Stochastic DEA models with different types of input-output disturbances

This paper presents stochastic models in data envelopment analysis (DEA) fo r the possibility of variations in inputs and outputs. Efficiency measure o f a decision making unit (DMU) is defined via joint probabilistic compariso ns of inputs and outputs with other DMUs and can be characterized by solvin g a chance constrained programming problem. By utilizing the theory of chan ce constrained programming, deterministic equivalents are obtained for both situations of multivariate symmetric random disturbances and a single rand om factor in the production relationships. The linear deterministic equival ent and its dual form are obtained via the goal programming theory under th e assumption of the single random factor. An analysis of stochastic variabl e returns to scale is developed using the idea of stochastic supporting hyp erplanes. The relationships of our stochastic DEA models with some conventi onal DEA models are also discussed.