A survey of DEA applications

The literature of data envelopment analysis (DEA) encompasses many surveys, yet all either emphasize methodologies or do not make a distinction between methodological and application papers. This study is the first literature survey that focuses on DEA applications, covering DEA papers published in journals indexed by the Web of Science database from 1978 through August 2010. The results show that on the whole around two-thirds (63.6%) of DEA papers embed empirical data, while the remaining one-third are purely-methodological. Purely-methodological articles dominated the first 20 years of DEA development, but the accumulated number of application-embedded papers caught up to purely-methodological papers in 1999. Among the multifaceted applications, the top-five industries addressed are: banking, health care, agriculture and farm, transportation, and education. The applications that have the highest growth momentum recently are energy and environment as well as finance. In addition to the basic statistics, we uncover the development trajectory in each application area through the main path analysis. An observation from these works suggests that the two-step contextual analysis and network DEA are the recent trends across applications and that the two-step contextual analysis is the prevailing approach.     

Data envelopment analysis 1978–2010: A citation-based literature survey

This study surveys the data envelopment analysis (DEA) literature by applying a citation-based approach. The main goals are to find a set of papers playing the central role in DEA development and to discover the latest active DEA subareas. A directional network is constructed based on citation relationships among academic papers. After assigning an importance index to each link in the citation network, main DEA development paths emerge. We examine various types of main paths, including local main path, global main path, and multiple main paths. The analysis result suggests, as expected, that Charnes et al. (1978) [Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research 1978; 2(6): 429–444] is the most influential DEA paper. The five most active DEA subareas in recent years are identified; among them the “two-stage contextual factor evaluation framework” is relatively more active. Aside from the main path analysis, we summarize basic statistics on DEA journals and researchers. A growth curve analysis hints that the DEA literature’s size will eventually grow to at least double the size of the existing literature.     

A data envelopment analysis approach for ranking journals

We create a data envelopment analysis (DEA) model to rank business journals, using data from the Thomson Reuters Journal Citation Reports^® (JCR). As opposed to previous models that ranked journals in only one field and mostly relied on survey data, this model is used to rank 358 business journals from five different JCR categories according to such citation-based factors as the number of articles, the number of citations, impact factor, five-year impact factor, immediacy index, eigenfactor score, and article influence score. We compute relative efficiencies of the journals and thereby create plausible journal rankings that largely, but not completely, corroborate three widely used business publication journal ranking lists. In addition, we show how the different characteristics of the JCR data impact the DEA ranking model. Finally, we identify journals that are not on the business publication lists but consistently perform very well relative to those benchmark journals, and should possibly be included in the business publication ranking lists. We also identify journals whose inclusion in widely used business publication rankings cannot be justified by our methodology.     

Efficiency decomposition in network data envelopment analysis with slacks-based measures

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted much attention for its ability to provide suitable efficiency measures, especially for weakly efficient production units. This paper proposes a general SBM model for network systems, and is able to decompose the system efficiency into a weighted average of the process efficiencies. This relationship holds for all types of network structure. An example shows that the network model has stronger discriminating power than the conventional black-box model, and the system efficiency is indeed a weighted average of the process efficiencies. The decomposition of the system efficiency helps identify key factors to improve the performance of a production unit.     

Diversification-consistent data envelopment analysis based on directional-distance measures

We propose new diversification-consistent DEA models suitable for assessing efficiency of investment opportunities available on financial markets. The formulations based on directional distance measures enable to use several risk measures as inputs and return measures as outputs, which can take both positive and negative values. We show that various models with different strength can be obtained and strongly, semi-strongly or weakly Pareto–Koopmans efficient investment opportunities can be identified. Moreover, the optimal solutions correspond to efficient investment opportunities and can be used by investors to revise the inefficient ones. If we consider discretely distributed returns, we can prove that under proper choice of the inputs (CVaRs) and outputs (expected return), the strongest model is able to identify efficient investment opportunities with respect to the second-order stochastic dominance. Moreover, the model can be formulated as a linear programming problem. In the numerical study, the proposed DEA models are applied to 48 representative industry portfolios from US stock markets.     

Evaluation of bank branch growth potential using data envelopment analysis

Banks occasionally employ frontier efficiency analyses to objectively identify best practices within their organizations. Amongst such methods, Data Envelopment Analysis (DEA) was found to be one of the leading approaches. DEA has been successfully applied in many bank branch performance evaluations using traditional intermediation, profitability and production approaches. However, there has been little focus on assessing the growth potential of individual branches.This research presents five models that examine three perspectives of branch growth. Each model was applied to the branch network of one of Canada׳s top five banks to gauge the growth potential of individual branches and to provide tailored improvement recommendations. Using various analysis methodologies, the results of each model were examined and their functionality assessed.     

A survey on bank branch efficiency and performance research with data envelopment analysis

The banking industry has been the object of DEA analyses by a significant number of researchers and probably is the most heavily studied of all business sectors. Various DEA models have been applied in performance assessing problems, and the banks' complex production processes have further motivated the extension and improvement of DEA techniques. This paper surveys 80 published DEA applications in 24 countries/areas that specifically focus on bank branches. Key issues related to the design of DEA models in these studies are discussed. Much advice is included on how to design future experiments and studies in this domain. A number of areas where further research could be fruitful are suggested.     

Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

Kuosmanen and Kazemi Matin [Theory of integer valued data envelopment analysis. European Journal of Operational Research 2009;192:658–67] developed an axiomatic foundation for a data envelopment analysis (DEA) model that assumes subsets of input and output variables to be integer valued. In this paper we extend and generalize the axiomatic foundation for the integer DEA under variable, non-decreasing and non-increasing returns to scale. These model variants are achieved by introducing new axioms of natural convexity and natural augmentability. We also develop mixed integer linear programming (MILP) formulations for computing efficiency scores in these environments. An empirical example illustrates the approach.     

Comparing products using data envelopment analysis

Using an application of linear programming known as Data Envelopment Analysis (DEA), a method is described to compare products which vary in excellence along a number of dimensions, and for each of which there might be a number of associated “costs”. The method is illustrated by comparing published benchmarks of 37 computer printers. Potential uses of a DEA analysis of products might be: to assist corporate buyers who may need to reconcile a diversity of present and future uses in one standardised purchase; in competitor analysis; in determining unexplored market niches; and as a normative model of product excellence against which product purchasing behaviour could be compared.     

A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach

The current paper proposes a slack-based version of the Super SBM, which is an alternative super-efficiency model for the SBM proposed by Tone. Our two-stage approach provides the same super-efficiency score as that obtained by the Super SBM model when the evaluated DMU is efficient and yields the same efficiency score as that obtained by the SBM model when the evaluated DMU is inefficient. The projection identified by the Super SBM model may not be strongly Pareto efficient; however, the projection identified from our approach is strongly Pareto efficient.     

Applying data envelopment analysis on accounting data to assess and optimize the efficiency of Greek local governments

The efficiency and effectiveness of local governments has become one of the main points of interest in public sector administration, as decision and policy making gradually move from the central to the local level. This paper introduces an efficiency analysis framework based on accrual accounting data obtained from the local governments’ financial statements. Data envelopment analysis is used to obtain efficiency estimates, which are analyzed through a second stage regression against a set of efficiency explanatory factors. Furthermore, the optimal reallocation of the municipalities’ inputs and outputs is explored to provide policy recommendations that a central government could implement in a budget reduction context. Detailed empirical results are presented from a panel data set of Greek municipalities over the period 2002–2009.     

Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems

Genetic algorithm (GA) approach is developed for solving the P-model of chance constrained data envelopment analysis (CCDEA) problems, which include the concept of “Satisficing”. Problems here include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. The basic solution technique for the above has so far been deriving “deterministic equivalents”, which is difficult for all stochastic parameters as there are no compact methods available. In the proposed approach, the stochastic objective function and chance constraints are directly used within the genetic process. The feasibility of chance constraints are checked by stochastic simulation techniques. A case of Indian banking sector has been presented to illustrate the above approach.     

Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks

In measuring the overall efficiency of a set of decision making units (DMUs) in a time span covering multiple periods, the conventional approach is to use the aggregate data of the multiple periods via a data envelopment analysis (DEA) technique, ignoring the specific situation of each period. This paper proposes using a relational network model to take the operations of individual periods into account in measuring efficiencies. The overall and period efficiencies of a DMU can be calculated at the same time. Notably, the overall efficiency is a weighted average of the period efficiencies, and the weights are the most favorable ones for the DMU being evaluated. This model, together with two existing ones, is applied to measure the efficiency of 22 Taiwanese commercial banks for the period of 2009–2011. The three-year multi-period analysis shows that the proposed model is more discriminative than the existing ones in ranking the performance of the banks. The period efficiencies for the three years increased steadily, indicating that the performances of the Taiwanese banks examined in this work were improving over this period.     

Allocating a fixed cost based on data envelopment analysis and satisfaction degree

This paper uses the Data Envelopment Analysis (DEA) technique to solve the problem of allocating a fixed cost across a set of comparable decision making units (DMUs) in a fair way. It first investigates the effect of the fixed cost on each DMU and on the collection of DMUs. Next we prove that there exist some cost allocations which can make each DMU and the collection of DMUs efficient. We show that such a cost allocation is unique and equivalent to the proportional sharing method if the fixed cost allocation problem is a one-dimensional case. In a multidimensional case, the fixed cost allocations may not be unique. This paper defines the concept of satisfaction degree, and proposes a maxmin model and a corresponding algorithm to generate a unique fixed cost allocation. Finally, the proposed approach has been applied to a data set from prior literature.     

Returns to scale vs. damages to scale in data envelopment analysis: An impact of U.S. clean air act on coal-fired power plants

This study proposes a use of Data Envelopment Analysis (DEA) to measure Returns to Scale (RTS) of US coal-fired power plants. The power plants produce not only desirable outputs (e.g., electricity) but also undesirable outputs (e.g., CO₂ and NO_x) as a result of their plant operations. Therefore, the proposed use of DEA also measures a new concept, or “DTS: Damages to Scale” (corresponding to RTS for undesirable outputs). Both scale measures discussed in this study are a quick-and-easy approach for assessing RTS and DTS, but not an exact method, because it does not consider a direct linkage between the two measures. This study applies the proposed approach to examine the legal validity of U.S. Clean Air Act (CAA). We find that the CAA has been legally effective and influential on the operation of coal-fired power plants in the United States because their plant operations belong to increasing RTS on a desirable output and increasing DTS on three undesirable outputs. The increasing DTS indicates a need for managerial improvement and/or engineering innovation such as advanced clean coal technology. This empirical result implies that U.S. federal and state governments need to expand the legal scope of CAA to the emission control of CO₂ because the current CAA excludes the regulation on CO₂ emission that is now considered as a main source of the global warming and climate change.     

Incorporating quality into data envelopment analysis of nursing home performance: A case study

When using data envelopment analysis (DEA) as a benchmarking technique for nursing homes, it is essential to include measures of the quality of care. We survey applications where quality has been incorporated into DEA models and consider the concerns that arise when the results show that quality measures have been effectively ignored. Three modeling techniques are identified that address these concerns. Each of these techniques requires some input from management as to the proper emphasis to be placed on the quality aspect of performance. We report the results of a case study in which we apply these techniques to a DEA model of nursing home performance. We examine in depth not only the resulting efficiency scores, but also the benchmark sets and the weights given to the input and output measures. We find that two of the techniques are effective in insuring that DEA results discriminate between high and low quality performance.     

Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture

In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (J Oper Res Soc 2004;55:1311–22). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches.     

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.     

Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis

This paper proposes a new method to measure productivity change of decision making units in the full input-output space. The new approach is based on the calculation of the least distance to the Pareto-efficient frontier and hence provides the closest targets for evaluated decision making units to reach the strongly efficient frontier with least effort. Another advantage of the new methodology is that it always leads to feasible solutions. The productivity change in the new approach is operationalized as a Luenberger-type indicator in the Data Envelopment Analysis framework and it is decomposed into efficiency change and technical change. The paper empirically illustrates the new method using recent data on the Spanish quality wine sector.     

A multicriteria sorting approach based on data envelopment analysis for R&D project selection problem

In this paper, multiple criteria sorting methods based on data envelopment analysis (DEA) are developed to evaluate research and development (R&D) projects. The weight intervals of the criteria are obtained from Interval Analytic Hierarchy Process and employed as the assurance region constraints of models. Based on data envelopment analysis, two threshold estimation models, and five assignment models are developed for sorting. In addition to sorting, these models also provide ranking of the projects. The developed approach and the well-known sorting method UTADIS are applied to a real case study to analyze the R&D projects proposed to a grant program executed by a government funding agency in 2009. A five level R&D project selection criteria hierarchy and an assisting point allocation guide are defined to measure and quantify the performance of the projects. In the case study, the developed methods are observed to be more stable than UTADIS.