Abstract: Generalized DEA method is a kind of relative efficiency evaluating method, which can solve the deci-sion making units'efficient comparison relative to any reference system. Be aimed at the decision making units and the sample units may be affected by random factors in the evaluation process, the fund amental genesatized DEA methad, the input and output indexes of the two kinds of units are stochastic, is reseawched in this papew. The stochastic programming is transformed into deterministic programming by expected value model and chance constrained programming. The definition of generalized expectation DEA efficiency and generalized chance con-straint DEA efficiency, the relationship between generalized expectation DEA efficiency and Pareto efficiency of multiple objective programming and the efficiency sorting method of decision making units by mobile factor are given. It can be seen from the calculation example that the evaluation result will be affected whether the variance is considered.

Key words: decision making unit, sample unit, random variable, expected value model, chance constraint programming, generalized DEA method

摘要： 广义DEA方法是基于任意参考系评价决策单元相对效率的评价方法。针对评价过程中决策单元和样本单元可能受到随机因素的影响,本文初步研究这两种单元的输入输出指标分量均随机的基本广义DEA方法。利用期望值模型和机会约束规划将随机模型转化为确定性模型进行求解,给出广义期望DEA有效与广义机会约束DEA有效的概念,广义期望DEA有效与多目标规划Pareto有效关系,以及利用移动因子的决策单元有效性排序方法。通过算例可以看到,是否考虑方差会对评价结果产生影响。

关键词: 决策单元, 样本单元, 随机变量, 期望值模型, 机会约束规划, 广义DEA方法