view the groups themselves as DMUs, and second to the issue of how to deal with several different ratings for any given DMU when groupings can be formed in different ways. In the present paper we introduce the concept of hierarchical DEA, where efficiency can be viewed at various levels. We provide a means for adjusting the ratings of DMUs at one level to account for the ratings received by the groups (into which these DMUs fall) at a higher level. We also develop models for aggregating different ratings for a DMU arising from different possible groupings. An application of these models to a set of power plants is given.     

Efficiency characterizations in different DEA models

Relations of efficiency and non-efficiency for the same sets of DMUs (Decision Making Units) are developed for the Charnes, Cooper and Rhodes (CCR) and Barker, Charnes, Cooper (BCC) ratio models, as well as DEA Additive and Multiplicative Models. Surprisingly, additively efficient DMUs are not necessarily multiplicatively efficient. A geometric “stretching” phenomenon is identified for the latter case.     

Centralized Resource Allocation Using Data Envelopment Analysis

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.     

A DEA evaluation of the successful implementation of HEALTH2020 policies

Health2020 is a promising framework of policies provided by World Health Organization (WHO) aiming to diminish the health and well-being inequalities among the citizens of countries. European Union (EU) and its member-states participate to this ambitious framework. The deterioration of major demographic, social and environmental factors, in addition to the escalation of the economic crisis prevent the successful and, without restrictions, implementation of this framework. Under such conditions, there is a strong need for all the EU member-states to utilize their health and economical resources efficiently and wisely. In order to provide a unified and value-based approach of the Heath2020 framework, we take advantage of the Data Envelopment Analysis (DEA) and Dynamic DEA methods to evaluate the impact of the Health2020 policies. This approach pinpoints the countries that can be characterized as outperformers and the lagged ones. We adopt several versions of evaluation, in relation to the regional targets of Health2020, measuring both the effectiveness and the efficiency of EU countries from 2011 to 2016. We, also, examine the stability of the technological frontier of the countries using dynamic DEA. Our results showed the existence of major dividend lines between the outperformers and the other countries. The results also reveal a stability in technological changes indicating, probably, the slow development in this sector at the field of Health.     

The Application of Mathematical Programming Approaches to Estimating Container Port Production Efficiency

Container terminal production is both an important and complicated element in the contemporary global economy. This paper aims to evaluate the efficiency of the world’s most important container ports and terminals using the two alternative techniques of Data Envelopment Analysis (DEA) and the Free Disposal Hull (FDH) model. The results give an insight into the current efficiency ranking of the world’s major container ports and terminals. They also confirm expectations that the available mathematical programming methodologies lead to different results and that appropriate variable definition of input and output factors is a crucial element in meaningful applications of DEA and FDH. It is also concluded that the availability of panel data, rather than cross-sectional data would greatly improve the validity of the efficiency estimates derived from all the mathematical programming techniques applied.JEL Classification:C61, D24, E23, L23, L25, L92