Stochastic DEA models with different types of input-output disturbances

This paper presents stochastic models in data envelopment analysis (DEA) for the possibility of variations in inputs and outputs. 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. By utilizing the theory of chance constrained programming, deterministic equivalents are obtained for both situations of multivariate symmetric random disturbances and a single random factor in the production relationships. The linear deterministic equivalent and its dual form are obtained via the goal programming theory under the assumption of the single random factor. An analysis of stochastic variable returns to scale is developed using the idea of stochastic supporting hyperplanes. The relationships of our stochastic DEA models with some conventional DEA models are also discussed.