中立型两阶段交叉效率评价方法

在数据包络分析中，已有的两阶段交叉效率评价方法，不仅只能用于基本两阶段网络结构，而且没有中立地分解子阶段效率。文章提出了一个既适用于基本两阶段网络结构，又适用于具有共享输入的两阶段网络结构的，中立型交叉效率评价方法。该方法定义自评时整体效率等于子阶段效率的加权和，在自评整体效率最大的前提下，从使各子阶段效率都尽可能大的角度为每个决策单元分别确定一组最优权重，进而通过互评计算决策单元整体和子阶段的最终效率得分。最后，通过两个实例验证了方法的实用、合理、有效。

A Neutral Two-stage Cross-efficiency Evaluation Approach

In data envelopment analysis, the existing two-stage cross-efficiency evaluation approach not only has not neutrally decomposed sub-stage efficiency, but also can only be applied to the basic two-stage network structure. A neutral cross-efficiency evaluation approach is present for both basic two-stage network structure and two-stage network structure with shared inputs. In this approach, the overall efficiency of self-evaluation is equal to the weighted sum of the sub-stage efficiency; on the premise of maximizing the overall efficiency of self-evaluation, an optimal set of weights is determined for each decision making unit from the perspective of maximizing the efficiency of each sub-stage; then the final efficiency scores of the whole and sub-stages of the decision making unit are calculated by mutual evaluation. Finally, according to the data in literature ［18］ and ［29］, 24 insurance companies decomposed into basic two-stage network structure and 27 banks decomposed into two-stage network structure with shared inputs are taken as examples. By comparing and analyzing the results of the existing approaches, it is verified that the proposed approach is applicable to a variety of complex network structures, and the approach is practical, reasonable and effective. The contribution of this paper is that the improved efficiency evaluation approach makes up for the limitations of the existing two-stage cross-efficiency evaluation approach and can be applied to many practical problems.