A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016

In recent years there has been an exponential growth in the number of publications related to theory and applications of Data Envelopment Analysis (DEA). Charnes, Cooper, and Rhodes (1978) introduced DEA as a tool for measuring efficiency and productivity of decision making units. DEA has immediately been recognized as a modern tool for performance measurement. Since then, a large and considerable amount of articles has been appeared, including significant breakthroughs in theory and a great portion of works on DEA applications, both public and private sectors, to assess the efficiency and productivity of their activities. Although there have been several bibliographic collections reported, a comprehensive analysis and listing of DEA-related articles covering its first four decades of history is still missing. This paper, thus, aims to report an extensive listing of DEA-related articles including theory and methodology developments and "real" applications in diversified scenarios from 1978 to end of 2016. Some summary statistics of the publications' growth, the most utilized academic journals, authorship analysis, as well as keywords analysis are also provided.     

DEA, DFA and SFA: A comparison

The nonparametric data envelopment analysis (DEA) model has become increasingly popular in the analysis of productive efficiency, and the number of empirical applications is now very large. Recent theoretical and mathematical research has also contributed to a deeper understanding of the seemingly simple but inherently complex DEA model. Less effort has, however, been directed toward comparisons between DEA and other competing efficiency analysis models. This paper undertakes a comparison of the DEA, the deterministic parametric (DFA), and the stochastic frontier (SFA) models. Efficiency comparisons across models in the above categories are done based on 15 Colombian cement plants observed during 1968–1988.     

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.     

基于DEA模型的企业员工绩效考评研究

利用数据包络分析(DEA)方法对企业员工进行绩效考评,目的是真实、客观地反映员工的工作表现。本文提出运用只有输出(输入)和二次相对有效性的DEA模型对企业员工进行静态与动态的绩效考评,并结合实例进行实证研究,为人力资源管理提供了有价值的方法。     

The origins,development and future directions of data envelopment analysis approach in transportation systems

Over the last two decades, application of Data envelopment analysis (DEA) in transportation problems have gained considerable research attention. This paper presents a literature review and classification of the applications of DEA in transportation systems (TSs). First by classifying 40 papers from 2007 to 2018, the origins of DEA in transportation problems have been reviewed. Then the development and an overall view of DEA applications in TSs have been presented. We have classified the applications of DEA into six different contexts. In each context, published papers have deeply been analyzed. Content of analysis includes “Number of published papers during the time”, “target journals”, “countries”, “keyword frequency”, “most cited papers”, “map of most co-cited publications”. More important, we reported the “inputs and outputs variables” used in each paper. Further “a review of the selected papers” and “gaps/future research directions” have been given within each cluster. The results show that DEA is one of the most useful approach in evaluating TSs for policy makers. On the other hand, DEA can help the decision makers in transportation especially regarding environmental factors, sustainable development and eco-design. Finally, we proposed subjects for future researches including guidance for new studies in the field of DEA applications in TSs.     

Data envelopment analysis with stochastic variations in data

The mathematical programming-based technique data envelopment analysis (DEA) has often treated data as being deterministic. In response to the criticism that in most applications there is error and random noise in the data, a number of mathematically elegant solutions to incorporating stochastic variations in data have been proposed. In this paper, we propose a chance-constrained formulation of DEA that allows random variations in the data. We study properties of the ensuing efficiency measure using a small sample in which multiple inputs and a single output are correlated, and are the result of a stochastic process. We replicate the analysis using Monte Carlo simulations and conclude that using simulations provides a more flexible and computationally less cumbersome approach to studying the effects of noise in the data. We suggest that, in keeping with the tradition of DEA, the simulation approach allows users to explicitly consider different data generating processes and allows for greater flexibility in implementing DEA under stochastic variations in data.     

Economic interpretations of DEA

Research on productive efficiency at the firm level has developed as an important and active strand of research the last decades, both within operations research, management science and economics. Two apparently different definitions of efficiency are examined, but it is shown that when both estimation methods are based on solving linear programming problems the definitions of efficiency are identical. The purpose of the paper is to give the basic ideas of efficiency analyses using DEA as a tool for researchers not so familiar with efficiency analysis and DEA. The concept of shadow prices is given special attention.     

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.     

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.      

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

Cross redundancy and sensitivity in DEA models

Data envelopment analysis (DEA) measures the efficiency of each decision making unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effect of such a dependency on DEA is not clear. In this paper, we call such a dependency a cross redundancy and examine the effect of a cross redundancy on DEA. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models. Furthermore, we present a sensitivity analysis to examine the effect of an imperfect cross redundancy on DEA by using accounting data obtained from United States exchange-listed companies.     

The Effect of Financial Liberalization on the Efficiency of Financial Institutions: The Case of Jordanian Commercial Banks

SUMMARY

Jordan undertook major financial sector liberalization starting in the early of 1990s. The effect of this reform on the efficiency of the banking sector is evaluated. A non-parametric method of Data Development Analysis (DEA) has been used to arrive at the efficiency scores for a panel data sample covering eight Jordanian commercial banks over the period 1984 to 2001. The findings suggest that liberalization program was followed by an observable increase in efficiency. Another finding of the study is that large banks demonstrated the faster productivity growth during the liberalization. The study has important implications such as guiding the government policy regarding deregulation and liberalization.     

An analysis of operations efficiency in large-scale distribution systems

This research applies Data Envelopment Analysis (DEA) methodology to evaluate the efficiency of units within a large-scale network of petroleum distribution facilities in the USA. Multiple inputs and outputs are incorporated into a broad set of DEA models, yielding a comprehensive approach to evaluating supply chain efficiency. This study empirically separates three recognized, important and yet different causes of performance shortfalls which have been generally difficult for managers to identify. They are: (1) managerial effectiveness; (2) scale of operations and potential for a given market area (and efficiency of resource allocation given the scale); and (3) understanding the resource heterogeneity via programmatic differences in efficiency. Overall, the efficiency differences identified raised insightful questions regarding top management’s selection of the appropriate form and type of inputs and outputs, as well as questions regarding the DEA model form selected.     

Analysis of Intertemporal Efficiency Trends Using Rank Statistics With an Application Evaluating the Macro Economic Performance of OECD Nations

This paper presents two applications of rank statistics to evaluate efficiency performance trends using productive efficiency measures derived through various Data Envelopment Analysis (DEA) models. The paper starts with a discussion of the difficulties in obtaining consistent ranks from DEA efficiency ratings. Next, a procedure is proposed to identify intertemporal performance trends using any one of several possible efficiency measures. Another procedure is then developed to test the stability over time of the rank positions of the analyzed units. For each statistical procedure, a small numerical example involving DEA efficiency measures is provided to illustrate the proposed technique. Finally, the new procedures are applied to data reflecting the macro-economic performance of 17 OECD nations in 1979–1988. The outcomes of the application are discussed and contrasted with previous research in this area.     

Applying efficiency measurement techniques to the measurement of productivity change

Deterministic frontier analysis (DFA), stochastic frontier analysis (SFA), and data envelopment analysis (DEA) are alternative analytical techniques designed to measure the efficiency of producers. All three techniques were originally developed within a cross-sectional context, in which the objective is to compare the efficiencies of producers. More recently all three techniques have been extended for use in a panel data context. In the latter context it is possible to measure productivity change, and to decompose measured productivity change into its sources, one of which is efficiency change. However when efficiency measurement techniques, particularly SFA, have been applied to panel data, it has infrequently been made clear what the objective of the analysis is: the measurement of efficiency, which may vary through time as well as across producers, or the measurement and decomposition of productivity change. In this paper I explore the use of each technique in a panel data context. I find DFA and DEA to have achieved a more satisfactory reorientation toward productivity measurement than SFA has.     

Efficiency and Technical Change in Intertemporal Intersectoral DEA

A new procedure for the measurement of efficiency and technical change is presented, using DEA with three-dimension data (box data), pooling over sectors, regions and time. Until now, when pooling the data in panel applications it has been assumed that technology remained unchanged, so productivity change was entirely attributed to technical efficiency change. However, patterns of technology change and the decomposition into efficiency and technical change elements can be accomplished by means of restrictions on the general structure of the technology indexes. Under the assumption of non-regressive technical change, upper and lower bounds for efficiency and technical change are obtained. The new methodology is illustrated in an analysis of productivity growth in 13 manufacturing sectors in the Spanish regions from 1980 to 1992.     

An insight into the specification of the input-output set for DEA-based bank efficiency measurement

Data envelopment analysis (DEA) has become one of the most widely used instruments for measuring bank efficiency. However, its application encounters many problems, which is evidenced by continuous evolvements in the DEA method so far. Our paper addresses the pitfalls of DEA in the context of measuring bank efficiency, with focus on the specification of performance factors. We aim at examining whether the input-output specification for banks in DEA applications is in consistence with the criteria upon which banks make decisions. Four bank behaviour models which are most popularly employed to determine input and output factors in DEA studies—the intermediation approach, production approach, user cost approach and value added approach—are comprehensively discussed and reviewed. The comparative reflection on the bank behaviour models and the standard DEA models shows that the input-output related pitfalls of a DEA application are associated with its implicitly fixed preference structure, flexible weight determination and limited explanatory power. Due to the pitfalls, the conventional DEA models may fail to capture bank behaviours. In such cases, DEA results can hardly reflect the performance in its true sense, i.e. how banks perform against the goals that they decide to pursue. The findings suggest focusing on (DEA-based) performance measurement from a goal-oriented perspective, i.e. from the point of view of multi criteria decision making.     

Exploring the operating efficiency of Technology Development Programs by an intellectual capital perspective—A case study of Taiwan

Government supported technological research and development can help the private sector to compete globally. A more accurate evaluation system considering multi-factor performance is highly desired. This study offers an alternative perspective and characterization of the performance of Technology Development Programs (TDPs) via a two-stage process that emphasizes research and development (R&D) and technology diffusion. This study shall employ a sequential data envelopment analysis (DEA) with a non-parametric statistical analysis to analyze differences in intellectual capital variables among various TDPs. The results reveal that R&D performance is better than technology diffusion performance for the TDPs. In addition, the “Mechanical, Mechatronic, and Transportation field” is more efficient than the other fields in both R&D and technology diffusion performance models. The findings of this study point to the importance of intellectual capital in achieving high levels of TDP efficiency. The potential applications and strengths of DEA and intellectual capital in assessing the performance of TDP are also highlighted.     

Developing foreign bank efficiency models for DEA grounded in finance theory

We develop foreign bank technical, cost and profit efficiency models for particular application with data envelopment analysis (DEA). Key motivations for the paper are (a) the often-observed practice of choosing inputs and outputs where the selection process is poorly explained and linkages to theory are unclear, and (b) foreign bank productivity analysis, which has been neglected in DEA banking literature. The main aim is to demonstrate a process grounded in finance and banking theories for developing bank efficiency models, which can bring comparability and direction to empirical productivity studies. We expect this paper to foster empirical bank productivity studies.     

The operating efficiency of financial holding and nonfinancial holding banks—Epsilou‐based measure metafrontier data envelopment analysis model

Previous bank efficiency studies assumed that the same efficient frontier system exists in different types of banks, but the conventional radial data envelopment analysis (DEA) model slacks are not counted in efficiency scores, and nonradial DEA models do not consider radial features. This paper develops an Epsilou‐based measure meta‐DEA approach for measuring the efficiencies and technology gaps of different bank types. The results are as the follows: The average efficiency and technology gaps of nonfinancial holding banks are better than those of financial holding banks. The nonfinancial holding banks are more efficient than financial holding banks in investment and other income.