Ranking efficient DMUs using the infinity norm and virtual inefficient DMU in DEA (original) (raw)
Related papers
Ranking Extreme and Non-Extreme Efficient Decision Making Units in Data Envelopment Analysis
2010
In evaluating decision making units (DMU) by using Data Envelopment Analysis (DEA) technique, it happens that more than one unit got efficiency score one. In such a case there should be some criterion for ranking these DMUs. Up to now, all of DEA model could rank only extreme efficient units. In this paper the authors proposed a method for ranking extreme and non extreme efficient units.
An approach to rank efficient DMUs in DEA based on combining Manhattan and infinity norms
2017
In many applications, discrimination among decision making units (DMUs) is a problematic technical task procedure to decision makers in data envelopment analysis (DEA). The DEA models unable to discriminate between extremely efficient DMUs. Hence, there is a growing interest in improving discrimination power in DEA yet. The aim of this paper is ranking extreme efficient DMUs in DEA based on exploiting the leave-one out idea and combining of Manhattan and infinity norms with constant and variable returns to scale. The proposed method has been able to overcome the existing difficulties in some ranking methods.
A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis
1999
The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.
A new approach for ranking efficient DMUs with data envelopment analysis
World Journal of Engineering, 2020
Purpose Classical models of data envelopment analysis (DEA) calculate the efficiency of decision-making units do not differentiate between efficient units. The purpose of this paper is to present a new method for ranking efficient units and compare it with the other methods presented in this field. Design/methodology/approach In this paper, a new method is presented for ranking efficient units. To validate the proposed method, a real case, which was studied by Li et al. (2016) is examined and the rankings of the efficient units are compared with four other methods including the Andersen and Petersen’s super-efficiency, game theory and the concept of Shapley value and the technique for order of preference by similarity to ideal solution methods. Findings The results show that there is a high correlation between the rankings of efficient units obtained by the new proposed method and the other methods such as Andersen and Petersen’s super-efficiency, game theory and Shapley value metho...
Applied Mathematical …, 2012
The inefficient DMUs are usually arranged after the technical efficient ones by DEA methods, however, it is possible that a technical efficient DMU neither be efficient nor be more efficient than some inefficient ones. This study distinguishes between the terms 'technical efficiency' and 'efficiency' and demonstrates that the technical efficiency is a necessary condition for being efficient and it is not an enough condition to call a DMU as efficient DMU. The study identifies the definitions of those terms and gives a new strong method to characterize efficient DMUs among the technical efficient ones. The new method, although, avoids the need for recourse to prices, weights or other assumptions between inputs and outputs of DMUs, it is also able to consider the prices and weights. A numerical example is also characterized the worth and benefits of the new proposed model in comparison with all current DEA models.
Prioritization Method for Non-Extreme Efficient Unitsin Data Envelopment Analysis
International Journal of Industrial Mathematics, 2009
Super e ciency data envelopment analysis(DEA) model can be used in ranking the performance of e cient decision making units(DMUs). In DEA, non-extreme e cient units have a super e ciency score one and the existing super e ciency DEA models do not provide a complete ranking about these units. In this paper, we will propose a method for ranking the performance of the extreme and non-extreme e cient units.
A New Method for Ranking Extreme Efficient DMUs Based on Changing the Reference Set Using L 2 -Norm
The purpose of this study is to utilize a new method for ranking extreme efficient decision making units (DMUs) based upon the omission of these efficient DMUs from reference set of inefficient and non-extreme efficient DMUs in data envelopment analysis (DEA) models with constant and variable returns to scale. In this method, an L 2 -norm is used and it is believed that it doesn't have any existing problems of such methods. Finally, two numerical examples for illustration and comparing the proposed method with other ranking approaches are presented.
Review of Ranking Models in Data Envelopment Analysis
2008
In the course of improving various abilities of data envelopment analysis (DEA) models, many investigations have been carried out for ranking decision-making units (DMUs). This is an important issue both in theory and practice. There exist a variety of papers which apply different ranking methods to a real data set. Here the ranking methods are divided into seven groups. As each of the existing methods can be viewed from different aspects, it is possible that somewhat these groups have an overlapping with the others. The first group conducts the evaluation by a cross-efficiency matrix where the units are self-and peer-evaluated. In the second one, the ranking units are based on the optimal weights obtained from multiplier model of DEA technique. In the third group, superefficiency methods are dealt with which are based on the idea of excluding the unit under evaluation and analyzing the changes of frontier. The fourth group involves methods based on benchmarking, which adopts the idea of being a useful target for the inefficient units. The fourth group uses the multivariate statistical techniques, usually applied after conducting the DEA classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The sixth approach involves multiple-criteria decision methodologies with the DEA technique. In the last group, some different methods of ranking units are mentioned.
A novel data envelopment analysis ranking based on a robust approach
2017
We propose a novel DEA ranking based on a robust optimization viewpoint: the higher ranking for those DMU's that remain efficient even for larger variations of data and vice versa. This ranking can be computed by solving generalized linear fractional programming problems, but we also present a tight linear programming approximation that preserves the order of rankings. We show some remarkable properties of our approach: It preserves the order of rankings compared to the classical approach. It is naturally normalized, so it can be used as universal ranking of DMU's of unrelated models. It gives ranking not only for inefficient, but also for efficient decision making units. It can also be easily extended to generalized model, for instance to deal with interval data. We present several examples confirming the desirable properties of the method.
A Review of Ranking Models in Data Envelopment Analysis
Journal of Applied Mathematics, 2013
In the course of improving various abilities of data envelopment analysis (DEA) models, many investigations have been carried out for ranking decision-making units (DMUs). This is an important issue both in theory and practice. There exist a variety of papers which apply different ranking methods to a real data set. Here the ranking methods are divided into seven groups. As each of the existing methods can be viewed from different aspects, it is possible that somewhat these groups have an overlapping with the others. The first group conducts the evaluation by a cross-efficiency matrix where the units are self- and peer-evaluated. In the second one, the ranking units are based on the optimal weights obtained from multiplier model of DEA technique. In the third group, super-efficiency methods are dealt with which are based on the idea of excluding the unit under evaluation and analyzing the changes of frontier. The fourth group involves methods based on benchmarking, which adopts the ...