Performance evaluation in stochastic environments using mean-variance data envelopment analysis

Traditional Data Envelopment Analysis neglects uncertainty for the input–output variables by treating the observations as if they were the true input–output variables to select reference units for efficiency estimation and performance benchmarking. In stochastic environments, the traditional framework may include stochastically dominated reference units and exclude stochastically undominated ones. To incorporate uncertainty for the input–output variables in DEA, we propose a mean-variance framework derived from the theory of stochastic dominance. From that framework an extension to the traditional model is derived that prevents the selection of stochastically dominated reference units. In addition, within the mean-variance approach, variance restrictions can be specified that reduce the uncertainty for the performance of the evaluated unit relative to its reference unit.