A review of inverse data envelopment analysis: origins, development and future directions (original) (raw)
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Computers & Industrial Engineering, 2011
This paper studies the inverse Data Envelopment Analysis (inverse DEA) for the case of variable returns to scale (inverse BCC). The developed inverse BCC model can preserve relative efficiency values of all decision making units (DMUs) in a new production possibility set composing of all current DMUs and a perturbed DMU with new input and output values. We consider the inverse BCC model for a resource allocation problem, where increases of some outputs and decreases of the other outputs of the considered DMU can be taken into account simultaneously. The inverse BCC problem is in the form of a multiobjective nonlinear programming model (MONLP), which is not easy to solve. We propose a linear programming model, which gives a Pareto-efficient solution to the inverse BCC problem. However, there exists at least an optimal solution to the proposed model if and only if the new output vector is in the set of current production possibility set. The proposed approach is illustrated via a case study of a motorcycle-part company.
Applied Mathematics and Computation, 2014
The changing economic conditions have challenged many organizations to search for more effective performance measurement methods. Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogeneous decision making units (DMUs) by evaluating their relative efficiency. Performance measurement in the conventional DEA is based on the assumptions that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some output variables should be minimized. We consider the concepts of technical efficiency (the ratio of the desirable outputs to inputs) and ecological efficiency (the ratio of the desirable outputs to undesirable outputs) in DEA. We then introduce a new measure called process environmental quality efficiency (the ratio of the inputs to the undesirable outputs) and use game theory to integrate these three different efficiency scores into one overall efficiency score. The cooperative and non-cooperative game theory concepts are used to integrate different efficiency ratios into a linear model. We also present a case study to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed models.
Data envelopment analysis (DEA) – Thirty years on
European Journal of Operational Research, 2009
This paper provides a sketch of some of the major research thrusts in data envelopment analysis (DEA) over the three decades since the appearance of the seminal work of Charnes et al. (1978) [Charnes, A., Cooper, W.W., Rhodes, E.L., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429-444]. The focus herein is primarily on methodological developments, and in no manner does the paper address the many excellent applications that have appeared during that period. Specifically, attention is primarily paid to (1) the various models for measuring efficiency, (2) approaches to incorporating restrictions on multipliers, (3) considerations regarding the status of variables, and (4) modeling of data variation.
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...
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: 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.
Data Envelopment Analysis - Basic Models and their Utilization
Organizacija, 2009
Data Envelopment Analysis - Basic Models and their Utilization Data Envelopment Analysis (DEA) is a decision making tool based on linear programming for measuring the relative efficiency of a set of comparable units. Besides the identification of relatively efficient and inefficient units, DEA identifies the sources and level of inefficiency for each of the inputs and outputs. This paper is a survey of the basic DEA models. A comparison of DEA models is given. The effect of model orientation (input or output) on the efficiency frontier and the effect of the convexity requirements on returns to scale are examined. The paper also explains how DEA models can be used to assess efficiency.
2015
In data envelopment analysis, the relative efficiency of a decision-making unit (DMU) is defined as the ratio of the sum of its weighted outputs to the sum of its weighted inputs allowing the DMUs to freely allocate weights to their inputs/outputs. However, this measure may not reflect a true efficiency of a DMU because some of its inputs/outputs may not contribute reasonably in computing the efficiency measure. Traditionally, to overcome this problem weights restrictions have been imposed. But, an approach for solving this problem by inclusion of some unobserved DMUs, obtained via a process with four steps, has been proposed in 2004. These unobserved DMUs are created by adjusting the output levels of certain observed relatively efficient DMUs. The method used in this research is regarded for DMUs that are operating under a constant return to scale (CRS) technology with a single input multi-output context. This method is implemented for 47 branches of bank Maskan in northeast of Teh...