Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA

Since the original Data Envelopment Analysis (DEA) study by Charnes et al. [Measuring the efficiency of decision-making units. European Journal of Operational Research 1978;2(6):429–44], there has been rapid and continuous growth in the field. As a result, a considerable amount of published research has appeared, with a significant portion focused on DEA applications of efficiency and productivity in both public and private sector activities. While several bibliographic collections have been reported, a comprehensive listing and analysis of DEA research covering its first 30 years of history is not available.This paper thus presents an extensive, if not nearly complete, listing of DEA research covering theoretical developments as well as “real-world” applications from inception to the year 2007.A listing of the most utilized/relevant journals, a keyword analysis, and selected statistics are presented.     

Measures in DEA with an Application to the Malmquist Index

This paper shows the importance of goal vectors G in measuring and dealing with DEA inefficiencies. It emphasizes the advantages of the family of additive relative to the traditional oriented DEA models and shifts the primary emphasis to measuring inefficiency rather than efficiency. This new (raw) inefficiency measure RIN incorporates both the traditional DEA efficiency and the DEA slacks and provides the background for a new approach to the Malmquist Index. The final section points out some deficiencies in existing computational procedures for selecting G and calls for continued research on the selection process, as well as showing a role for G in returns to scale studies.     

Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry

The banking industry in Canada is essentially an oligopoly with five large participants controlling about 90% of the market. To evaluate the industry's performance over time, we need to deal with the problem of a small number of DMU's compared to the number of relevant inputs and outputs. To overcome this problem we use data envelopment analysis (DEA) window analysis, whereby efficiency scores for the 20 year period 1981–2000 are obtained. To measure productivity changes over time, Malmquist indices can be calculated from DEA scores. Using DEA window analysis scores, however, raise the question of how to define the same period frontier in a DEA window analysis. We show that for both the adjacent and the base period Malmquist index and for all suggested definitions of same period frontier, the standard decomposition into frontier shift and catching up effects gives inappropriate results when Malmquist indices are based on DEA window analysis scores.     

Weight restrictions in DEA: misplaced emphasis?

Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of inefficient units to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function.     

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.     

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.     

基于超效率DEA和Tobit模型的中国上市煤炭企业经营效率现状分析

本文运用数据包络分析（DEA）方法和Tobit回归模型,首先选取2011年沪深两市具有代表性的18家煤炭上市公司为研究对象,以货币资金、流动资产合计、长期股权投资、固定资产和非流动资产合计为投入变量,主营业务收入、主营业务利润、利润总额为产出变量,运用CCR模型从技术效率、纯技术效率和规模效率等方面对其经营效率进行评价和分析;其次运用超效率DEA模型对CCR模型下DEA有效的决策单元计算其超效率值,从而为所有决策单元提供完整的效率值排序;最后,本文运用Tobit模型,分析影响中国上市煤炭企业经营效率的重要因素,为决策者提供提高企业经营效率的方向和政策。     

基于超DEA的皖江九市产业用地效率评价

本文以皖江九市作为研究区,在采用传统DEA评价方法 C2R模型评价2001至2010年10年间皖江九市总体产业用地投入产出效率的基础上,采用超效率DEA评价法对2010年皖江九市各市产业用地投入产出效率进行评价排序。结果表明:2001年至2010年10年间,皖江九市总体上仅2008及2010年两年产业用地投入产出为DEA有效,其余年份均存在产业用地投入冗余、产出不足现象;2010年,产业用地投入产出达到DEA有效的城市有六个,运用超DEA模型排序产业用地投入产出效率,结果从高到低依次为合肥、马鞍山、滁州、芜湖、巢湖及池州。     

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.     

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.     

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.     

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.     

Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.

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.     

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.     

Management of nursing homes using data envelopment analysis.

Data envelopment analysis (DEA) is used to evaluate the relative technical efficiency and assist in the management of a chain of nursing homes. As with any DEA model, variables chosen are particularly important. The study looks at two possibly critical issues. The first is the appropriateness of models that include only financial and economic measures to evaluate administrators when quality care is an expected output. The second issue is the appropriateness of using noncontrollable variables, in this case operating income, to evaluate administrators. We show how efficiency scores differ when quality variables and/or operating income are included. We also demonstrate the usefulness of DEA information to both the home administrator and chain managers for improving operating efficiency.     

基于超效率DEA的城市效率演变特征

以我国15个副省级城市为研究样本,首先构建了基于效率的副省级城市的投入产出评价指标体系,采用超效率的数据包络分析模型,克服了一般文献中由于通常使用数据包络分析的DI,BC2和DEC2R模型,而陷入对有效的决策单元无法做进一步分析评价的困惑,比较客观地评价了1995-2005我国15个副省级城市效率的演变特征:其一,超效率DEA值变化呈倒U字型.且超效率值有趋同性的态势;其二,超效率DEA值大于1的副省级城市数量逐年增多;其三,超效率DEA值整体变化比较稳定,但少数某些城市的超效率值变化剧烈.     

DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea—Ratio Analysis. Our model, called DEA-R, treats all possible ratios “output/input” as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts’ opinions via flexible restrictive conditions on individual “output/input” pairs.     

A cross-national comparison and taxonomy of DEA-based hospital efficiency studies

This paper provides the first taxonomy of hospital efficiency studies that uses data envelopment analysis (DEA) and related techniques. We provide a systematic review of 79 such studies published from 1984–2004 that represent 12 countries. Only studies written in English are considered. A cross-national comparison reveals significant differences with respect to important study characteristics such as type of DEA model selected and choice of input and output categories. Compared with US studies, European efforts are more likely to measure allocative rather than technical efficiency, use longitudinal data, and use fewer observations. We take a longitudinal perspective that illustrates the life cycle of this research, as well as its diffusion across disciplines. Our taxonomy can be used by policy makers and researchers to review past, and assemble new, DEA models.     

中国省际高技术产业效率测度与分解——基于共享投入关联DEA模型

本文基于高技术产业科技成果产出和科技成果转化为生产力两阶段视角,考虑"中间产品产出再投入"和"初始投入在两个子系统间的分配结构",构建共享投入关联DEA模型,利用1999～2010年我国29个省份的面板数据,测算高技术产业系统效率和子系统的纯技术效率,并与关联DEA模型、BCC模型的结果进行比较。结果表明,共享投入关联DEA模型在计算效率水平的同时,还可得到中间产品的转化信息和初始投入的配置信息。