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

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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.

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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.

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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
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  2. Madjid Tavana
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  3. Vincent Charles
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Correspondence to Madjid Tavana.

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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

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

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