A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach (original) (raw)
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A slacks-based measure of super-efficiency in data envelopment analysis: A comment
European Journal of Operational Research, 2010
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 ]. 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.
Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis
Omega
In this paper, we develop an integrated model for slacks-based measure (SBM) simultaneously of both the eciency and the super-eciency for decision-making units (DMUs) in data envelopment analysis (DEA). Unlike the traditional solution approaches in which we need to identify the ecient DMUs by the SBM model of Tone [20] before applying the super SBM model of Tone [21] for the DMUs to achieve their super-eciency scores, our integration can obtain the eciency scores of the inecient DMUs and the super-eciency scores of the ecient DMUs by solving simultaneously these two models by an onestage approach. Therefore, it may save computational time for large-scale practical applications. Due to the non-linearity in the objective function of this integrated model, we develop a linearisation technique to deal with the non-linear model. The numerical experiments, carried out on several examples in the literature and a case study, have demonstrated the accuracy and the computational time eectiveness of our proposed model as compared with the traditional solution approaches.
A super-efficiency model for ranking efficient units in data envelopment analysis
Applied Mathematics and Computation, 2007
Data envelopment analysis (DEA) is a body of research methodologies to evaluate overall efficiencies and identify the sources and estimate the amounts of inefficiencies in inputs and outputs. In DEA, the best performers are called DEA efficient and the efficiency score of a DEA efficient unit is denoted by an unity. In the last decade, ranking DEA efficient units has become the interests of many DEA researchers and a variety of models (called super-efficiency models) were developed to rank DEA efficient units. While the models developed in the past are interesting and meaningful, they have the disadvantages of being infeasible or instable occasionally. In this research, we develop a super-efficiency model to overcome some deficiencies in the earlier models. Both theoretical results and numerical examples are provided.
A slacks-based measure of efficiency in data envelopment analysis
European Journal of Operational Research, 2001
In this paper, we will propose a Slacks-Based measure (SBM) of efficiency in DEA. This scalar measure deals directly with the input surplus and the output shortage of the decision making unit (DMU) concerned. It is unit invariant and monotone decreasing with respect to input surplus and output shortage. Furthermore, this measure is decided only by consulting with the reference set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., CCR and BCC. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.
The Scientific World Journal, 2014
There are a number of methods for ranking decision making units (DMUs), among which calculating super efficiency and then ranking the units based on the obtained amount of super efficiency are both valid and efficient. Since most of the proposed models do not provide the projection of Pareto efficiency, a model is developed and presented through this paper based on which in the projection of Pareto-efficient is obtained, in addition to calculating the amount of super efficiency. Moreover, the model is unit invariant, and is always feasible and makes the amount of inefficiency effective in ranking.
Computers & Industrial Engineering, 2015
Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decisionmaking units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.
Components of efficiency evaluation in data envelopment analysis
European Journal of Operational Research, 1995
This paper examines three essential components which comprise efficiency evaluation in data envelopment analysis. The three components are present in each DEA model and determine the implicit evaluation scheme associated with the model. These components provide a framework for classifying the various DEA models with respect to (i) the form of envelopment surface, (ii) the orientation, and (iii) the pricing mechanism implicit in the multiplier lower bounds. The discussion focuses on the standard DEA models, includes additional issues relating to efficiency evaluation, and is illustrated by a computational example.
A new model to Measuring efficiency and returns to scale on Data Envelopment Analysis
International Journal of Research, 2021
We extend the concept of returns to scale in Data Envelopment Analysis (DEA) to the weight restriction environments. By adding weight restrictions, the status of returns to scale, i.e. increasing, constant, and decreasing, may need a change. We first define "returns to scale" underweight restrictions and propose a method for identifying the status of returns to scale. Then, we demonstrated that this addition would usually narrow the region of the most productive scale size (MPSS). Finally, for an inefficient decision-making unit (DMU), we will present a simple rule for determining the status of returns to the scale of its projected DMU. Here, we carry out an empirical study to compare the proposed method's results with the BCC model. In addition, we demonstrate the change in the MPSS for both models. We have presented different models of DEA to determine returns to scale. Here, we suggested a model that determines the whole status to scale in decision-making units.Diff...
Journal of Global Optimization, 2011
Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. However, DEA does not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs. This research proposes a methodology to determine an Euclidean distance-based measure of super-efficiency. Then, the DMUs are ranked according to their super-efficiency score. The applicability of the proposed model is illustrated in the context of the analysis of gas companies performance.