Employing super-efficiency analysis as an alternative to DEA: An application in outpatient substance abuse treatment

A common technique for conducting efficiency analyses consists of a two-stage procedure that combines data envelopment analysis (DEA) with Tobit regression. As the DEA scores are censored at one, this method has the drawback of masking important information at the upper tail of the distribution of scores. In this paper, we present a DEA-based methodology for a two-stage efficiency analysis where the upper bound constraint of one for the efficiency scores is relaxed. This method, super-efficiency DEA, is contrasted with the two-stage approach that employs traditional, bounded DEA scores. We use data from the National Drug Abuse Treatment Survey to examine how the relative efficiency of the treatment units is affected by the organizational structures, operating characteristics and treatment modalities of a nationally representative sample of outpatient substance abuse treatment units. Our results show that the super-efficiency DEA approach offers advantages over the traditional methodology. It is easy to implement, and, for the same sample size provides more information.     

Sensitivity analysis of inefficient units in data envelopment analysis

One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.     

Cost,Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the $\alpha$-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.     

Integrating DEA into Six Sigma methodology for measuring health service efficiency

As a linear programming technique that is used to assess performance efficiency among organizational units, data envelopment analysis (DEA) has the practical value for planners to identify the most efficient units and thus project a best possible course of actions. This is also the fundamental goal of Six Sigma methodology for process improvement. Therefore, it is natural to integrate the DEA method into the framework of Six Sigma to enhance both the usefulness of Six Sigma and the effectiveness of DEA for assessing and improving health service efficiency. In this paper, the implementation of DEA is well incorporated into the Define, Measure, Analyze, Improve and Control process. The procedure can be well fitted into the Blackbelts training curriculum, which can also serve as a roadmap for Six Sigma practitioners to implement the DEA-enhanced projects. To illustrate how to integrate DEA into the Six Sigma framework, we present a Six Sigma project implemented to measure physician productivity in a clinical department.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

DEA and the discriminant analysis of ratios for ranking units

The purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the Data Envelopment Analysis (DEA), in order to rank all the units on the same scale. This new method, Discriminant Data Envelopment Analysis of Ratios (DR/DEA), presents a further post-optimality analysis of DEA for organizational units when their multiple inputs and outputs are given. We construct the ratio between the composite output and the composite input, where their common weights are computed by a new non-linear optimization of goodness of separation between the two pregiven groups. A practical use of DR/DEA is that the common weights may be utilized for ranking the units on a unified scale. DR/DEA is a new use of a two-group discriminant criterion that has been presented here for ratios, rather than the traditional discriminant analysis which applies to a linear function. Moreover, non-parametric statistical tests are employed to verify the consistency between the classification from DEA (efficient and inefficient units) and the post-classification as generated by DR/DEA.     

Equivalent standard DEA models to provide super-efficiency scores

DEA super-efficiency models were introduced originally with the objective of providing a tie-breaking procedure for ranking units rated as efficient in conventional DEA models. This objective has been expanded to include sensitivity analysis, outlier identification and inter-temporal analysis. However, not all units rated as efficient in conventional DEA models have feasible solutions in DEA super-efficiency models. We propose a new super-efficiency model that (a) generates the same super-efficiency scores as conventional super-efficiency models for all units having a feasible solution under the latter, and (b) generates a feasible solution for all units not having a feasible solution under the latter. Empirical examples are provided to compare the two super-efficiency models.     

Demystifying DEA — A Visual Interactive Approach Based on Multiple Criteria Analysis

Both Data Envelopment Analysis (DEA) and Multiple Criteria Analysis (MCA) can be used to assess the efficiency with which units perform similar tasks. This paper describes an approach derived from the integration of data envelopment analysis and a multi-attribute value function. This approach is implemented as a visual interactive decision support system, the use of which is illustrated by a practical application. The authors feel that this approach overcomes some of the limitations of the original DEA approach and, in particular, increases users' understanding of DEA. The approach is particularly well suited to the analysis of the efficiency of a small number of units.     

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.     

Experimental evidence on robustness of data envelopment analysis

There is an on-going debate about variable selection in data envelopment analysis (DEA) as there are no diagnostic checks for model misspecification. This paper contributes to this debate by investigating the sensitivity of DEA efficiency estimates to including inappropriate and/or omitting several important variables in a large-sample DEA model. Data are simulated from constant, increasing and decreasing returns-to-scale (RS) Cobb–Douglas production processes. For constant and decreasing RS processes with irrelevant inputs, DEA tends to overestimate efficiency in almost all production units. When relevant variables are omitted, variable RS appears to be a safer option. The correct RS specification is vital when the DEA model includes irrelevant variables. The effect of omission of relevant inputs on individual production unit efficiency is more adverse compared to the inclusion of irrelevant ones.     

Deriving the DEA frontier for two-stage processes

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model provides not only an overall efficiency score for the entire process, but as well yields an efficiency score for each of the individual stages. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current paper develops an approach for determining the frontier points for inefficient DMUs within the framework of two-stage DEA.     

A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis

The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.     

Random effects logistic regression model for data envelopment analysis with correlated decision making units

This study attempts to exploit information from environmental variables together with data envelopment analysis (DEA) efficiency scores for efficiency predictions of groups with more limited information. Based on DEA efficiency scores, decision-making units (DMUs) are sorted into two sets containing efficient and inefficient units, respectively. Then they are reshuffled into homogeneous groups with respect to environmental factors. We assume that the efficiency of DMUs in such a homogeneous group would be correlated. However, efficiency of different groups would vary. A beta binomial logistic model is proposed to fit such phenomena and is applied to predict the performance of a new group of commercialization projects for given environmental characteristics.     

Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.     

Relative Efficiency Assessments Using Data Envelopment Analysis: An Application to Data on Rates Departments

This paper examines the nature of information obtained from data envelopment analysis (DEA) in comparative studies of the efficiency of decision-making units, and it discusses the interpretation and practical usefulness of such information. The themes developed in the paper are illustrated by an application of DEA to data on the rate-collection function of London Boroughs and Metropolitan District Councils. The paper begins with an overview of DEA, followed by a discussion of some of the practical considerations arising in the application of DEA. It then describes the structuring of the rate-collection function for assessment by DEA, and explores the extent to which units can be classified as relatively efficient or inefficient. In respect of relatively inefficient units, it illustrates the construction of target inputs and outputs so that their relative efficiency may improve. In respect of relatively efficient units, it is argued that their identification is weak in the sense that for some of them their apparent efficiency may be simply a reflection of an uncommon input-output profile. It is shown, nevertheless, that information about relatively efficient units can be used to identify those of them which may prove examples of good operating practice in given aspects of their function. (Readers not familiar with British taxes may wish to note that rates are a tax on property, levied by local authorities.)     

Variables reduction in data envelopment analysis

In real applications of data envelopment analysis (DEA), there are a number of pitfalls that could have a major influence on the efficiency. Some of these pitfalls are avoidable and the others remain problematic. One of the most important pitfalls that the researchers confront is the closeness of the number of operational units and the number of inputs and outputs. In performance measurement using DEA, the closeness of these two numbers could yield a large number of efficient units. In this article, some inputs or outputs will be aggregated and the number of inputs and outputs are reduced iteratively. Numerical examples show that in comparison to the single DEA method, our approach has the fewest efficient units. This means that our approach has a superior ability to discriminate the performance of the DMUs.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.     

Computation of efficient targets in DEA models with production trade-offs and weight restrictions

Recently new models of data envelopment analysis (DEA) were introduced that incorporate production trade-offs between inputs and outputs or based on them weight restrictions. In this paper, we develop a computational procedure suitable for the practical application of such models. We show that the standard two-stage optimisation procedure used in DEA to test the full efficiency of units and identify their efficient targets may work incorrectly in the new models. The modified procedure consists of three stages: the first evaluates the radial efficiency of the unit, the second identifies its efficient target, and the third its reference set of efficient peers. Each stage requires solving one linear program for each unit.     

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.