Measurement of returns to scale in DEA using the CCR model (original) (raw)
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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...
European Journal of Operational Research, 1996
This paper discusses alternative methods for determining returns to scale in DEA. The methods for estimating returns to scale in DEA, as developed by Banker (1984), Banker, Charnes and Cooper (1984) and Banker and Thrall (1992), are proved to be conceptually equivalent to the two-stage methods of F~ire, Grosskopf and Lovell (1985) when their assumptions apply. Here the emphasis is on the CCR model of DEA and very simple methods are introduced for determining returns to scale locally with this model by reference to Banker's conCept of Most Productive Scale Size.
An investigation of returns to scale in data envelopment analysis
Omega, 1999
This paper discusses the determination of returns to scale (RTS) in data envelopment analysis (DEA). Three basic RTS methods and their modi®cations are reviewed and the equivalence between these dierent RTS methods is presented. The eect of multiple optimal DEA solutions on the RTS estimation is studied. It is shown that possible alternate optimal solutions only aect the estimation of RTS on DMUs which should be classi®ed as constant returns to scale (CRS). Modi®cations to the original RTS methods are developed to avoid the eects of multiple optimal DEA solutions on the RTS estimation. The advantages and disadvantages of these alternative RTS methods are presented so that a proper RTS method can be selected within the context of dierent applications. #
Estimating right and left returns to scales in data envelopment analysis: A new approach
2013
In this research a new returns to scale (RTS) method is proposed to estimate the right and left returns to scales (RTSs) of the frontier decision making units (DMUs) in data envelopment analysis (DEA). This study modifies Golany and Yu’s RTS method in such a matter that it always can fit within estimating the right and left returns to scales of efficient DMUs. It is necessary to say that, since an inefficient decision making unit (DMU) has more than one projection on the empirical frontier function hence, the different right and left returns to scales can be determined for the inefficient DMU by using our proposed RTS method. Then, an illustrative example highlights the method and also the obtained results of the proposed RTS method are compared with Golany and Yu’s RTS method. A concluding comment, future extensions and suggest possible future direction of research are all summarized in the last section.
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.
Sensitivity analysis of inefficient units in data envelopment analysis
Mathematical and Computer Modelling, 2011
In data envelopment analysis (DEA) efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. By means of modified CCR model, in which the test DMU is excluded from the reference set, we are able to determine what perturbations of data can be tolerated before frontier DMUs become nonfrontier. In this paper we discuss simultaneous data perturbations in all DMUs, where the efficiency of the test DMU is deteriorating while the efficiencies of the other DMUs are improving. Necessary and sufficient conditions for preserving a DMU's efficiency classification presented by Zhu [8] are developed and improved when various data changes are applied to all DMUs. The region, for preserving a DMU's classification, that is, greater than the region presented in Zhu [8] is then calculated.
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.
On alternative optimal solutions in the estimation of returns to scale in DEA
European Journal of Operational Research, 1998
Zhu and Shen [European Journal of Operational Research 81 (1995) 5901 show that alternative optimal solutions in the estimation of returns to scale (RTS) are caused by a particular linear dependency among a set of extreme efficient DMUs when one employs the concept of most productive scale size [European Journal of Operational Research 17 (1984) 351 in data envelopment analysis (DEA). This paper demonstrates that the presence of weakly efficient DMUs may also lead to alternative optima and extends the results of Zhu and Shen to the entire frontier. Necessary and sufficient conditions for the presence of multiple optimal solutions for constant returns to scale (CRS) DMUs are established. 0 1998 Elsevier Science B.V.
An enhanced procedure for estimating returns-to-scale in DEA
Applied Mathematics and Computation, 2005
In this paper, by improving the Golany and YuÕs method [Estimating returns to scale in DEA, European Journal of Operational Research 103 (1) (1997) 28-37], a new algorithm to estimate returns-to-scale (RTS) in data envelopment analysis (DEA) models is proposed. We show that the proposed algorithm overcomes existing disadvantages in the Golany and YuÕs method, introduced for this purpose. The advantages of the new algorithm are illustrated.