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The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models

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  • A L Johnson

    (Texas A&M University)

  • L F McGinnis

    (Georgia Institute of Technology)

Abstract

The infeasibility problem in traditional super efficiency models has been well established. A generalization of traditional input- or output-oriented super efficiency models, the directional distance function also suffers from infeasibility and related problems. The hyperbolic-oriented efficiency measure provides an alternative to the input-oriented, output-oriented, and directional efficiency measures in super efficiency models and it has the distinct advantage of eliminating the infeasibility problem for positive input/output data. We also show that using a hyperbolic orientation in a super efficiency model allows us to find feasible solutions for certain cases when the requirement for all data to be positive is relaxed. Further we demonstrate the hyperbolic orientated super efficiency method in an outlier detection application. Together, these results establish the use of the hyperbolic orientation in super efficiency analysis as a realistic alternative in practice.

Suggested Citation

  • A L Johnson & L F McGinnis, 2009. "The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1511-1517, November.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:11:d:10.1057_jors.2009.71
    DOI: 10.1057/jors.2009.71
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    3. Li, Yongjun & Xie, Jianhui & Wang, Meiqiang & Liang, Liang, 2016. "Super efficiency evaluation using a common platform on a cooperative game," European Journal of Operational Research, Elsevier, vol. 255(3), pages 884-892.
    4. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.
    5. Simar, Léopold & W. Wilson, Paul, 2019. "Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices," European Journal of Operational Research, Elsevier, vol. 277(2), pages 756-769.
    6. Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2024. "A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 312(1), pages 298-314.
    7. Mustapha D. Ibrahim & Sahand Daneshvar & Mevhibe B. Hocaoğlu & Olasehinde-Williams G. Oluseye, 2019. "An Estimation of the Efficiency and Productivity of Healthcare Systems in Sub-Saharan Africa: Health-Centred Millennium Development Goal-Based Evidence," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(1), pages 371-389, May.
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