Skip to main content
SpringerLink
Log in

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

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. Subsequently, Wilson (1995) also suggested exactly the same use of the super-efficiency model for identifying outliers.

  2. While the super-efficiency model is specified in (1) for the BCC model, similar models can be specified corresponding to other DEA specifications. The CCR (Charnes et al. 1978) super-efficiency specification is the same linear program as in (1) except that the constraint in (1c) is deleted. The NDRS (non-decreasing returns to scale) specification is the same linear program as in (1) except that the constraint in (1c) is a less-than-or-equal-to (=) constraint instead of an equality (=) constraint. The NIRS (non-increasing returns to scale) specification is the same linear program as in (1) except that the constraint in (1c) is a greater-than-or-equal-to (=) constraint instead of an equality (=) constraint.

  3. Observe that there always exists an optimal solution to (2) with either \({\uplambda }_\mathrm{k}^*=0\) or \({\uplambda }_\mathrm{k}^*=1\).

  4. We chose the shifted Cobb–Douglas because it provides a parsimonious parametric form that exhibits both increasing and decreasing returns to scale for \(\alpha _i >0.\)

  5. Table 2 has the same structure as Table 1, but with the results from each region. When interpreting Table 2 results, one should not expect the results of Table 1 as the average of the three corresponding regions in Table 2 because of different sample sizes.

References

  • Andersen, P., & Petersen, N. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, 1261–1264.

    Article  Google Scholar 

  • Banker, R. D. (1993). Maximum likelihood, consistency and data envelopment analysis: A statistical foundation. Management Science, 39, 1265–1273.

    Article  Google Scholar 

  • Banker, R. D., & Chang, H. (2006). The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operations Research, 175, 1311–1320.

    Article  Google Scholar 

  • Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.

    Article  Google Scholar 

  • Banker, R. D., Das, S., & Datar, S. M. (1989). Analysis of cost variances for management control in hospitals. Research in Governmental and Nonprofit Accounting, 5, 269–291.

    Google Scholar 

  • Banker, R. D., & Gifford, J. L. (1988). A relative efficiency model for the evaluation of public health nurse productivity. Pittsburgh: Mimeo, Carnegie Mellon University.

    Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.

    Article  Google Scholar 

  • Charnes, A., & Neralic, L. (1990). Sensitivity analysis of the additive model in data envelopment analysis. European Journal of Operational Research, 48, 332–341.

    Article  Google Scholar 

  • Charnes, A., & Neralic, L. (1992). Sensitivity analysis of the proportionate change of inputs (or outputs) in data envelopment analysis. Glasnik Matematicki, 27, 393–405.

    Google Scholar 

  • Timmer, C. P. (1971). Using a probabilistic frontier production function to measure technical efficiency. Journal of Political Economy, 79, 776–794.

    Article  Google Scholar 

  • Wilson, P. (1995). Detecting influential observations in data envelopment analysis. Journal of Productivity Analysis, 6, 27–45.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fox School of Business, Temple University, Philadelphia, PA, USA

    Rajiv D. Banker

  2. LeBow College of Business, Drexel University, Philadelphia, PA, USA

    Hsihui Chang

  3. Jindal School of Management, University of Texas at Dallas, Richardson, TX, USA

    Zhiqiang Zheng

Authors
  1. Rajiv D. Banker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hsihui Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiqiang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hsihui Chang.

Additional information

We acknowledge many helpful discussions with W.W. Cooper on this subject.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banker, R.D., Chang, H. & Zheng, Z. On the use of super-efficiency procedures for ranking efficient units and identifying outliers. Ann Oper Res 250, 21–35 (2017). https://doi.org/10.1007/s10479-015-1980-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-015-1980-8

Keywords

Search

Navigation