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A universal solution for units-invariance in data envelopment analysis

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  • Xu, Jin
  • Zervopoulos, Panagiotis
  • Qian, Zhenhua
  • Cheng, Gang

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 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.

Suggested Citation

  • Xu, Jin & Zervopoulos, Panagiotis & Qian, Zhenhua & Cheng, Gang, 2012. "A universal solution for units-invariance in data envelopment analysis," MPRA Paper 41633, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41633
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    References listed on IDEAS

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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. 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.
    3. 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.
    4. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    5. 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.
    6. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Data Envelopment Analysis; Data normalization; Units-invariance; Directional distance function;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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