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Sensitivity and stability analysis in DEA with bounded uncertainty

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Abstract

Measurement errors, incomplete information and noisy input and output data create difficulties in assessing the efficiency of data envelopment analysis (DEA). Previous studies have addressed uncertainty using interval analysis to extend the classical DEA problem to the case of bounded uncertainties. This paper proposes an approach to analyze the sensitivity and stability radius. By assuming that the data vary within a bounded interval, all of the decision making units (DMUs) can be classified as \(\hbox {E}^{++}, \hbox {E}^{+},\) and \(\hbox {E}^{-}\). To determine how sensitive these classifications are to possible data perturbations, the paper develops programs to calculate the stability radius within which the percentage data variation does not change the class of efficiency unit. In addition, the data changes are applied to not only the DMU that is being evaluation but also all of the DMUs and the various input and output subsets.

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Acknowledgments

We appreciate the support from Projects No. 71272160 and No. 71172011 of the National Natural Science Foundation of China, and the major Project No. KJW-A-1410 of strategic research of the Science and Technology Commission of Ministry of Education. This paper was completed as expected.

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Authors and Affiliations

  1. Donlinks School of Economics and Management, University of Science and Technology Beijing, No. 30 Xueyuan Road, Haidian District, 100083, Beijing, People’s Republic of China

    Feng He & Na Zhang

  2. School of Economics and Management, Tsinghua University, No. 30 Shuangqing Road, Haidian District, 100084, Beijing, People’s Republic of China

    Xiaoning Xu & Rong Chen

Authors
  1. Feng He
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  2. Xiaoning Xu
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  3. Rong Chen
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  4. Na Zhang
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Correspondence to Xiaoning Xu.

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He, F., Xu, X., Chen, R. et al. Sensitivity and stability analysis in DEA with bounded uncertainty. Optim Lett 10, 737–752 (2016). https://doi.org/10.1007/s11590-015-0895-2

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  • DOI: https://doi.org/10.1007/s11590-015-0895-2

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