Dea Model
European Journal of Operational Research 154 (2004) 345–362 www.elsevier.com/locate/dsw
Returns to scale in different DEA models
Rajiv D. Banker a, William W. Cooper b, Lawrence M. Seiford c, Robert M. Thrall d, Joe Zhu e,* c School of Management, The University of Texas at Dallas, Richardson, TX 75083-0658, USA Graduate School of Business, The University of Texas at Austin, Austin, TX 78712-1174, USA Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109-2117, USA d 12003 Pebble Hill Drive, Houston, TX 77024, USA e Department of Management, Worcester Polytechnic Institute, Worcester, MA 01609, USA b a
Abstract 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. Ó 2003 Elsevier B.V. All rights reserved.
Keywords: DEA; Efficiency; RTS
1. Introduction It has long been recognized that data envelopment analysis (DEA) by its use of mathematical programming is particularly adept at estimating inefficiencies in multiple input and multiple output production correspondences. Following Charnes, Cooper and Rhodes (CCR, 1978), a number of different DEA models have
Returns to scale in different DEA models
Rajiv D. Banker a, William W. Cooper b, Lawrence M. Seiford c, Robert M. Thrall d, Joe Zhu e,* c School of Management, The University of Texas at Dallas, Richardson, TX 75083-0658, USA Graduate School of Business, The University of Texas at Austin, Austin, TX 78712-1174, USA Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109-2117, USA d 12003 Pebble Hill Drive, Houston, TX 77024, USA e Department of Management, Worcester Polytechnic Institute, Worcester, MA 01609, USA b a
Abstract 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. Ó 2003 Elsevier B.V. All rights reserved.
Keywords: DEA; Efficiency; RTS
1. Introduction It has long been recognized that data envelopment analysis (DEA) by its use of mathematical programming is particularly adept at estimating inefficiencies in multiple input and multiple output production correspondences. Following Charnes, Cooper and Rhodes (CCR, 1978), a number of different DEA models have
References: and DEA-Solver Software. Kluwer Academic Publishers, Boston. F€re, R., Grosskopf, S., Lovell, C.A.K., 1985. The Measurea ment of Efficiency of Production. Kluwer Nijhoff, Boston. F€re, R., Grosskopf, S., Lovell, C.A.K., 1994. Production a Frontiers. Cambridge University Press. Førsund, F.R., 1996. On the calculation of scale elasticities in DEA models. Journal of Productivity Analysis 7, 283–302. Frisch, R.A., 1964. Theory of Production. Reidel, Dordrecht. Fukuyama, H., 2000. Returns to scale and scale elasticity in Data Envelopment Analysis. European Journal of Operational Research 125, 93–112. Golany, B., Yu, G., 1994. Estimating returns to scale in DEA. European Journal of Operational Research 103, 28–37. Lovell, C.A.K., Pastor, J., 1995. Units invariant and translation invariant DEA models. Operations Research Letters 18, 147–152. Panzar, J.C., Willig, R.D., 1977. Economics of scale in multioutput production. Quarterly Journal of Economics XLI, 481–493. Read, L., Thanassoulis, E., 2000. Improving the identification of returns to scale in Data Envelopment Analysis. Journal of the Operational Research Society 51, 102–110.