Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A note and new extensions on “interval efficiency measures in data envelopment analysis with imprecise data”

  • Original paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

This paper deals with imprecise data in data envelopment analysis (DEA). We construct a new pair of mathematical programming models by using the concepts of ‘inf’ and ‘sup’ to calculate the exact values of the lower- and upper-bound efficiency scores in the presence of interval and ordinal data. The method proposed in this study is motivated by the approach introduced by Kao (Eur J Oper Res 174(2):1087–1099, 2006) where a pair of two-level mathematical DEA models are converted into linear programming (LP) models to calculate the lower- and upper-bound efficiency scores in the presence of pure ordinal data. We show that the LP model proposed by Kao (2006) for finding the lower-bound efficiency score yields the upper-bound efficiency score. We propose an improved model that overcomes this drawback and successfully calculates the lower- and upper-bound efficiency scores. We demonstrate the applicability of our models with a numerical example and exhibit its efficacy through comparison with Kao’s (2006) approach.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Baumol WJ (1977) Economic theory and operations analysis. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

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

    Article  Google Scholar 

  • Cooper WW, Park KS, Yu G (1999) IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Manag Sci 45(4):597–607

    Article  Google Scholar 

  • Despotis DK, Smirlis YG (2002) Data envelopment analysis with imprecise data. Eur J Oper Res 140(1):24–36

    Article  Google Scholar 

  • Ebrahimi B, Khalili M (2018) A new integrated AR-IDEA model to find the best DMU in the presence of both weight restrictions and imprecise data. Comput Ind Eng 125:357–363

    Article  Google Scholar 

  • Ebrahimi B, Tavana M, Rahmani M, Santos-Arteaga FJ (2018) Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data. Neural Comput Appl 30(6):1971–1982

    Article  Google Scholar 

  • Kao C (2006) Interval efficiency measures in data envelopment analysis with imprecise data. Eur J Oper Res 174(2):1087–1099

    Article  Google Scholar 

  • Khalili M, Camanho AS, Portela M, Alirezaee M (2010) The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs. Eur J Oper Res 203:761–770

    Article  Google Scholar 

  • Wang YM, Greatbanks R, Yang JB (2005) Interval efficiency assessment using data envelopment analysis. Fuzzy Sets Syst 153(3):347–370

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. Dr. Madjid Tavana is grateful for the partial support he received from the Czech Science Foundation (GAˇCR19-13946S) for this research.

Author information

Authors and Affiliations

  1. FernUniversität in Hagen, Hagen, Germany

    Bohlool Ebrahimi

  2. Business Systems and Analytics Department, Distinguished Chair of Business Analytics, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, Paderborn, Germany

    Madjid Tavana

  4. School of Management, University of Bradford, Bradford, UK

    Vincent Charles

Authors
  1. Bohlool Ebrahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madjid Tavana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Charles
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Madjid Tavana.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ebrahimi, B., Tavana, M. & Charles, V. A note and new extensions on “interval efficiency measures in data envelopment analysis with imprecise data”. Oper Res Int J 21, 2719–2737 (2021). https://doi.org/10.1007/s12351-019-00524-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-019-00524-x

Keywords

Search

Navigation