Efficiency improvement of decision making units: a new data envelopment analysis model (original) (raw)
Related papers
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.
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.
Data Envelopment Analysis and Performance Measurement
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.
In the determination of the most efficient decision making unit in data envelopment analysis
Computers & Industrial Engineering, 2015
In recent years, several mixed integer linear programming (MILP) models have been proposed for determining the most efficient decision making unit (DMU) in data envelopment analysis. However, most of these models do not determine the most efficient DMU directly; instead, they make use of other less related objectives. This paper introduces a new MILP model that has an objective similar to that of the super-efficiency model. Unlike previous models, the new model's objective is to directly discover the most efficient DMU. Similar to the super-efficiency model, the aim is to choose the most efficient DMU. However, unlike the super-efficiency model, which requires the solution of a linear programming problem for each DMU, the new model requires that only a single MILP problem be solved. Consequently, additional terms in the objective function and more constraints can be easily added to the new model. For example, decision makers can more easily incorporate a secondary objective such as adherence to a publicly stated preference or add assurance region constraints when determining the most efficient DMU. Furthermore, the proposed model is more accurate than two recently proposed models, as shown in two computational examples.
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.
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 Mathematics and Computation, 2005
The assumption of classical Data Envelopment Analysis (DEA) models is based on complete homogeneity of Decision Making Units (DMUs). The objective of this paper is to propose a method of determining relative efficiency of slightly non-homogeneous DMUs by using DEA. First missing values are inserted by series mean. Then relative weights of DMUs are measured by Analytic Hierarchy Process (AHP) and finally relative efficiency of DMUs is computed by chance-constrained DEA. A case study demonstrates the application of the proposed method.
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...
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.
Benchmarking Inefficient Decision Making Units in DEA
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.