Stochastic models and variable returns to scales in data envelopment analysis

Stochastic Data Envelopment Analysis models were developed by taking random disturbances into account for the possibility of variations in input–output data structure. The stochastic efficiency measure of a Decision Making Unit (DMU) is defined via joint probabilistic comparisons of inputs and outputs with other DMUs, and can be characterized by solving a chance constrained programming problem. Deterministic equivalents are derived for both situations of multivariate symmetric random disturbances and a single random factor in the production relationships. An analysis of stochastic variable returns to scale is developed.