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A note on imposing strong complementary slackness conditions in DEA

Author

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  • Krivonozhko, Vladimir E.
  • Førsund, Finn R.
  • Lychev, Andrey V.

Abstract

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems also that the basic matrices may be inherently ill-conditioned, leading to erroneous results. Numerical experiments have been carried out on two real datasets of medium size with 163 and 920 units. These experiments, using well known reliable software, show pervasive existence of ill-conditioned matrices leading to obviously wrong estimates of efficiency scores, and units declared as efficient reference units while actually being inefficient.

Suggested Citation

  • Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "A note on imposing strong complementary slackness conditions in DEA," European Journal of Operational Research, Elsevier, vol. 220(3), pages 716-721.
  • Handle: RePEc:eee:ejores:v:220:y:2012:i:3:p:716-721
    DOI: 10.1016/j.ejor.2012.01.050
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    References listed on IDEAS

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    1. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    2. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2012. "Returns-to-scale properties in DEA models: the fundamental role of interior points," Journal of Productivity Analysis, Springer, vol. 38(2), pages 121-130, October.
    3. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    4. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    5. Sueyoshi, Toshiyuki & Goto, Mika, 2010. "Measurement of a linkage among environmental, operational, and financial performance in Japanese manufacturing firms: A use of Data Envelopment Analysis with strong complementary slackness condition," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1742-1753, December.
    6. 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.
    7. Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    8. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
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    Cited by:

    1. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2014. "Measurement of returns to scale using non-radial DEA models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 664-670.
    2. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    3. Grebel, Thomas & Stützer, Michael, 2014. "Assessment of the environmental performance of European countries over time: Addressing the role of carbon leakage and nuclear waste," Ilmenau Economics Discussion Papers 90, Ilmenau University of Technology, Institute of Economics.

    More about this item

    Keywords

    Data envelopment analysis; BCC model; Strong complementary slackness conditions; DEA/SCSC model;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General

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