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

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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.

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  1. This paper has been cited by 88 researchers by 2012 based on Scopus.

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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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Authors and Affiliations

  1. Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Amir H. Shokouhi & Hamid Shahriari

  2. Louvain School of Management, Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, 34 voie du roman pays, L1.03.01, 1348 , Louvain-la-Neuve, Belgium

    Per J. Agrell & Adel Hatami-Marbini

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  1. Amir H. Shokouhi
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  2. Hamid Shahriari
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  3. Per J. Agrell
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  4. Adel Hatami-Marbini
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Correspondence to Per J. Agrell.

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All authors made an equal contribution to this work.

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Shokouhi, A.H., Shahriari, H., Agrell, P.J. et al. Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data. OR Spectrum 36, 133–160 (2014). https://doi.org/10.1007/s00291-013-0336-5

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