Two non-radial measures of super-efficiency in DEA with data uncertainty

Measuring errors or uncertainties in inputs and outputs create difficulties for performance evaluation in data envelopment analysis (DEA). The literature deals with the uncertainty using fuzzy or stochastic approaches. However, specifying the membership function or probability distribution is not always easy. This paper proposes a new method by assuming the inputs and outputs vary within a bounded interval and using interval analysis to extend the classic radial DEA models to two non-radial DEA models with bounded uncertainty, respectively. One is used to obtain efficiencies on the basis of slacks-based measurement (SBM) of super-efficiency DEA model, and the other is used to identify specific inefficiencies on the basis of additive super-efficiency DEA model for the decision making units (DMU) under evaluation. To solve the interval non-radial DEA models, the paper adopts the optimization theory to transform the uncertain two-level programs into deterministic one-level programs, and an acceptability index to compare and rank any of the resulting interval efficiencies. Numerical analysis illustrates the advantage of this new approach against conventional methods.