Xu, Jin and Zervopoulos, Panagiotis and Qian, Zhenhua and Cheng, Gang (2012): A universal solution for unitsinvariance in data envelopment analysis.

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Abstract
The directional distance function model is a generalization of the radial model in data envelopment analysis (DEA). The directional distance function model is appropriate for dealing with cases where undesirable outputs exist. However, it is not a unitsinvariant measure of efficiency, which limits its accuracy. In this paper, we develop a data normalization method for DEA, which is a universal solution for the problem of unitsinvariance in DEA. The efficiency scores remain unchanged when the original data are replaced with the normalized data in the existing unitsinvariant DEA models, including the radial and slackbased measure models, i.e., the data normalization method is compatible with the radial and slackbased measure models. Based on normalized data, a unitsinvariant efficiency measure for the directional distance function model is defined.
Item Type:  MPRA Paper 

Original Title:  A universal solution for unitsinvariance in data envelopment analysis 
Language:  English 
Keywords:  Data Envelopment Analysis; Data normalization; Unitsinvariance; Directional distance function 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67  InputOutput Models D  Microeconomics > D2  Production and Organizations > D24  Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity 
Item ID:  41633 
Depositing User:  Panagiotis Zervopoulos 
Date Deposited:  01 Oct 2012 13:35 
Last Modified:  27 Sep 2019 01:02 
References:  Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 10781092. Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and Distance Functions. Journal of Economic Theory, 70, 407419. Chambers, R. G., Chung, Y., & Färe, R. (1998). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98, 351364. Charnes, A. (1994). Data envelopment analysis: theory, methodology, and application: Kluwer Academic Publishers. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429444. Chung, Y. H., Färe, R., & Grosskopf, S. (1997). Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management, 51, 229240. Cook, W. D., & Seiford, L. M. (2009). Data envelopment analysis (DEA)  Thirty years on. European Journal of Operational Research, 192, 117. Färe, R., & Knox Lovell, C. A. (1978). Measuring the technical efficiency of production. Journal of Economic Theory, 19, 150162. Lovell, C. A. K., & Pastor, J. T. (1995). Units invariant and translation invariant DEA models. Operations Research Letters, 18, 147151. Seiford, L. M. (1996). Data envelopment analysis: The evolution of the state of the art (1978–1995) The Journal of Productivity Analysis, 6, 99137. Tone, K. (2001). A slacksbased measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130, 498509. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/41633 