Abstract: 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.

Key words: data envelopment analysis; two-stage structures; closest targets; range-adjusted measure; listed banks