Continuity of DEA efficiency measures

Data envelopment analysis (DEA) is a methodology that allows, in one way or other, the assignment of efficiency scores to members of a group of decision-making units. We call an efficiency measure continuous if small perturbations of the input-output data cause only small changes in the score. Continuity is a desirable property of an-efficiency measure, in particular in the presence of measurement tolerances. Continuity is also desirable from a,numerical point of view because the scores are computed by linear programming software. Focusing on convex production possibility sets we give examples where radial DEA measures fail to be continuous, i.e., they jump under small data perturbations. We present necessary I and sufficient conditions for continuity in terms of the data and show that these conditions are satisfied for almost all data. We also discuss continuity of nonradial measures and identify possible problems of multistage approaches to compute mix efficiencies.