基于样本评价的广义SBM方法及其有效性

The Efficiency Measure of Generalized SBM by Using Sample Units

基于样本评价的广义DEA方法可以通过不同参考集对决策单元的有效性进行评价,但是现有的模型基本都是径向模型,鉴于此提出基于样本生产可能集的广义SBM模型。首先给出决策单元广义SBM有效的定义及其与多目标规划Pareto有效之间的关系,然后改进广义SBM模型,给出决策单元不属于样本生产可能集的判断条件和决策单元效率值的定义,讨论决策单元在样本生产可能集中的投影性质,最后通过算例分析决策单元的广义SBM有效性排序问题。结果表明,广义SBM方法能给出较为完整的有效性排序,且随着移动因子d的增大,可以进一步预测有效决策单元的改进方向。

By using sample units,the generalized DEA method can evaluate the efficiency of decision making units through different reference sets,but the existing models are radial models.In view of this,a generalized SBM model based on the sample production possible set is proposed.First,the definition of generalized SBM efficiency is presented,the relationship between the generalized SBM efficiency and Pareto efficiency of multi-objective programming are explored.Then,the improved generalized SBM is proposed,the judgement condition of decision making unit does not belong to the sample production possible set,and the efficiency score of decision making unit are given.The projection property of decision making unit in the sample production possible set is discussed.Finally,the ranking of generalized SBM efficiency is analyzed by an example.The results show that the generalized SBM method can provide relatively complete efficiency sequencing,and with the increase of moving factor d,the improvement direction of efficient decision making unit can be further predicted.