Abstract: The cross-efficiency evaluation is an extension tool of Data Envelopment Analysis（DEA）, however, the existing method which only evaluates all Decision Making Units（DMUs） together does not consider the problem of non-homogeneous between units. This paper proposes a group cross-efficiency model considering the non-homogeneous between DMUs, and it can be used to evaluate performance by assembling reasonably all efficiency values between non-homogeneous groups. Specifically, the first is using benevolent model to analyze each group’s internal relative efficiency values, and then using improved entropy to get group overall optimal weight vectors by assigning appropriate weight for group’s internal DMUs, and finally using traditional cross-efficiency model to evaluate, analyze and rank the relative efficiency value between groups. To prove the theoretical and legal validity of this method, it has been applied to evaluate performance of 16 Chinese Commercial Banks in 2015 and the result showed that the method is effective.

Key words: Data Envelopment Analysis（DEA）, cross-efficiency, non-homogeneous, improved entropy, performance of banks

摘要： 交叉效率评价方法是数据包络分析（DEA）的拓展工具，但是现存交叉效率方法是对所有决策单元（DMUs）统一测评，没有考虑决策单元间的异质性问题。提出了一种考虑决策单元异质性的群组交叉效率模型，将具有异质性的群组间效率值进行合理集结的绩效评价方法。运用仁慈型交叉效率模型分析各群组内部的相对效率值；运用改进的熵权法为群组内部各决策单元分配适当权重，得到群组整体的最优权重向量；运用传统交叉效率模型评价与分析群组之间的相对效率值，并以此进行综合排序。为证明该方法具有理论与适用效力，2015年应用于16家中国商业银行的绩效评价，结果表明该方法行之有效。

关键词: 数据包络分析（DEA）, 交叉效率, 异质性, 改进熵, 银行绩效