A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

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.     

Resampling DEA estimates of investment fund performance

Data envelopment analysis (DEA) is attractive for comparing investment funds because it handles different characteristics of fund distribution and gives a way to rank funds. There is substantial literature applying DEA to funds, based on the time series of funds’ returns. This article looks at the issue of uncertainty in the resulting DEA efficiency estimates, investigating consistency and bias. It uses the bootstrap to develop stochastic DEA models for funds, derive confidence intervals and develop techniques to compare and rank funds and represent the ranking. It investigates how to deal with autocorrelation in the time series and considers models that deal with correlation in the funds’ returns.     

DEA有效单元排序的一种新方法

通过对DEA有效单元排序中超有效性方法的探讨,提出了一种新的方法.利用对构造模型目标函数的处理,新的方法能够实现对有效单元的完全排序.最后,通过两个算例进一步验证了新方法的可行性和优越性.     

Super-efficiency infeasibility and zero data in DEA

Lee et al. (2011) and Chen and Liang (2011) develop a data envelopment analysis (DEA) model to address the infeasibility issue in super-efficiency models. In this paper, we point out that their model is feasible when input data are positive but can be infeasible when some of input is zero. Their model is modified so that the new super-efficiency DEA model is always feasible when data are non-negative. Note that zero data can make the super-efficiency model under constant returns to scale (CRS) infeasible. Our discussion is based upon variable returns to scale (VRS) and can be applied to CRS super-efficiency models.     

Fuzzy data envelopment analysis (DEA): Model and ranking method

Data Envelopment Analysis (DEA) is a very effective method to evaluate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.     

Super-efficiency DEA in the presence of infeasibility

It is well known that super-efficiency data envelopment analysis (DEA) approach can be infeasible under the condition of variable returns to scale (VRS). By extending of the work of Chen (2005), the current study develops a two-stage process for calculating super-efficiency scores regardless whether the standard VRS super-efficiency mode is feasible or not. The proposed approach examines whether the standard VRS super-efficiency DEA model is infeasible. When the model is feasible, our approach yields super-efficiency scores that are identical to those arising from the original model. For efficient DMUs that are infeasible under the super-efficiency model, our approach yields super-efficiency scores that characterize input savings and/or output surpluses. The current study also shows that infeasibility may imply that an efficient DMU does not exhibit super-efficiency in inputs or outputs. When infeasibility occurs, it can be necessary that (i) both inputs and outputs be decreased to reach the frontier formed by the remaining DMUs under the input-orientation and (ii) both inputs and outputs be increased to reach the frontier formed by the remaining DMUs under the output-orientation. The newly developed approach is illustrated with numerical examples.     

Measuring overall efficiency and effectiveness using DEA

This paper presents a framework where data envelopment analysis (DEA) is used to measure overall efficiency and show how to apply this framework to assess effectiveness for more general behavioral goals. The relationships between various cone-ratio DEA models and models to measure overall efficiency are clarified. Specifically it is shown that as multiplier cones tighten, the cone-ratio DEA models converge to measures of overall efficiency. Furthermore, it is argued that multiplier cone and cone-ratio model selection must be consistent with the behavioral goals assigned or assumed for purposes of analysis. Consistent with this reasoning, two new models are introduced to measure effectiveness when value measures are represented by separable or linked cones, where the latter can be used to analyze profit-maximizing effectiveness.     

Super-efficiency DEA in the presence of infeasibility: One model approach

A two-stage procedure is developed by Lee et al. (2011) [European Journal of Operational Research doi:10.1016/j.ejor.2011.01.022] to address the infeasibility issue in super-efficiency data envelopment analysis (DEA) models. We point out that their two-stage procedure can be solved in a single DEA-based model.     

An ellipsoidal frontier model: Allocating input via parametric DEA

This paper presents the ellipsoidal frontier model (EFM), a parametric data envelopment analysis (DEA) model for input allocation. EFM addresses the problem of distributing a single total fixed input by assuming the existence of a predefined locus of points that characterizes the DEA frontier. Numeric examples included in the paper show EFM’s capacity to allocate shares of the total fixed input to each DMU so that they will all become efficient. By varying the eccentricities, input distribution can be performed in infinite ways, gaining control over DEA weights assigned to the variables in the model. We also show that EFM assures strong efficiency and behaves coherently within the context of sensitivity analysis, two properties that are not observed in other models found in the technical literature.     

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 new DEA ranking system based on changing the reference set

This research proposes a new ranking system for extreme efficient DMUs (Decision Making Units) based upon the omission of these efficient DMUs from reference set of the inefficient DMUs. We state and prove some facts related to our model. A numerical example where the proposed method is compared with traditional ranking approaches is shown.     

DEA as a tool for bankruptcy assessment: A comparative study with logistic regression technique

This paper proposes data envelopment analysis (DEA) as a quick-and-easy tool for assessing corporate bankruptcy. DEA is a non-parametric method that measures weight estimates (not parameter estimates) of a classification function for separating default and non-default firms. Using a recent sample of large corporate failures in the United States, we examine the capability of DEA in assessing corporate bankruptcy by comparing it with logistic regression (LR). We find that DEA outperforms LR in evaluating bankruptcy out-of-sample. This feature of DEA is appealing and has practical relevance for investors. Another advantage of DEA over LR is that it does not have assumptions associated with statistical and econometric methods. Furthermore, DEA does not need a large sample size for bankruptcy evaluation, usually required by such statistical and econometric approaches. The need for such a large sample size is a significant disadvantage to practitioners when investment decisions are made using small samples. DEA can bypass such a difficulty related to a sample size. Thus, DEA is a practically appealing method for bankruptcy assessment.     

Equivalence in two-stage DEA approaches

Data envelopment analysis (DEA) is a linear programming problem approach for evaluating the relative efficiency of peer decision making units (DMUs) that have multiple inputs and outputs. DMUs can have a two-stage structure where all the outputs from the first stage are the only inputs to the second stage, in addition to the inputs to the first stage and the outputs from the second stage. The outputs from the first stage to the second stage are called intermediate measures. This paper examines relations and equivalence between two existing DEA approaches that address measuring the performance of two-stage processes.     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.     

Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market

We propose a way of using DEA cross-efficiency evaluation in portfolio selection. While cross efficiency is an approach developed for peer evaluation, we improve its use in portfolio selection. In addition to (average) cross-efficiency scores, we suggest to examine the variations of cross-efficiencies, and to incorporate two statistics of cross-efficiencies into the mean-variance formulation of portfolio selection. Two benefits are attained by our proposed approach. One is selection of portfolios well-diversified in terms of their performance on multiple evaluation criteria, and the other is alleviation of the so-called “ganging together” phenomenon of DEA cross-efficiency evaluation in portfolio selection. We apply the proposed approach to stock portfolio selection in the Korean stock market, and demonstrate that the proposed approach can be a promising tool for stock portfolio selection by showing that the selected portfolio yields higher risk-adjusted returns than other benchmark portfolios for a 9-year sample period from 2002 to 2011.     

Selecting non-zero weights to evaluate effectiveness of basketball players with DEA

In this paper, we show how DEA may be used to identify component profiles as well as overall indices of performance in the context of an application to assessments of basketball players. We go beyond the usual uses of DEA to provide only overall indexes of performance. Our focus is, instead, on the multiplier values for the efficiently rated players. For this purpose we use a procedure that we recently developed that guarantees a full profile of non-zero weights, or “multipliers.” We demonstrate how these values can be used to identify relative strengths and weaknesses in individual players. Here we also utilize the flexibility of DEA by introducing bounds on the allowable values to reflect the views of coaches, trainers and other experts on the basketball team for which evaluations are being conducted. Finally we show how these combinations can be extended by taking account of team as well as individual considerations.     

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

非期望产出的DEA效率评价

将非期望产出作为投入应用到传统DEA模型上,解决了非期望产出生产活动的效率评价问题.结合生产可能集,将非期望产出直接反映到生产可能集中,建立了基于投入导向的径向和非径向两种DEA模型.并对两种DEA模型效率值的大小关系、相对有效性的等价性问题进行了证明,指出非径向DEA模型更能准确的实现效率定量评价.     

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.