Identifying production units with outstanding performance

In many applications of data envelopment analysis, there are situations in which a central body manages a large set of similar units delivering some services. In such multi-unit organizations, the central management desires a mechanism by which the local management of each unit is incentivized to perform towards the improvement of the performance of the organization as a whole. In a recent paper, Afsharian et al. (2017) have proposed a system of incentives under these circumstances. In their approach, – which relies on the original concept of super-efficiency – units with outstanding performance are identified and incentivized by some reward compatible with the level of their impact on the overall performance of the organization. We discuss why the conventional super-efficiency approach may not be optimal in such situations. We revisit the definition of the collective impact and propose a new method, which can identify – in a controlled manner – a subset of k outstanding DMUs among n existing units in the system. The proposed approach is illustrated using data from a German retail bank.