基于最近距离投影的DEA两阶段效率评价方法研究

数据包络分析是进行效率评价最重要的方法之一。传统的数据包络分析理论主要寻找有效前沿面上的最远距离投影，在极大化无效性指数的同时也面临着效率改进的巨大难度和高额成本。对于具有两阶段内部生产结构的决策单元，本文从考虑最小改进难度的视角出发，提出了最近距离投影的两阶段效率评价方法。该方法首先得到所有强有效决策单元的线性组合，且这些组合均占优于被评价的两阶段决策单元。然后建立了两阶段范围调整效率评价模型，在确定具有最近投影距离的占优组合的同时，得到了两阶段评价效率。最后，本文运用我国32家上市银行的年度数据对所提出方法进行了应用验证。

A Two-stage DEA Efficiency Evaluation Approach Based on Closest Targets

Data envelopment analysis (DEA) is one of the most important approaches for efficiency evaluation. The basic logic behind the DEA methodology is that a convex combination of a set of comparable and homogeneous decision-making units (DMUs) is calculated to construct an efficient frontier. Then the DMUs can be projected onto that frontier and each DMU is evaluated by calculating the distance to its projection. The traditional DEA theory is mainly based on farthest targets that have the longest distance to the efficient frontier, which would cause huge improvement difficulties and costs by maximizing inefficiencies. On the contrary, there are closest targets for projections, which are more easily attainable and can provide the most relevant solution to remove inefficiency. From this perspective, a new DEA approach is proposed for evaluating DMUs with two-stage structures based on closest targets, whereas previous studies on closest targets ignored DMUs’ internal production structures. To this end, a traditional range-adjusted measure (RAM) model is first used to calculate the relative efficiency for DMUs with two-stage structures, and it obtains some extremely efficient DMUs. Afterward, all linear combinations of extremely efficient DMUs are constructed, which also dominate the evaluated DMU. Then a new RAM model is developed, which calculates the relative efficiency considering the shortest distance to these linear combinations. The proposed approach can compute a two-stage efficiency for DMUs based on closest targets, and also indicate improvement targets for inefficient DMUs with the least efforts on output expansion and input reduction. Finally, the proposed approach is illustrated with an empirical study of 32 Chinese listed banks, with each bank having a two-stage process of fund business and profit earning.