Practical benchmarking in DEA using artificial DMUs

This paper introduces two virtual decision making units (DMUs) called ideal DMU (IDMU) and anti-ideal DMU (ADMU) into the data envelopment analysis (DEA). The resultant DEA models are, respectively, referred to as the data envelopment analysis with ideal and anti-ideal decision making units. One evaluates DMUs from the viewpoint of the best possible relative efficiency, while the other evaluates them from the perspective of the worst possible relative efficiency. The two distinctive efficiencies are combined to form a comprehensive index called the relative closeness (RC) to the IDMU just like the well-known TOPSIS approach in multiple attribute decision making (MADM). The RC index is then used as the evidence of overall assessment of each DMU, based on which an overall ranking for all the DMUs can be obtained. Two numerical examples are provided to illustrate the applications of the proposed DEA models and the RC index.

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...

Advances in Decision Sciences, 2013

Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data. The least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study. Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution. Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating the effectiveness of this SDEA model.

2014

Data Envelopment Analysis (DEA) which is applied to evaluate the relative efficiency of decision making units (DMU), is a mathematical programming approach. The efficiency in the classical DEA is "the ratio of the sum of the weighted outputs to the sum of weighted inputs". In order to obtain the maximum efficiency score for each DMU under evaluation, different weights are assigned to the inputs and outputs of the DMU. Classical DEA models allow weight flexibility. Thus, zero weights can be assigned to some important inputs and outputs of the DMU. In this case, such inputs and outputs will be ignored in the evaluation and will be found unrealistic results. Weight restrictions are utilized to eliminate the problem. Input and output variables in the production process are associated with the degree of correlations between these variables. Previous papers didn't consider the relationship between inputs and outputs. In this study, the weights are defined by correlations between input and output variables. So, the new DEA models constrained with correlation coefficients (CCRCOR and BCCCOR) are developed. The CCRCOR and BCCCOR models and other known DEA models were applied on some datasets in the literature. The results were compared with the Spearman rank test. According to the results, the CCRCOR and BCCCOR models provided a more balanced weight distribution than the other models.

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Data Envelopment Analysis (DEA) measures relative efficiency among the Decision Making Units (DMU) without consider noise in data. Least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output and the efficiency of other DMUs are measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of Stochastic Data Envelopment Ana lysis (SDEA) is a DEA method which considers noise in data is proposed in this study. Using bounded Pareto distribution, we estimate DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using Pareto distribution. Rank correlations were estimated between observed efficiency and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating effectiveness of this SDEA model.

Applied Mathematics and Computation, 2005

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.

The perspective of internal structure of the decision making units (DMUs) was considered as the "black box" when employing data envelopment analysis (DEA) models. However, in the actual world there are always some DMUs that are composed of several sub-units or subsystems, each utilizes the same inputs to generate same outputs. Numerous instances can be listed, such as a firm with a few of plants. In this paper we present models that evaluated the efficiency of DMU which is comprised of same several parallel subsystems, the foremost contribution of our work is that we take the different importance of the subsystems into account in the model, which can be obviously distinguished to the existing DEA model. Secondly, since the alternative optimal multipliers may emerge in the model, the efficiency of each subsystem may be non-unique and we simultaneously develop models of efficiency decomposition for each subsystem. At last a case of technological innovation activities of each province in China is used as an example to state the models.

Annals of Operations Research, 2016

Data Envelopment Analysis (DEA) is a non-parametric technique for evaluating a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs. Various DEA methods have been proposed to rank all the DMUs or to select a single efficient DMU with a single constant input and multiple outputs [i.e., without explicit inputs (WEI)] as well as multiple inputs and a single constant output [i.e., without explicit outputs (WEO)]. However, the majority of these methods are computationally complex and difficult to use. This study proposes an efficient method for finding a single efficient DMU, known as the most efficient DMU, under WEI and WEO conditions. Two compact forms are introduced to determine the most efficient DMU without solving an optimization model under the DEA-WEI and DEA-WEO conditions. A comparative analysis shows a significant reduction in the computational complexity of the proposed method over previous studies. Four numerical examples from different contexts are presented to demonstrate the applicability and exhibit the effectiveness of the proposed compact forms.

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.

2012

Data Envelopment Analysis (DEA) is a non-parametric approach to operations research for assessing the relative efficiencies of a set of peer units, called Decision Making Units (DMUs), with multiple inputs and multiple outputs. DEA provides a fair benchmarking tool that includes a technical efficiency score for each DMU, a technical efficiency reference set with peer DMUs, a target for a technically inefficient DMU, and information detailing by how much inputs can be decreased or outputs can be increased to improve performance of DMUs. In this paper, we compare DEA models to benchmark technically inefficient DMUs, and prove that popular models like the Slack-Based Measure (SBM) and Charnes, Cooper and Rhodes (CCR) may not give the acceptable results for benchmarking technically inefficient DMUs as strong as the weighted additive (ADD) model. The study also warns against applying the conventional DEA models for most of applications and suggests using the Kourosh and Arash Method to (KAM) assess the performance evaluation of DMUs.