Skip to main content
SpringerLink
Log in

Derivation of the Maximin Efficiency Ratio model from the maximum decisional efficiency principle

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

Abstract

The Maximin Efficiency Ratio (MER) model was originally proposed as a common weights model for further prioritization of the DEA efficient subset of DMUs. Theoretical support for it in that context was based on principles of group decision making proposed earlier by P.L. Yu. Subsequently, the model has been found useful for one-step ranking of the full set of DMUs, albeit without theoretical support in that context. This paper provides a derivation of the MER model in a way which is potentially suitable for either context by use of the Maximum Decisional Efficiency (MDE) principle for aggregating expert estimates. This approach provides theoretical support for the MER model by demonstrating that it is a Maximum Likelihood procedure under certain plausible assumptions. It is necessary to assume that all the DMUs desire to maximize their own efficiency ratio computed on a common weights basis. However, this context is not vacuous since top management will typically wish to evaluate all divisions, projects, individuals, etc., respectively, on a common standard. This paper seeks to extend the frontiers of DEA by supposing the existence of a common performance measure for the DMUs.

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

Similar content being viewed by others

References

  1. P. Anderson and N.C. Peterson, A procedure for ranking efficient units in Data Envelopment Analysis, Management Science 39(1993)1261–1264.

    Google Scholar 

  2. P. Berck and K. Sydsæter, Economists' Mathematical Manual, Springer, Berlin, 1991.

    Google Scholar 

  3. A. Charnes, W.W. Cooper and E. Rhodes, Evaluating program and managerial efficiency: An application of Data Envelopment Analysis to program follow through, Management Science 27 (1981)668–697.

    Google Scholar 

  4. A. Charnes, W.W. Cooper, A. Lewin and L.M. Seiford, Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Academic, New York, 1995.

    Google Scholar 

  5. A. Charnes, W.W. Cooper, Z.M. Huang and D.B. Sun, Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks, Joumal of Econometrics 46(1990).

  6. W.D. Cook, Y. Roll and A. Kazakov, A DEA model for measuring the relative efficiency of highway maintenance patrols, INFORS 28(199)113–124.

  7. W.D. Cook, M. Kress and L.M. Seiford, Prioritization models for frontier decision making units in DEA, European Journal of Operational Research 59(1993)319–323.

    Article  Google Scholar 

  8. R.G. Dyson and E. Thanassoulis, Reducing weight flexibility in Data Envelopment Analysis, Journal of the Operational Research Sociery 38(1988)563–576.

    Article  Google Scholar 

  9. W.H. Greene, Maximum likelihood estimation of econometric frontier functions, Journal of Econometrics 13(1980)27–56.

    Article  Google Scholar 

  10. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. 2, Charles Griffin, London 1961.

    Google Scholar 

  11. A.M. Mood and F.A. Graybill, Introduction to the Theory of Statistics, 2nd ed., McGraw-Hill, New York, 1963.

    Google Scholar 

  12. C.R. Rao, Linear Statistical Inference and Its Applications, Wiley, New York, 1965.

    Google Scholar 

  13. P. Schmidt, On the statistical estimation of parametric frontier production functions, Review of Economics and Statistics 58(1975)238–239.

    Article  Google Scholar 

  14. R.G. Thompson, F.D. Singleton, Jr., R.M. Thrall and B.A. Smith, Comparative site evaluations for locating a high energy physics lab in Texas, Interfaces 16,no. 6 (1986)35–49.

    Article  Google Scholar 

  15. M.D. Troutt, A maximum decisional efficiency estimation principle, Management Science 41 (1995)76–82.

    Google Scholar 

  16. M.D. Troutt, Extension of Bolzano search to rectangles which preserves rectangles as iterates, Naval Research Logistics 34(1987)593–603.

    Google Scholar 

  17. M.D. Troutt, A. Zhang and M.D. Pettypool, A Maximin Efficiency Ratio model for consensus weights and extended ranking of technically efficient units, Working Paper, Department of Management, Southern Illinois University, Carbondale, IL 62901-4627, 1993.

    Google Scholar 

  18. M.D. Troutt and A. Zhang, The Maximin Efficiency Ratio model as a one-step ranking device — comparison to two modified DEA analyses, Working Paper, Department of Management, Southern Illinois University, Carbondale, IL 62901-4627, 1993.

    Google Scholar 

  19. P.L. Yu, A class of solutions for group decision problems, Management Science 19(1973)936–946.

    Google Scholar 

Download references

Authors
  1. M.D. Troutt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Troutt, M. Derivation of the Maximin Efficiency Ratio model from the maximum decisional efficiency principle. Annals of Operations Research 73, 323–338 (1997). https://doi.org/10.1023/A:1018989414181

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018989414181

Search

Navigation