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A Universal Solution For Units - Invariance In Data Envelopment Analysis

Listed author(s):
  • Jin XU


    (China Center for Health Development Studies, Peking University, Beijing, China)

  • Panagiotis D. ZERVOPOULOS


    (China Center for Health Development Studies,Peking University, Beijing, China; Department of Business Administration of Food and Agricultural Enterprises, University of Ioannina, Agrinio, Greece)

  • Zhenhua QIAN


    (School of Social Science, University of Science and Technology Beijing, China)

  • Gang CHENG


    (China Center for Health Development Studies, Peking University, Beijing, China)

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 units-invariant 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 units-invariance in DEA. The efficiency scores remain unchanged when the original data are replaced with the normalized data in the existing units-invariant DEA models, including the radial and slack-based measure models, i.e., the data normalization method is compatible with the radial and slack-based measure models. Based on normalized data, a units-invariant efficiency measure for the directional distance function model is defined.

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Article provided by ASERS Publishing in its journal Theoretical and Practical Research in Economic Fields.

Volume (Year): III (2012)
Issue (Month): 2 (January)
Pages: 124-131

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Handle: RePEc:srs:tpref1:5:v:3:y:2012:i:2:p:124-131
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  1. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  2. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
  3. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
  4. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  5. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  6. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
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