An integrated data envelopment analysis and simulation method for group consensus ranking (original) (raw)
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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...
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 ...
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.
Mathematical Sciences
The initial issue that must be addressed in teamwork is the manner in which decisions are made by the group and its members. Voting is a procedure to aggregate individual votes to achieve a collective decision. Since individuals have varied opinions and preferences, preferential voting assists in conveying the priorities of the voters to the society or community. In many circumstances, such as voting-based managerial decisions, voters are of a voting preference of unequal voting power. This paper presents a method for the ranking of preferential voting with voters of unequal voting power, which, in addition to the utilization of preference voting models, employs the DEA and assurance region techniques. The deployment of DEA technique causes an increment in the competence of discriminating the ranking of candidates, and in the finale the proposed method is expressed for an empirical example to rank the petrochemical companies in the Tehran Stock Exchange.
Review of ranking methods in the data envelopment analysis context
Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to im- prove the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical tech- niques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA ap- proach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.
A Ranking Method Based on Common Weights and Benchmark Point
The highest efficiency score 1 (100% efficiency) is regarded as a common benchmark for Decision Making Units (DMUs). This brings about the existence of more than one DMU with the highest score. Such a case normally occurs in all Data Envelopment Analysis (DEA) models and also in all the Common Set of Weights (CSWs) methods and it may lead to the lack of thorough ranking of DMUs. And ideal DMU based on its specific structure is a unit that no unit would do better than. Therefore, it can be utilized as a benchmark for other units. We are going to take advantage of this feature to introduce a linear programming problem that will produce CSWs. The proposed method assures that the efficiency of all the units is less than that of the benchmark unit. As a result, it provides a comprehensive ranking of DMUs. Moreover, the proposed method is also noteworthy regarding computation. A numerical example is suggested to clarify and explain the proposed method and compare it to two other CSWs methods. Finally, 33 universities in Iran were ranked and compared using the proposed method.
Groups performance ranking based on inefficiency sharing
International Journal of Industrial Mathematics, 2013
In the real world there are groups which composed of independent units. The conventional data envelopment analysis(DEA) model treats groups as units, ignoring the operation of individual units within each group.The current paper, investigates parallel system network approach proposed by Kao and modifies it. As modi ed Kao' model is more eligible to recognize ecient groups, a new ranking method is proposed based on a model which calculates eciencies with additional constraint that made model share constant ineciency among groups.To show advantages, modi es model is applied to eciency calculation of both arti cial and real groups and results is compared with conventional DEA model and parallel system network model as well.Finally it is shown by tow numerical and empirical examples that ecient groups recognized by modi ed model how can be ranked according to proposed ranking model.
International Journal of Academic Research in Business and Social Sciences, 2021
Globally, insurance and takaful companies play a crucial role in economic and financial development of a country. Malaysia's insurance sector has undergone substantial changes compared to two decades ago. Due to intense competition observed in Malaysian insurance industry, efficiency measurement and a complete efficiency ranking of insurance companies are very important for the decision makers so that necessary changes and improvement can be made. Data Envelopment Analysis (DEA) is a non-parametric method that has been acknowledged as an effective method to measure the efficiency of homogeneous decisionmaking units (DMUs). The main advantage of DEA is its ability to handle multiple inputs and outputs. However, standard DEA has poor discrimination power since it generates too many efficient units especially when the number of DMUs under study is insufficient in comparison to number of inputs and outputs. It cannot discriminate efficient units and therefore unable to give a complete ranking of DMUs. This study aimed to overcome the ranking problem found in standard DEA by integrating DEA and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) II. The hybrid method was applied to evaluate the efficiency and ranking of 22 life insurance and takaful companies in Malaysia from the period of 2017 to 2018. Input variables used in this study comprised of fees and commission, and management expenses. Meanwhile, output variables were net premium and generated investment income. The proposed method involved two stages. In the first stage, DEA was applied to obtain the efficient scores for the DMUs. In the second stage, PROMETHEE II was implemented to rank the efficient units. This hybrid method has successfully obtained full ranking of all the insurance companies under study. The inefficient companies can learn strategies and practices from efficient companies to enhance their services. It is recommended for future research to integrate DEA with other Multi Criteria Decision Making (MCDM) methods such as TOPSIS and VIKOR to fully rank the DMUs.
One DEA ranking method based on applying aggregate units
Expert Systems with Applications, 2011
Data envelopment analysis (DEA) initiated in 1978 by Charnes, Cooper and Rhodes (henceforth CCR model) is a powerful mathematical tool to evaluate the relative efficiency of DMUs (Decision Making Units). In these last decades, the DEA as a powerful approach has been very popular into different contexts, but despite its popularity, it cannot provide adequate information in its initial framework to discriminate between all efficient DMUs. So lately, invention of and pay attention to different approaches to mitigate and eliminate this flaw has been very significant. In this paper a ranking method is revealed based on investigating some effects relative to deletion of an efficient DMU on another efficient ones. To this end, some artificial units called aggregate units are defined. Moreover, two numerical examples illustrate how the proposed method works in actual practices in comparison with some other conventional ranking methods.