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

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Listed:
  • Bohlool Ebrahimi

    (FernUniversität in Hagen)

  • Madjid Tavana

    (La Salle University
    University of Paderborn)

  • Vincent Charles

    (University of Bradford)

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.

Suggested Citation

  • Bohlool Ebrahimi & Madjid Tavana & Vincent Charles, 2021. "A note and new extensions on “interval efficiency measures in data envelopment analysis with imprecise data”," Operational Research, Springer, vol. 21(4), pages 2719-2737, December.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:4:d:10.1007_s12351-019-00524-x
    DOI: 10.1007/s12351-019-00524-x
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    References listed on IDEAS

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    1. Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.
    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. Kao, Chiang, 2006. "Interval efficiency measures in data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1087-1099, October.
    4. Despotis, Dimitris K. & Smirlis, Yiannis G., 2002. "Data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 140(1), pages 24-36, July.
    5. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
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    Cited by:

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