Sensitivity and stability analysis in DEA with bounded uncertainty

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 E++,E+,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {E}^{++}, \hbox {E}^{+},$$\end{document} and E-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {E}^{-}$$\end{document}. 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.