Data Envelopment Analysis - Basic Models and their Utilization (original) (raw)
Related papers
European Journal of Operational Research, 2017
In a recent paper to this journal, the authors developed a methodology that allows the incorporation of ratio inputs and outputs in the variable and constant returns-to-scale DEA models. Practical evaluation of efficiency of decision making units (DMUs) in such models generally goes beyond the application of standard linear programming techniques. In this paper we discuss how the DEA models with ratio measures can be solved. We also introduce a new type of potential ratio (PR) inefficiency. It characterizes DMUs that are strongly efficient in the model of technology with ratio measures but become inefficient if the volume data used to calculate ratio measures become available. Potential ratio inefficiency can be tested by the programming approaches developed in this paper.
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...
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.
Preservation of efficiency and inefficiency classification in data envelopment analysis
2004
Sufficient conditions for simultaneous efficiency preservation of all efficient Decision Making Units (DMUs) and for inefficiency preservation of all inefficient DMUs in the Additive model of Data Envelopment Analysis (DEA) under the simultaneous non-negative perturbations of all data of all DMUs are obtained. An illustrative example is provided.
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.
Data envelopment analysis: theory and applications
Journal of the Operational Research Society, 2009
The common weights approach is one of the most prominent methods to further prioritize the subset of DEA efficient units. This approach can be modeled as a multiobjective problem, where one seeks for a common set of weights that locates the efficiency ratio of each unit as close as possible to the target score of 1. In such a setting, different metrics can be applied to measure the distance of the efficiency ratios from target, such as the L 1 , L 2 and L ∞. When L 1 and L 2 metrics are used the models derived are non-linear. In case of the L ∞ metric, the problem can be heuristically solved by the bisection method and a series of linear programs. We investigate in this paper the ability of genetic algorithms to solve the problem for estimating efficiency scores, by using an evolutionary optimization method based on a variant of the Nondominated Sorted Genetic Algorithm.
Archives of Computational Methods in Engineering
DEA, incepted in 80s, has emerged as a popular decision-making technique, for determining the efficiency of similar units. Due to its simplicity and applicability, DEA has gained the attention of scientists and researchers working in diverse areas, which has contributed towards a rich literature both in terms of theoretical development as well as different applications. This paper tries to bring together the near 40 years of existence of DEA in a concise format by discussing the popular DEA models, their advantages and shortcomings, and different applications of DEA. It also provides a brief bibliometric analysis to highlight the development of DEA over the years in terms of publication trends, highly cited papers, journal citation, etc.
Data Envelopment Analysis Models in Non-Homogeneous Environment
Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis
Data envelopment analysis (DEA) is a non-parametric method that is widely used for relative efficiency and performance evaluation of the set of decision-making units (DMUs). It is based on maximization of a weighted sum of outputs produced by the unit under evaluation divided by the weighted sum of inputs of the same unit, and the assumption that this ratio for all other units has to be lower or equal to 1. An important assumption for applications of DEA models is the homogeneity of the units. Unfortunately, the homogeneity assumption is not fulfilled in many real applications. The paper deals with the analysis of efficiency using DEA models in the non-homogeneous environment. One of the problems lies in non-homogeneous outputs. In this case, the units under evaluation spend the same inputs but produce completely or at least partly different set of outputs. The paper formulates several models how to deal with this problem and compares the results on a numerical example. Other main s...