Equivalence and implementation of alternative methods for determining returns to scale in data envelopment analysis (original) (raw)
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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.
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. #
Estimation of returns to scale using data envelopment analysis: A comment
European Journal of Operational Research, 1994
Generalization of the measure of returns-to-scale from a single number to an interval permits extension of the concept to DEA data domains with multiple inputs and multiple outputs. The key new approach is a partition of the optimal frontier into three parts corresponding, respectively to increasing, constant, and decreasing returns to scale. These parts are characterized in terms of optimal primal solutions, and optimal dual solutions for both the original Charnes, Cooper, Rhodes model (1978) and the later Banker, Charnes, Cooper model (1984) and relying on concepts developed by R.D. Banker .
International Series in Operations Research & Management Science, 2011
This chapter discusses returns to scale (RTS) in data envelopment analysis (DEA). The BCC and CCR models described in Chap. 1 of this handbook are treated in input-oriented forms, while the multiplicative model is treated in output-oriented form. (This distinction is not pertinent for the additive model, which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing, or constant. This is discussed for each type of model, and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research and an Appendix discusses other approaches in DEA treatment of RTS.
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.
Returns to scale in different DEA models
European Journal of Operational Research, 2004
This paper discusses returns to scale (RTS) in data envelopment analysis (DEA) for each of the presently available types of models. The BCC and CCR models are treated in input oriented forms while the multiplicative model is treated in output oriented form. (This distinction is not pertinent for the additive model which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing or constant. This is discussed for each type of model and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research.
Measurement of returns to scale in DEA using the CCR model
In data envelopment analysis (DEA) literature, the returns to scale (RTS) of an inefficient decision making unit (DMU) is determined at its projected point on the efficient frontier. Under the occurrences of multiple projection points, however, this evaluation procedure is not precise and may lead to erroneous inferences as to the RTS possibilities of DMUs. To circumvent this, the current communication first defines the RTS of an inefficient DMU at its projected point that lies in the relative interior of the minimum face. Based on this definition, it proposes an algorithm by extending the latest developed method of measuring RTS via the CCR model. The main advantage of our proposed algorithm lies in its computational efficiency.
DIFFERENT TYPES OF RETURN TO SCALE IN DEA
Pesquisa Operacional, 2019
The format of the efficient frontier is an important measure of technical efficiency; additionally , it determines the type of return to scale verified by the model. The classical Data Envelopment Analysis (DEA) model, CCR (Charnes et al., 1978), assumes constant returns to scale; conversely, the BCC (Banker et al., 1984) model presents a concave downward efficient frontier that presumes variable returns to scale. This study examines how different returns to scale can be revealed in DEA, considering the possibility of the existence of a concave upward efficient frontier. This kind of frontier, not yet explored by the DEA literature, can also represent viable production, seeing that an increase of the inputs causes an increase of the outputs. Considering this, a concave upward efficient frontier presents a variable return to scale, but with different characteristics from those of the concave downward BCC efficient frontier. This proposal is important because it considers the possibility of an efficient frontier that represents different samples of decision-making units (DMUs). An upward curve would better represent DMUs of smaller production scales that have increased marginal productivity but cannot act as efficiently as larger scale units.
A Simple Characterization of Returns to Scale in Dea
Journal of the Operations Research Society of Japan, 1996
In this paper, we will present a simple method for declding the local returns-t}scale characteristics of DMUs (Decision Making Units) in Data Envelopment Analysis. This method proceeds as followsT first, we solve the BCC (Banker-Charnes-Cooper) model and find the returns-to-scale of BCC-eMcient DMUs and at reference set to each BCC-ineMcient DMU. We can then decide the local returns-to-scale characteristics ofeach BCC-ineMcient DMU by observing only the returns-to-scale characteristics of DMUs in their respective reference sets. No extra computation is required.