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Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

Author

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  • Ahti Salo

    () (Systems Analysis Laboratory, Aalto University School of Science, 00076 Aalto, Finland)

  • Antti Punkka

    () (Systems Analysis Laboratory, Aalto University School of Science, 00076 Aalto, Finland)

Abstract

We develop comparative results for ratio-based efficiency analysis (REA) based on the decision-making units' (DMUs') relative efficiencies over sets of feasible weights that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals, which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs; (ii) dominance relations, which show what other DMUs a given DMU dominates in pairwise efficiency comparisons; and (iii) efficiency bounds, which show how much more efficient a given DMU can be relative to some other DMU or a subset of other DMUs. Unlike conventional efficiency scores, these results are insensitive to outlier DMUs. They also show how the DMUs' efficiency ratios relate to each other for all feasible weights, rather than for those weights only for which the data envelopment analysis (DEA) efficiency score of some DMU is maximized. We illustrate the usefulness of these results by revisiting reported DEA studies and by describing a recent case study on the efficiency comparison of university departments. This paper was accepted by Teck-Hua Ho, decision analysis.

Suggested Citation

  • Ahti Salo & Antti Punkka, 2011. "Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis," Management Science, INFORMS, vol. 57(1), pages 200-214, January.
  • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:200-214
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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1265
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Schang, Laura & Hynninen, Yrjänä & Morton, Alec & Salo, Ahti, 2016. "Developing robust composite measures of healthcare quality – Ranking intervals and dominance relations for Scottish Health Boards," Social Science & Medicine, Elsevier, vol. 162(C), pages 59-67.
    2. Kangaspunta, Jussi & Liesiö, Juuso & Salo, Ahti, 2012. "Cost-efficiency analysis of weapon system portfolios," European Journal of Operational Research, Elsevier, vol. 223(1), pages 264-275.
    3. repec:spr:scient:v:112:y:2017:i:1:d:10.1007_s11192-017-2380-4 is not listed on IDEAS
    4. Miłosz Kadziński & Krzysztof Ciomek & Paweł Rychły & Roman Słowiński, 2016. "Post factum analysis for robust multiple criteria ranking and sorting," Journal of Global Optimization, Springer, vol. 65(3), pages 531-562, July.
    5. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    6. Kadziński, Miłosz & Labijak, Anna & Napieraj, Małgorzata, 2017. "Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports," Omega, Elsevier, vol. 67(C), pages 1-18.
    7. Chen, Ya & Li, Yongjun & Liang, Liang & Salo, Ahti & Wu, Huaqing, 2016. "Frontier projection and efficiency decomposition in two-stage processes with slacks-based measures," European Journal of Operational Research, Elsevier, vol. 250(2), pages 543-554.
    8. Lim, Sungmook & Oh, Kwang Wuk & Zhu, Joe, 2014. "Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market," European Journal of Operational Research, Elsevier, vol. 236(1), pages 361-368.
    9. 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.

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