Modified super-efficiency DEA models for solving infeasibility under non-negative data set

ABSTRACT It is well known that the super-efficiency (SE) data envelopment analysis (DEA) model can discriminate efficient decision-making units (DMUs), but it is infeasible under the variable returns to scale (VRS) condition. This paper introduces a new modified input-oriented VRS SE model and its corresponding algorithm. Compared with existing modified VRS SE models, the proposed approach has the following advantages: it is feasible in the presence of zero data; it can provide a robust SE score when a tiny perturbation occurs for some zero input of the evaluated DMU; it determines a unique and bounded SE score for all DMUs; it has a good ability of discriminating efficient DMUs. The proposed model can also be used under the constant returns to scale (CRS) condition to settle the infeasibility caused by zero data. To characterize SE further when infeasibility occurs, this paper provides the corresponding output-oriented VRS SE model. The proposed input-oriented and output-oriented VRS SE approaches give the same efficiency identification as the conventional input-oriented and output-oriented VRS SE models do, respectively. Numerical examples are used to demonstrate the practicality and superiority of our approach.