Building And Evaluation Of The DEA Models For DMUs With Undesirable Outputs

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 with multiple inputs and multiple outputs. In this paper, the development of DEA theories, DEA methods and DEA applications are discussed. The basic DEA, DEA efficiency theories are analyzed.Extended to the prediction field, DEA methods can solve the prediction problem with multiple inputs and outputs which can not be solved easily by the Regression Analysis method. But the traditional DEA models can not solve the problem with undesirable outputs, so this paper will explore the inherent relationship between goal programming and the DEA method based on the relationship between multiple goal programming and goal programming and build a mixed DEA model which can make all factors of inputs and undesirable outputs decrease in different proportions, and at the same time all the factors of desirable outputs increase in different proportions.Additionally, this paper investigates the relationship between Data Envelopment Analysis (DEA) and Nash-equilibrium Theory in Game-Theory and builds game-DEA models from a Game-Theory perspective. Especially, it will be solved the problem of DMUs with undesirable outputs through these game-DEA models. In the meantime, it is proved that in Game-Theory, it has been shown that Nash-equilibrium is a balance point to protect both players' benefits. On the other hand, Nash-equilibrium is a criterion of the efficiency of DMUs in game-DEA models.Finally, in this paper, it can be showed that the evaluation of investment funds via game-DEA models does not need to select from market combinations and make the results of evaluation more reliable.