Data Envelopment Analysis And Chance Constrained Models

In this paper, firstly, the development of date envelopment analysis (DEA)theories, DEA methods and DEA application are discussed, the basic DEA models,DEA efficiency theories are analyzed. Secondly, this paper presents the developmentof stochastic models in DEA. The random in inputs and outputs can be characterizedby probability. Efficiency measure of a DMU is defined and can be characterized bysolving a chance constrained programming problem. We build joint chanceconstrained models, marginal chance constrained models and satisficing DEA models.By utilizing the theory of chance constrained programming, deterministic equivalentsare obtained for both situations of multivariate symmetric random disturbances and asingle random factor in the production relationships. We prove the existence ofoptimal solution and deterministic equivalents of the models. The linear deterministicequivalent and its dual form are obtained via the goal programming theory under theassumption of the single random factor. We introdnce the relation of E-models andP-models. Finally, a case and analyses on the models are given to point out the modelhas a promising use in practice.