考虑投入和产出指标偏好的广义DEA模型

Generalized DEA Considering Preference of Inputs and Outputs

广义DEA是一种基于决策单元和非决策单元自由选择参考集的扩展DEA模型.传统DEA模型的最优解大多是由线性规划随机计算的,未能充分考虑投入和产出指标的重要程度.将投入和产出指标的决策者偏好引入到广义DEA模型约束条件中,首先定义投入和产出指标偏好矩阵,再将该矩阵纳入广义DEA模型的约束条件,构建了带投入和产出指标偏好的广义DEA模型(GDEA-IP).接下来给出决策单元GDEA-IP有效性与评价指标的量纲选择无关性的证明,以及决策单元为GDEA-IP弱有效和有效的理论证明.算例分析说明GDEA-IP模型的有效性,通过和其它经典模型的对比分析,进一步说明该模型比广义DEA模型具有更大的灵活性和通用性,拓展了DEA方法的理论研究.

Generalized-DEA is an extended DEA model which selects its reference set based on DMUs and non-DMUs.The optimal solution of traditional DEA model is computed randomly by LP solver in most cases,which can’t consider fully importance degrees of inputs and outputs.In this paper,decision maker ’s preferences for inputs and outputs are introduced into the constraints of generalized DEA.The generalized-DEA model with indicator preferences(GDEA-IP) is constructed by defining the indicator preference matrices and incorporating these matrices into the constraints of generalized-DEA model.Next,a proof that the GDEA-IP validity of DMUs is independent of the choice of magnitude of the evaluation indicators is given,as well as a theoretical proof that DMU is GDEA-IP weakly valid or GDEA-IP valid.The analysis of the cases illustrates the validity of GDEA-IP.The comparative analysis of the cases with other classical DEA models shows that GDEA-IP has greater flexibility and generality than generalized-DEA model,which extends the theoretical study of DEA methods.