| Data Envelopment Analysis(DEA) is an intersectional field of operation research, management science and mathematical economics. DEA depends on mathematical programming to evaluate the relative efficiency of DMUs multiple inputs and multiple outputs. In this dissertation, the development of DEA theories, DEA methods and DEA application are discussed. The basic DEA models and DEA efficiency theories are analyzed.However, the traditional models have many limitations. In the practical environment, the inputs or outputs of the decision making units can not be controlled or adjusted by the decision maker because of the environment restrictions, so called uncontrollable factors; in the mean time, the production process may produce some pollutants that were undesired, such as waste water, exhaust gas and so on, so called undesirable outputs. To estimate the efficiency of these kinds of decision making units, we should consider both the uncontrollable factors and the undesirable outputs. So this paper constructs a collective DEA model with both two factors mentioned above. We also find that DEA models are based on an anterior and exact data set, but in practical situations the data of inputs and the outputs are ever-changeful and unexpectedly. As a result, DEA efficiency measurement may be sensitive to such stochastic variations. This dissertation is to randomization the collective DEA model based on the expected value theory, propose the definition of the expected efficiency score and analysis of the relative efficiency of decision making units based on the expected value approach.Finally, we apply the new type of stochastic DEA model into practice. The model is used in a HIV immunology model and the efficient drug treatment strategies are then explored. Age of patients, stochastic errors and side effects are considered in this model, which is an advantage over other deterministic efficiency models. Some of our conclusions agree with those published in related papers. |
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