Skip to main content
SpringerLink
Log in

A new method for ranking non-extreme efficient units in data envelopment analysis

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Data envelopment analysis (DEA) evaluates the performance of decision making units (DMUs). When DEA models are used to calculate efficiency of DMUs, a number of them may have the equal efficiency 1. In order to choose a winner among DEA efficient candidates, some methods have been proposed. But most of these methods are not able to rank non-extreme efficient DMUs. Since, the researches performed about ranking of non-extreme efficient units are very limited, incomplete and with some difficulties, we are going to develop a new method to rank these DMUs in this paper. Therefore, we suppose that DMU o is a non-extreme efficient under evaluating DMU. In continue, by using “Representation Theorem”, DMU o can be represented as a convex combination of extreme efficient DMUs. So, we expect the performance of DMU o be similar to the performance of convex combination of these extreme efficient DMUs. Consequently, the ranking score of DMU o is calculated as a convex combination of ranking scores of these extreme efficient DMUs. So, the rank of this unit will be determined.

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. Abello J.M., Pardalos P.M., Resende M.G.C.: Handbook of massive data sets. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  2. Amirteimoori A., Jahanshahloo G.R., Kordrostami S.: Ranking of decision making units in data envelopment analysis. A distance-based approach. Appl. Math. Comput. 171, 122–135 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Anderson P., Petersen N.C.: A procedure for ranking efficient units in data envelopment analysis. Manag. Sci. 39(10), 1261–1264 (1993)

    Article  Google Scholar 

  4. Banker R.D., Charnes A., Cooper W.W.: Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30(9), 1078–1092 (1984)

    Article  MATH  Google Scholar 

  5. Charnes A., Cooper W.W., Rhodes E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–444 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen L.-H., Wen Lu H.: An approximate approach for ranking fuzzy numbers based on left and right dominance. Comput. Math. Appl. 41, 1589–1602 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cooper W., Seiford L., Tone K.: Data envelopment analysis a comprehensive text with models applications references, DEA solved software, 3rd printing. Kluwer, Dordrecht (2002)

    Google Scholar 

  8. Hang Z., Rousseau J.: Determining rates of change in data envelopment analysis. Oper. Res. Soc. 48, 591–599 (1997)

    Google Scholar 

  9. Hosseinzadeh Lotfi F., Noora A.A., Jahanshahloo G.R., Reshadi M.: One DEA ranking method based on applying aggregate units. Expert Syst. Appl. 38(10), 13468–13471 (2011)

    Article  Google Scholar 

  10. Jahanshahloo G.R., Hosseinzadeh Lotfi F., Shoja N., Tohidi G., Razavian S.: Ranking using L 1 norm in data envelopment analysis. Appl. Math. Comput. 153(1), 215–224 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jahanshahloo G.R., Sanei M., Hosseinzadeh Lotfi F., Shoja N.: Using the gradient line for ranking DMUs in DEA. Appl. Math. Comput. 151(1), 209–219 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jahanshahloo G.R., Hosseinzadeh Lotfi F., Zhiani Rezai H., Rezai Balf F.: Using Mont Carlo method for ranking efficient DMUs. Appl. Math. Comput. 162(1), 371–379 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jahanshahloo G.R., Afzalinejad M.: A ranking method based on a full-inefficient frontier. Appl. Math. Model. 30, 248–260 (2006)

    Article  MATH  Google Scholar 

  14. Jahanshahloo G.R., Pourkarimi L., Zarepisheh M.: Modified MAJ model for ranking decision making units in data envelopment analysis. Appl. Math. Comput. 174, 1054–1059 (2006)

    Article  MATH  Google Scholar 

  15. Jahanshahloo G.R., Hosseinzadeh Lotfi F., Khanmohammadi M., Kazemimanesh M., Rezai V.: Ranking of units by positive ideal DMU with common weights. Expert Syst. Appl. 37, 7483–7488 (2010)

    Article  Google Scholar 

  16. Jahanshahloo G.R., Hosseinzadeh Lotfi F., Shoja N., Fallah Jelodar M., Gholam abri A.: Ranking extreme and non-extreme efficient decision making units in data envelopment analysis. Math. Comput. Appl. 15(2), 299–308 (2010)

    MATH  Google Scholar 

  17. Jahanshahloo G.R., Hosseinzadeh Lotfi F., Shoja N., Gholam Abri A., Fallah Jelodar M., Jamali Firouzabadi K.: Sensitivity analysis of inefficient units in data envelopment analysis. Math. Comput. Model. 53, 587–596 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mehrabian S., Alirezaee M.R., Jahanshahloo G.R.: A complete efficiency ranking of decision making units in data envelopment analysis. Comput. Optim. Appl. 14, 261–266 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mokhtar S.B., John J.J., Hanif D.S.: Linear programming and network flows. Wiley, New York (1990)

    MATH  Google Scholar 

  20. Pardalos P.M., Resende M.G.C.: Handbook of applied optimization. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  21. Rezai Balf F., Zhiani Rezai H., Jahanshahloo G.R., Hosseinzadeh Lotfi F.: Ranking efficient DMUs using the Tchebycheff norm. Appl. Math. Model. 36, 45–56 (2012)

    Article  MathSciNet  Google Scholar 

  22. Ross A., Ernstberger K.: Benchmarking the IT productivity paradox: recent evidence from the manufacturing sector. Math. Comput. Model. 44, 30–42 (2006)

    Article  MATH  Google Scholar 

  23. Saati M.S., Zarafat Angiz M., Jahanshahloo G.R.: A model for ranking decision making units in data envelopment analysis. Ricerca Operativa 31(97), 47–59 (2001)

    Google Scholar 

  24. Sexton T.R., Silkman R.H., Hogan A.J.: Data envelopment analysis: critique and extensions. In: Silkman, R.H. (ed) Measuring efficiency: an assessment of data envelopment analysis, pp. 73–105. Jossy-Bass, San Francisco (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

    A. Gholam Abri, N. Shoja & M. Fallah Jelodar

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    G. R. Jahanshahloo & F. Hosseinzadeh Lotfi

Authors
  1. A. Gholam Abri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. R. Jahanshahloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Hosseinzadeh Lotfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. Shoja
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Fallah Jelodar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Gholam Abri.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gholam Abri, A., Jahanshahloo, G.R., Hosseinzadeh Lotfi, F. et al. A new method for ranking non-extreme efficient units in data envelopment analysis. Optim Lett 7, 309–324 (2013). https://doi.org/10.1007/s11590-011-0420-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-011-0420-1

Keywords

Search

Navigation