A homothetic reference technology in data envelopment analysis

The assumption of a homothetic production function is often maintained in production economics. In this paper we explore the possibility of maintaining homotheticity within a nonparametric DEA framework. The main contribution of this paper is to use the approach suggested by Hanoch and Rothschild (1972) to define a homothetic reference technology. We focus on the largest subset of data points that is consistent with such a homothetic production function. We use the HR-approach to define a piecewise linear homothetic convex reference technology. We propose this reference technology with the purpose of adding structure to the flexible non-parametric BCC DEA estimator. Motivation for why such additional structure sometimes is warranted is provided. An estimation procedure derived from the BCC-model and from a maintained assumption of homotheticity is proposed. The performance of the estimator is analyzed using simulation.     

Forward search outlier detection in data envelopment analysis

In this paper we tackle the problem of outlier detection in data envelopment analysis (DEA). We propose a procedure where we merge the super-efficiency DEA and the forward search. Since DEA provides efficiency scores which are not parameters to fit the model to the data, we introduce a distance, to be monitored along the search. This distance is obtained through the integration of a regression model and the super-efficiency DEA. We simulate a Cobb-Douglas production function and we compare the super-efficiency DEA and the forward search analysis in both uncontaminated and contaminated settings. For inference about outliers, we exploit envelopes obtained through Monte Carlo simulations.     

Generalizing cross redundancy in data envelopment analysis

Lee and Choi (2010) proved that a cross redundant output in a CCR or BCC DEA study is unnecessary and can be eliminated from the model without affecting the results of the study. A cross redundant output, as characterized by Lee and Choi, can be expressed as a specially constrained linear combination of both some outputs and some inputs. This article extends the contributions of Lee and Choi (2010) in at least three ways: (i) by adding precision and clarity to some of their definitions; (ii) by introducing specific definitions that complement the ones in their paper; and (iii) by conducting some additional analysis on the impact of the presence of other types of linear dependencies among the inputs and outputs of a DEA model. One reason that it is important to identify and remove cross redundant inputs or outputs from DEA models is that the computational burden of the DEA study is decreased, especially in large applications.     

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.     

Equivalent solutions to additive two-stage network data envelopment analysis

In the additive approach of two-stage network data envelopment analysis (DEA), the non-linear DEA model is transformed into a parametric linear model and then solved by computing a series of linear programs. Lim and Zhu (2013; Integrated data envelopment analysis: Global vs. local optimum.European Journal of Operational Research, 229(1), 276–278) and Ang and Chen (2016; Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega, 58, 139–153) propose two parametric linear approaches to solve additive two-stage network DEA model. The current study shows that the two approaches are equivalent and use the same parameter in searching for the global optimal solution.     

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.     

Supply chain performance evaluation with data envelopment analysis and balanced scorecard approach

One of the most complicated decision making problems for managers is the evaluation of supply chain (SC) performance which involves various criteria. Though vast studies have been recorded on supply chain efficiency evaluation via balanced scorecard (BSC) approach, these studies do not focus on the relationships between the four perspectives of BSC approach. The present paper is an attempt focusing on these relationships, especially the returnable ones. To do so, at first, all relationships between the four perspectives of BSC were determined and then the DEMATEL approach was employed to obtain a network structure. This network structure was then used to create a network DEA model. Since it was not possible to calculate the efficiency evaluation score by BSC, the data envelopment analysis (DEA) model was used for such an evaluation. Moreover, after reviewing different tools to evaluate the performance of supply chain, a new approach, relying on network DEA with BSC approach, was generated. Finally, this model was applied in the Iranian food industry to evaluate its supply chains efficiency and the results proved the high efficiency of the model designed. The findings could be used in various evaluation processes in different industries.     

An effective transformation in ranking using l1-norm in data envelopment analysis

Jahanshahloo et al. [G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, S. Razavyan, Ranking using l₁-norm in data envelopment analysis, Applied Mathematics and Computation, 153 (2004) 215-224] present a method for ranking extremely efficient decision making units (DMUs) in data envelopment analysis (DEA) by exploiting the leave-one-out idea and l₁-norm. It is shown that the proposed method is able to remove the existing difficulties in some methods. This paper suggests an effective procedure to transfer the proposed model from the nonlinear programming form into a linear programming form. We show that the model with this transformation is equivalent to the nonlinear model, while it is much easier to solve than the treatment in [1].     

A bi-objective generalized data envelopment analysis model and point-to-set mapping projection

This work introduces a bi-objective generalized data envelopment analysis (Bi-GDEA) model and defines its efficiency. We show the equivalence between the Bi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set (PPS) and discuss the returns to scale under the Bi-GDEA model. The most essential contribution is that we further define a point-to-set mapping and the mapping projection of a decision making unit (DMU) on the frontier of the PPS under the Bi-GDEA model. We give an effective approach for the construction of the point-to-set-mapping projection which distinguishes our model from other non-radial models for simultaneously considering input and output. The Bi-GDEA model represents decision makers’ specific preference on input and output and the point-to-set mapping projection provides decision makers with more possibility to determine different input and output alternatives when considering efficiency improvement. Numerical examples are employed for the illustration of the procedure of point-to-set mapping.     

Performance evaluation: An integrated method using data envelopment analysis and fuzzy preference relations

In a multi-attribute decision-making (MADM) context, the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives. This paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations. This proposed approach includes three stages. First, pairwise efficiency scores are computed using two DEA models: the CCR model and the proposed cross-evaluation DEA model. Second, the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation. Third, by use of the row wise summation technique, we yield a priority vector, which is used for ranking decision-making units (DMUs). For the case of a single output and a single input, the preference relation can be directly obtained from the original sample data. The proposed approach is validated by two numerical examples.     

Benefit-cost analysis using data envelopment analysis

Benefit-cost analysis is required by law and regulation throughout the federal government. Robert Dorfman (1996) declares ‘Three prominent shortcomings of benefit-cost analysis as currently practiced are (1) it does not identify the population segments that the proposed measure benefits or harms (2) it attempts to reduce all comparisons to a single dimension, generally dollars and cents and (3) it conceals the degree of inaccuracy or uncertainty in its estimates.’ The paper develops an approach for conducting benefit-cost analysis derived from data envelopment analysis (DEA) that overcomes each of Dorfman's objections. The models and methodology proposed give decision makers a tool for evaluating alternative policies and projects where there are multiple constituencies who may have conflicting perspectives. This method incorporates multiple incommensurate attributes while allowing for measures of uncertainty. An application is used to illustrate the method. This work was funded by grant N00014-99-1-0719 from the Office of Naval Research     

Enhancement of equity portfolio performance using data envelopment analysis

This paper examines the applicability of data envelopment analysis (DEA) as a basis of selection criteria for equity portfolios. It is the first DEA application for constructing a combined equity investment strategy that aims to integrate the benefits of both value investing and momentum investing. The 3-quantile portfolios are composed of a comprehensive sample of Finnish non-financial stocks based on their DEA efficiency scores that are calculated using three variants of DEA models (the constant returns-to-scale, the super-efficiency, and the cross-efficiency models). The performance of portfolios is evaluated on the basis of the average return and several risk-adjusted performance metrics throughout the 1994–2010 sample period.     

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.     

An extension to data envelopment analysis with preference structure for estimating overall inefficiency

This paper extends data envelopment analysis (DEA) with preference structure by fully considering the substitution effects among different inputs or outputs. When the unit cost and price information on inputs and outputs are available, the generalized weighted CCR (GWCCR) models proposed in this paper can provide some scalar values for measuring the overall inefficiency. It is found that the GWCCR models focus on the relative aspects of overall inefficiency instead of the absolute aspects focused on by the weighted additive DEA model.     

Data envelopment analysis application in sustainability: The origins,development and future directions

Sustainable development and sustainability assessment have been of great interest to both academe and practitioners in the past decades. In this study, we review the literature on data envelopment analysis (DEA) applications in sustainability using citation-based approaches. A directional network is constructed based on citation relationships among DEA papers published in journals indexed by the Web of Science database from 1996 to March 2016. We first draw the citation chronological graph to present a complete picture of literature development trajectory since 1996. Then we identify the local main DEA development paths in sustainability research by assigning an importance index, namely search path count (SPC), to each link in the citation network. The local main path suggests that the current key route of DEA applications in sustainability focus on the environmental sustainability. Through the Kamada–Kawai layout algorithm, we find four research clusters in the literature including corporate sustainability assessment, regional sustainability assessment, sustainability composite indicator construction, and sustainability performance analysis. For each of the clusters, we further identify the key articles based on citation network and local citation scores, demonstrate the developmental trajectory of the literature, and suggest future research directions.     

A new clustering approach using data envelopment analysis

In this paper, we present a new clustering method that involves data envelopment analysis (DEA). The proposed DEA-based clustering approach employs the piecewise production functions derived from the DEA method to cluster the data with input and output items. Thus, each evaluated decision-making unit (DMU) not only knows the cluster that it belongs to, but also checks the production function type that it confronts. It is important for managerial decision-making where decision-makers are interested in knowing the changes required in combining input resources so it can be classified into a desired cluster/class. In particular, we examine the fundamental CCR model to set up the DEA clustering approach. While this approach has been carried for the CCR model, the proposed approach can be easily extended to other DEA models without loss of generality. Two examples are given to explain the use and effectiveness of the proposed DEA-based clustering method.     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis

An issue which has received widespread attention in rapidly growing field of DEA is the sensitivity of the results of analysis to perturbations in the data.     

A survey of data envelopment analysis in energy and environmental studies

Data envelopment analysis has gained great popularity in energy and environmental (E&E) modeling in recent years. In this paper, we present a literature survey on the application of data envelopment analysis (DEA) to E&E studies. We begin with an introduction to the most widely used DEA techniques, which is followed by a classification of 100 publications in this field. The main features observed are summarized. Issues related to the selection of DEA models in E&E studies are discussed.     

Efficiency decomposition in network data envelopment analysis: A relational model

Traditional studies in data envelopment analysis (DEA) view systems as a whole when measuring the efficiency, ignoring the operation of individual processes within a system. This paper builds a relational network DEA model, taking into account the interrelationship of the processes within the system, to measure the efficiency of the system and those of the processes at the same time. The system efficiency thus measured more properly represents the aggregate performance of the component processes. By introducing dummy processes, the original network system can be transformed into a series system where each stage in the series is of a parallel structure. Based on these series and parallel structures, the efficiency of the system is decomposed into the product of the efficiencies of the stages in the series and the inefficiency slack of each stage into the sum of the inefficiency slacks of its component processes connected in parallel. With efficiency decomposition, the process which causes the inefficient operation of the system can be identified for future improvement. An example of the non-life insurance industry in Taiwan illustrates the whole idea.