Stochastic DEA Models With Different Types of Input-Output Disturbances

This paper presents stochasticmodels in data envelopment analysis (DEA) for the possibilityof variations in inputs and outputs. Efficiency measure of adecision making unit (DMU) is defined via joint probabilisticcomparisons of inputs and outputs with other DMUs and can becharacterized by solving a chance constrained programming problem.By utilizing the theory of chance constrained programming, deterministicequivalents are obtained for both situations of multivariatesymmetric random disturbances and a single random factor in theproduction relationships. The linear deterministic equivalentand its dual form are obtained via the goal programming theoryunder the assumption of the single random factor. An analysisof stochastic variable returns to scale is developed using theidea of stochastic supporting hyperplanes. The relationshipsof our stochastic DEA models with some conventional DEA modelsare also discussed. Copyright Kluwer Academic Publishers 2001