A slacks-based measure of super-efficiency in data envelopment analysis
01 May 2001-European Journal of Operational Research (EUROPEAN JOURNAL OF OPERATIONAL RESEARCH)-Vol. 143, Iss: 1, pp 32-41
TL;DR: This paper addresses the "super-efficiency" issue of Data Envelopment Analysis by using the slacks-based measure (SBM) of efficiency, which the author proposed in his previous paper [European Journal of Operational Research 130 (2001) 498].
About: This article is published in European Journal of Operational Research.The article was published on 2001-05-01 and is currently open access. It has received 2575 citations till now. The article focuses on the topics: Data envelopment analysis.
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TL;DR: A sketch of some of the major research thrusts in data envelopment analysis (DEA) over the three decades since the appearance of the seminal work of Charnes et al. is provided.
1,390 citations
Cites background from "A slacks-based measure of super-eff..."
...See Tone (2001), Cooper et al. (2001), Portela and Thanassoulis (2007), Portela et al. (2003), and others....
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...Tone (2001) introduced the so-called slacks-based measure (SBM) which is invariant to the units of measurement and is monotone increasing in each input and output slack....
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...It is shown in Tone (2001) that (2.9) can be transformed into a linear programming problem....
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TL;DR: A literature survey on the application of data envelopment analysis (DEA) to E&E studies is presented and an introduction to the most widely used DEA techniques is introduced.
1,068 citations
TL;DR: A slacks-based network DEA model is proposed, called Network SBM, that can deal with intermediate products formally and evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).
954 citations
TL;DR: In this article, the authors proposed a dynamic DEA model that incorporates carry-over activities into the DEA model and enables measuring period specific efficiency based on the long time optimization during the whole period.
Abstract: In data envelopment analysis, there are several methods for measuring efficiency changes over time, e.g. the window analysis and the Malmquist index. However, they usually neglect carry-over activities between two consecutive terms and only focus on the separate time period independently aiming local optimization in a single period, even if these models can take into account the time change effect. In the actual business world, a long time planning and investment is a subject of great concern. For these cases, single period optimization model is not suitable for performance evaluation. To cope with long time point of view, the dynamic DEA model incorporates carry-over activities into the model and enables us to measure period specific efficiency based on the long time optimization during the whole period. Dynamic DEA model proposed by Fare and Grosskopf is the first innovative contribution for such purpose. In this paper we develop their model in the slacks-based measure (SBM) framework, called dynamic SBM (DSBM). The SBM model is non-radial and can deal with inputs/outputs individually, contrary to the radial approaches that assume proportional changes in inputs/outputs. Furthermore, according to the characteristics of carry-overs, we classify them into four categories, i.e. desirable, undesirable, free and fixed. Desirable carry-overs correspond, for example, to profit carried forward and net earned surplus carried to the next term, while undesirable carry-overs include, for example, loss carried forward, bad debt and dead stock. Free and fixed carry-overs indicate, respectively, discretionary and non-discretionary ones. We develop dynamic SBM models that can evaluate the overall efficiency of decision making units for the whole terms as well as the term efficiencies.
701 citations
Cites methods from "A slacks-based measure of super-eff..."
...In this paper, we extend their model within the slacks-based measure framework proposed by Tone [17] and Pastor et al....
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TL;DR: In this article, the authors address several issues related to the use of data envelopment analysis (DEA), including model orientation, input and output selection/definition, use of mixed and raw data, and number of inputs and outputs to use versus the number of DMUs.
Abstract: 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.
654 citations
Cites background from "A slacks-based measure of super-eff..."
...If both input reduction and output enhancement are desirable goals in a particular application, then a slacks-based measure [26] may provide the appropriate model structure to capture a DMU's performance measure....
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References
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TL;DR: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.
25,433 citations
TL;DR: The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs as mentioned in this paper.
Abstract: In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."
14,941 citations
Book•
30 Nov 1999TL;DR: In this article, the basic CCR model and DEA models with restricted multipliers are discussed. But they do not consider the effect of non-discretionary and categorical variables.
Abstract: List of Tables. List of Figures. Preface. 1. General Discussion. 2. The Basic CCR Model. 3. The CCR Model and Production Correspondence. 4. Alternative DEA Models. 5. Returns to Scale. 6. Models with Restricted Multipliers. 7. Discretionary, Non-Discretionary and Categorical Variables. 8. Allocation Models. 9. Data Variations. Appendices. Index.
4,395 citations
"A slacks-based measure of super-eff..." refers background in this paper
...Refer to Tone (2001) and Cooper et al. (2000) for details....
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...In most models of Data Envelopment Analysis (DEA) (Charnes et al., 1978; Cooper et al., 2000), the best performers have efficiency score unity, and, from experience, we know that usually there are plural Decision Making Units (DMUs) which have this ‘‘efficient status’’....
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TL;DR: In this paper, a modified version of DEA based upon comparison of efficient DMUs relative to a reference technology spanned by all other units is developed, which provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods.
Abstract: Data Envelopment Analysis DEA evaluates the relative efficiency of decision-making units DMUs but does not allow for a ranking of the efficient units themselves. A modified version of DEA based upon comparison of efficient DMUs relative to a reference technology spanned by all other units is developed. The procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods.
3,320 citations
2,617 citations