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Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

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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
    DOI: 10.1287/mnsc.1100.1265
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    4. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    5. Harju, Mikko & Liesiö, Juuso & Virtanen, Kai, 2019. "Spatial multi-attribute decision analysis: Axiomatic foundations and incomplete preference information," European Journal of Operational Research, Elsevier, vol. 275(1), pages 167-181.
    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. Roza Azizi & Reza Kazemi Matin, 2016. "Ranking Two-Stage Production Units in Data Envelopment Analysis," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-19, February.
    8. Akram Dehnokhalaji & Behjat Hallaji & Narges Soltani & Jafar Sadeghi, 2017. "Convex cone-based ranking of decision-making units in DEA," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 861-880, July.
    9. Liesiö, Juuso & Andelmin, Juho & Salo, Ahti, 2020. "Efficient allocation of resources to a portfolio of decision making units," European Journal of Operational Research, Elsevier, vol. 286(2), pages 619-636.
    10. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2013. "Weight Restrictions and Free Production in Data Envelopment Analysis," Operations Research, INFORMS, vol. 61(2), pages 426-437, April.
    11. Kairui Zuo & Jiancheng Guan, 2017. "Measuring the R&D efficiency of regions by a parallel DEA game model," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 175-194, July.
    12. Labijak-Kowalska, Anna & Kadziński, Miłosz & Dias, Luis C., 2024. "Robustness analysis for imprecise additive value efficiency analysis with an application to evaluation of special economic zones in Poland," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    13. 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.
    14. 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.
    15. Ahti Salo, 2012. "A Seminar for Solving Client Problems in Project Teams," INFORMS Transactions on Education, INFORMS, vol. 13(1), pages 17-27, September.
    16. 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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