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On the use of super-efficiency procedures for ranking efficient units and identifying outliers

Author

Listed:
  • Rajiv D. Banker

    (Temple University)

  • Hsihui Chang

    (Drexel University)

  • Zhiqiang Zheng

    (University of Texas at Dallas)

Abstract

Prior research (Banker and Chang in Eur J Oper Res 175: 1311–1320, 2006) has found that super-efficiency based procedures are effective in identifying outliers, but not in ranking efficient units. In this paper, we investigate why the procedures failed to rank efficient units satisfactorily and examine the performance of super-efficiency procedures in different “regions” of production set. We find that the unsatisfactory results mainly originate from the “left corners” of DMUs, those units with relatively smaller values. We further examine the effect of different noise levels on outlier detection using the BG procedure (Banker and Gifford in A relative efficiency model for the evaluation of public health nurse productivity. Mimeo, Carnegie Mellon University, Pittsburgh, 1988). Our results show that the BG procedure is more effective when the noise level is high. We conduct extensive simulation experiments by considering different production functions (Cobb–Douglas and Polynomial), different DEA formulations (BCC and CCR) and different returns-to-scale (CRS and NIRS) assumptions. Our simulation results confirm that the findings in Banker and Chang (2006) are robust under different DEA formulations, production functions and returns to scale assumptions.

Suggested Citation

  • Rajiv D. Banker & Hsihui Chang & Zhiqiang Zheng, 2017. "On the use of super-efficiency procedures for ranking efficient units and identifying outliers," Annals of Operations Research, Springer, vol. 250(1), pages 21-35, March.
    • Handle: RePEc:spr:annopr:v:250:y:2017:i:1:d:10.1007_s10479-015-1980-8
    DOI: 10.1007/s10479-015-1980-8
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    References listed on IDEAS

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    1. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    2. 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.
    3. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    4. 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.
    5. Charnes, A. & Neralic, L., 1990. "Sensitivity analysis of the additive model in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 48(3), pages 332-341, October.
    6. Banker, Rajiv D. & Chang, Hsihui, 2006. "The super-efficiency procedure for outlier identification, not for ranking efficient units," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1311-1320, December.
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