A novel radial super-efficiency DEA model handling negative data

Super-efficiency model in the presence of negative data is a relatively neglected issue in the DEA field. The existing super-efficiency models have some shortcomings in practice. In this paper, a novel VRS radial super-efficiency DEA model based on Directional Distance Function (DDF) is proposed to provide a complete ranking order of units (including efficient and inefficient ones). The proposed model is feasible no matter whether data are non-negative or not. This model shows more reliability on differentiating efficient units from inefficient ones via a new bounded super-efficiency measure. It can project each unit onto the super-efficiency frontier along a new non-negative direction and produce improved targets for inefficient units. The model overcomes the infeasibility issues occur in Nerlove–Luenberger supper-efficiency model. The proposed model conveys good properties such as monotonicity, unit invariance and translation invariance. Apart from numerical examples, an empirical study in bank sector demonstrates the superiority of the proposed model.