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OR Spectrum

, Volume 36, Issue 1, pp 133–160 | Cite as

Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data

  • Amir H. Shokouhi
  • Hamid Shahriari
  • Per J. AgrellEmail author
  • Adel Hatami-Marbini
Regular Article

Abstract

Data envelopment analysis (DEA) is a non-parametric method for measuring the relative efficiency of a set of decision making units using multiple precise inputs to produce multiple precise outputs. Several extensions to DEA have been made for the case of imprecise data, as well as to improve the robustness of the assessment for these cases. Prevailing robust DEA (RDEA) models are based on mirrored interval DEA models, including two distinct production possibility sets (PPS). However, this approach renders the distance measures incommensurate and violates the standard assumptions for the interpretation of distance measures as efficiency scores. We propose a modified RDEA (MRDEA) model with a unified PPS to overcome the present problem in RDEA. Based on a flexible formulation for the number of variables perturbed, MRDEA calculates the empirical distribution for the interval efficiency for the case of a random number of variables affected. The MRDEA approach also decreases the computational complexity of the RDEA model, as well as significantly increases the discriminatory power of the model without additional information requirements. The properties of the method are demonstrated for four different numerical instances.

Keywords

Data envelopment analysis Robust optimization Imprecise data Robust ranking 

Notes

Acknowledgments

The authors would like to thank Prof. Stefan Minner, Managing Editor of OR Spectrum, for his admirable support. They also would like to thank the anonymous reviewers for their insightful and constructive comments. This research project is partially supported by the French Community of Belgium ARC project on managing shared resources in supply chains.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Amir H. Shokouhi
    • 1
  • Hamid Shahriari
    • 1
  • Per J. Agrell
    • 2
    Email author
  • Adel Hatami-Marbini
    • 2
  1. 1.Department of Industrial EngineeringK. N. Toosi University of TechnologyTehranIran
  2. 2.Louvain School of Management, Center of Operations Research and Econometrics (CORE)Université catholique de LouvainLouvain-la-NeuveBelgium

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