Recent models in data envelopment analysis: Theory and applications

A critical review of the recent models of data envelopment analysis (DEA) is attempted here. Three new lines of approach involving dynamic changes in parameters, the error correction models and a stochastic sensitivity analysis are discussed in some detail. On the applications side, two new formulations are presented and discussed, e.g. a model of technical change and a cost frontier for testing economies of scale and adjustment due to risk factors. Thus the critical review of recent DEA models of productivity measurement provides new insight into the frontier of research in this field.     

Duality in data envelopment analysis under constant returns to scale

This paper explores duality in models of data envelopment analysis(DEA) for assessing the productive efficiencies of organizationalunits where efficient production is characterized by constantreturns to scale. The paper identifies dualityof the spacesin which efficiency is measured and discusses the practicalimplications of duality in DEA.     

Guidelines for using variable selection techniques in data envelopment analysis

Model misspecification has significant impacts on data envelopment analysis (DEA) efficiency estimates. This paper discusses the four most widely-used approaches to guide variable specification in DEA. We analyze efficiency contribution measure (ECM), principal component analysis (PCA-DEA), a regression-based test, and bootstrapping for variable selection via Monte Carlo simulations to determine each approach’s advantages and disadvantages. For a three input, one output production process, we find that: PCA-DEA performs well with highly correlated inputs (greater than 0.8) and even for small data sets (less than 300 observations); both the regression and ECM approaches perform well under low correlation (less than 0.2) and relatively larger data sets (at least 300 observations); and bootstrapping performs relatively poorly. Bootstrapping requires hours of computational time whereas the three other methods require minutes. Based on the results, we offer guidelines for effectively choosing among the four selection methods.     

Improving weak efficiency frontiers in the fuzzy data envelopment analysis models

Evaluating the performance of activities or organization by common data envelopment analysis models requires crisp input/output data. However, the precise inputs and outputs of production processes cannot be always measured. Thus, the data envelopment analysis measurement containing fuzzy data, called “fuzzy data envelopment analysis”, has played an important role in the evaluation of efficiencies of real applications. This paper focuses on the fuzzy CCR model and proposes a new method for determining the lower bounds of fuzzy inputs and outputs. This improves the weak efficiency frontiers of the corresponding production possibility set. Also a numerical example illustrates the capability of the proposed method.     

Returns to scale in multiplicative models in data envelopment analysis

One class of models introduced in DEA is called multiplicative models, in which, as shown by Banker and Maindiratta (Manag. Sci. 32:126–135, 1986), the piecewise linear frontiers usually employed in DEA are replaced by a frontier that is piecewise Cobb-Douglas(=log  linear). Banker and Maindiratta (Manag. Sci. 32:126–135, 1986) introduced a model to identify the most productive scale size pattern, and Banker et al. (Eur. J. Oper. Res. 154:345–362, 2004) presented a two-stage method for the identification of returns to scale (RTS) in multiplicative models. In this paper it is shown that both the RTS situation and the MPSS pattern could be determined by a single model in one step. The new method is important in the computational point of view.     

E-DEA: Enhanced data envelopment analysis

Data envelopment analysis (DEA) has enjoyed a wide range of acceptance by researchers and practitioners alike as an instrument of performance analysis and management since its introduction in 1978. Many formulations and thousands of applications of DEA have been reported in a considerable variety of academic and professional journals all around the world. Almost all of the formulations and applications have basically centered at the concept of “relative self-evaluation”, whether they are single or multi-stage applications. This paper suggests a framework for enhancing the theory of DEA through employing the concept of “relative cross-evaluation” in a multi-stage application context. Managerial situations are described where such enhanced-DEA (E-DEA) formulations had actually been used and could also be potentially most meaningful and useful.     

Supplier selection by the pair of nondiscretionary factors-imprecise data envelopment analysis models

Discretionary models for evaluating the efficiency of suppliers assume that all criteria are discretionary, that is, controlled by the management of each supplier and varied at its discretion. These models do not assume supplier selection in the conditions that some factors are nondiscretionary. The objective of this paper is to propose a new pair of nondiscretionary factors-imprecise data envelopment analysis (NF-IDEA) models for selecting the best suppliers in the presence of nondiscretionary factors and imprecise data. A numerical example demonstrates the application of the proposed method.     

The explicit role of weight bounds in models of data envelopment analysis

In this paper, we suggest that weight bounds used in models of data envelopment analysis (DEA) can be assessed using production trade-offs between inputs and outputs. This development is based on a transformation of the envelopment DEA model to a special form, which exhibits an explicit link between weight bounds and production trade-offs. This allows us to specify the guidelines to the construction of weight bounds, which ensure that the envelopment form has a clear economic meaning. In this development, the radial efficiency measure retains its standard meaning as a technologically realistic improvement factor. This contrasts with the methods based on value judgements for which this traditional meaning of efficiency becomes void. We show that the exact economic meaning of the same weight bounds depends on the unit under the assessment and the orientation (input-minimization or output-maximization) of the model. The suggested approach is valid under the assumptions of constant and variable returns to scale.     

Sensitivity and stability analysis in data envelopment analysis

One of the topics of interest in data envelopment analysis (DEA) is sensitivity and stability and stability analysis of the specific decision making unit (DMU), which is under evaluation. In DEA, efficient DMUs are of primary importance as they define the efficient frontier. In this paper, we develop a new sensitivity analysis approach for the CCR, BCC and Additive models, when variations in the data are considered for a specific efficient DMU and the data for the remaining DMUs are assumed fixed.     

Dynamic data envelopment analysis: A relational analysis

This paper proposes a dynamic data envelopment analysis (DEA) model to measure the system and period efficiencies at the same time for multi-period systems, where quasi-fixed inputs or intermediate products are the source of inter-temporal dependence between consecutive periods. A mathematical relationship is derived in which the complement of the system efficiency is a linear combination of those of the period efficiencies. The proposed model is also more discriminative than the existing ones in identifying the systems with better performance. Taiwanese forests, where the forest stock plays the role of quasi-fixed input, are used to illustrate this approach. The results show that the method for calculating the system efficiency in the literature produces over-estimated scores when the dynamic nature is ignored. This makes it necessary to conduct a dynamic analysis whenever data is available.     

Modelling undesirable outputs with zero sum gains data envelopment analysis models

Data envelopment analysis (DEA) literature has proposed alternative models for performance assessment in the presence of undesirable outputs, such as pollutant emissions, where increased outputs imply reduced performance. However, the case where global equilibrium of outputs should be imposed has not yet been considered. We propose that the zero sum gains DEA (ZSG-DEA) models look especially suitable for treating equilibrium models, where the sum of the quantities produced by all decision-making units can be set as the upper admissible bound. This paper uses ZSG-DEA models to evaluate the carbon dioxide emission case study, which can be considered part of the Kyoto Protocol statement.     

Network data envelopment analysis: A review

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional black-box approach, where the operations of the component processes are ignored. This paper reviews studies on network DEA by examining the models used and the structures of the network system of the problem being studied. This review highlights some directions for future studies from the methodological point of view, and is inspirational for exploring new areas of application from the empirical point of view.     

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.     

Sensitivity and stability analysis in fuzzy data envelopment analysis

As a useful management and decision tool, data envelopment analysis (DEA) has become a pop area of research. One of the topics of interests in DEA is sensitivity and stability analysis of decision making units (DMUs). Due to the uncertainty of the data in real life, this paper will give some DEA models in fuzzy environment. It is followed by a series analysis of sensitivity and stability for all DMUs. Finally a numerical example will be presented to give an illustration of the sensitivity and stability analysis.     

Financial statement analysis: A data envelopment analysis approach

Ratio analysis is a commonly used analytical tool for verifying the performance of a firm. While ratios are easy to compute, which in part explains their wide appeal, their interpretation is problematic, especially when two or more ratios provide conflicting signals. Indeed, ratio analysis is often criticized on the grounds of subjectivity, that is the analyst must pick and choose ratios in order to assess the overall performance of a firm.In this paper we demonstrate that Data Envelopment Analysis (DEA) can augment the traditional ratio analysis. DEA can provide a consistent and reliable measure of managerial or operational efficiency of a firm. We test the null hypothesis that there is no relationship between DEA and traditional accounting ratios as measures of performance of a firm. Our results reject the null hypothesis indicating that DEA can provide information to analysts that is additional to that provided by traditional ratio analysis. We also apply DEA to the oil and gas industry to demonstrate how financial analysts can employ DEA as a complement to ratio analysis.     

Sensitivity and stability in stochastic data envelopment analysis

Sensitivity and stability for Banker's model of Stochastic Data Envelopment Analysis (SDEA) is studied in this paper. In the case of the DEA model, necessary and sufficient conditions to preserve the efficiency of efficient decision-making units (DMUs) and the inefficiency of inefficient DMUs are obtained for different perturbations of data in the model. The cases of perturbations of all inputs, of perturbations of output and of the simultaneous perturbations of output and all inputs are considered. An illustrative example is provided.