Handling negative data in slacks-based measure data envelopment analysis models
TL;DR: The proposed SBM DEA models are consistent with ordinary SBM models and units invariant, they handle various types of returns to scale, and they avoid division by zero.
About: This article is published in European Journal of Operational Research.The article was published on 2020-05-01. It has received 43 citations till now. The article focuses on the topics: Data envelopment analysis.
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TL;DR: This paper modifies the SBM model which measures SBM-efficiency score for inefficient DMUs and SupSBM- efficiency score for strong efficient DMUs, simultaneously, simultaneously and demonstrates the superiority of this model over the existing models with various problem sizes.
68 citations
TL;DR: In this article, a composite super-efficiency index was proposed to resolve the problem of zero data and negative data in the SBM and Super-SBM models, where the input savings and output surpluses are incorporated into the Modified Nonpositive SBM so that the Pareto efficient projection can be determined.
Abstract: SBM and Super-SBM models will not function correctly when zero data or negative data appear in the inputs or outputs. This paper generalizes the SBM model and Super-SBM model so that zero data and negative data can be dealt with. Nonpositive SBM extends SBM, and Nonpositive Super-SBM extends Super-SBM. Both Nonpositive SBM and Nonpositive Super-SBM can deal with negative data and zero data. If the data are positive, Nonpositive SBM and Nonpositive Super-SBM are the same as SBM and Super-SBM, respectively. Nonpositive Super-SBM does not guarantee that the projection is Pareto efficient. A two-stage approach like that in [7] is proposed to resolve this issue. Nonpositive Super-SBM is employed to identify input savings and output surpluses, which are incorporated into the Modified Nonpositive SBM so that the Pareto efficient projection can be determined. The super-efficiency measure proposed by Fang et al. [7] and Lin et al. [11] do not account for the slacks identified at the second stage when the super-efficiency obtained at the first stage is larger than one. We will propose a composite super-efficiency index to resolve such issue.
17 citations
TL;DR: A distance-based analytic hierarchy process/data envelopment analysis (AHP-DEA) super-efficiency approach was proposed and applied to adapt DEA to the needs of predefined groups by using slack variables.
Abstract: Existing research on electric bike sharing systems (e-BSS) emphasises the importance of the sustainability of the systems and the need to respect the views of all stakeholders when planning e-BSS. However, this research overlooks the fact that the sustainability of e-BSS depends to a large extent on the skills and knowledge of the parties who select an electric bike provider, which in most cases is the investor in the e-BSS. There is no previous paper that provides support for investors in (1) defining a set of criteria for selecting a provider that takes into account all of the three domains of sustainability (economic, social, and environmental) and (2) developing a tool that best meets sustainability standards on the one hand and the needs and requirements of all stakeholders (including e-bike users and investors) on the other hand. A distance-based analytic hierarchy process/data envelopment analysis (AHP-DEA) super-efficiency approach was proposed and applied to adapt DEA to the needs of predefined groups by using slack variables. The approach takes into account the fact that not all outputs have a positive impact on the final outcome; the approach also allows decision-makers to define the hierarchical structure of the importance of the criteria directly based on the responses of the selected group. A case study in Slovenia illustrated the application of the approach.
16 citations
TL;DR: In this paper, the authors used the Weighted Russel Directional Distance approach and established an equivalence model between this Data Envelopment Analysis model and the super-ideal point model, which was then combined with an interactive algorithm.
Abstract: This paper is aimed at casting new light on the assessment of secondary schools’ performance in Portugal by considering data from the Programme for International Student Assessment 2015. We use the Weighted Russel Directional Distance approach and establish an equivalence model between this Data Envelopment Analysis model and the super-ideal point model, which is then combined with an interactive algorithm. Besides, a procedure to perform robustness analysis has been proposed, allowing decision-makers to understand how sensitive the efficiency of each school to data variation is. Overall, our findings suggest that the average efficient public school has mean scores across all competences above the scores attained by the average public national school, but below the OECD average. In addition, we have concluded that schools operating with the lowest efficiency scores usually need to make a greater effort to improve results in reading when compared to maths and science competences. Finally, schools more often selected as a reference in terms of best practices and which are classified as robust in terms of efficiency are not necessarily performing with high test results, highlighting the need of seeking new benchmarks more consistent with the preferences of the decision-maker.
12 citations
TL;DR: This research aims at developing nested dynamic network DEA models, an additive model being nested within a slacks-based measure (SBM) DEA model, that explicitly utilizes the information in each individual time period to fully and simultaneously measure the multi-period efficiency of a portfolio and its comprised financial assets.
12 citations
Cites methods from "Handling negative data in slacks-ba..."
...(2016), the SBM dynamic DEA models with network structure proposed in Tone and Tsutsui (2014), and the additive DEA models proposed in Charnes et al....
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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
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].
2,575 citations
31 Jan 2001
TL;DR: In this paper, the slacks-based measure (SBM) of efficiency was proposed to discriminate the efficient decision making units (DMUs) based on the existence of slacks.
Abstract: In most models of Data Envelopment Analysis (DEA), the best performers have the full efficient status denoted by unity (or 100%), and, from experience, we know that usually plural Decision Making Units (DMUs) have this “efficient status”. To discriminate between these efficient DMUs is an interesting subject. This paper addresses this “super-efficiency” issue 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]. The method differs from the traditional one based on the radial measure, e.g. Andersen and Petersen model, in that the former deals directly with slacks in inputs/outputs, while the latter does not take account of the existence of slacks. We will demonstrate the rationality of our approach by comparing it with the radial measure of super-efficiency. The proposed method will be particularly useful when the number of DMUs are small compared with the number of criteria employed for evaluation.
1,979 citations
TL;DR: In this paper, the additive model of DEA is developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure) and the need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in l 1, or weighted l 1 measure) and thereby simultaneously maximize outputs and minimize inputs.
Abstract: Generalized Efficiency Measures (GEMS) for use in DEA are developed and analyzed in a context of differing models where they might be employed. The additive model of DEA is accorded a central role and developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure). The need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in l1, or weighted l1, measure) and thereby simultaneously maximize outputs and minimize inputs. Contacts with other models and approaches are maintained with theorems and accompanying proofs to ensure the validity of the thus identified relations. New criteria are supplied, both managerial and mathematical, for evaluating proposed measures. The concept of “approximating models” is used to further extend these possibilities. The focus of the paper is on the “physical” aspects of performance involved in “technical” and “mix” inefficiencies. However, an Appendix shows how “overall,” “allocative” and “technical” inefficiencies may be incorporated in additive models.
632 citations