A novel DEA approach for integrating ordinary and super-efficiency slacks-based measure

Slacks-based measure (SBM) is a non-radial DEA model that considers the assumption of non-proportional changes in resources and products. The traditional DEA models cannot differentiate between efficient units. Although the super-efficiency model has been widely used in literature to distinguish among efficient units, its use for ranking has been criticized by some scholars. This paper proposes an integrated model to simultaneously evaluate both efficient and inefficient DMUs within a unified framework. Although previous studies have proposed SBM-based models that attempt to rank all DMUs simultaneously, some of these approaches may suffer from infeasibility or lack of discriminatory power. This paper proposes a novel model to enhance ranking discrimination while ensuring feasibility and interpretability. A theoretical branch analysis shows that the proposed formulation can be implemented by solving n + q linear programs for all n DMUs, where q ≤ n is the number of evaluations requiring the super-efficiency branch. This LP count and the reported wall-clock times refer to the Phase-1 integrated evaluation only and do not include the subsequent Phase-2 projection adjustment. Controlled experiments covering six data configurations and 20 independent replications show that the proposed Phase-1 implementation attains the lowest median total wall-clock time in all tested configurations. Relative to the sequential SBM-SupSBM procedure and the integrated models of Tone et al. and Lee, the reductions in median computational time range from (0.9%) to (10.5%), from (30.0%) to (75.6%), and from (25.1%) to (71.3%), respectively. These empirical findings are restricted to the reported implementation and computational environment. Guaranteed feasibility, unit invariance, and independence from a user-selected big-(M) parameter are the main structural properties of the proposed model. In addition to integrating the SBM and SupSBM models, the extended framework applies a second-stage Pareto adjustment to weakly efficient initial projections. Its additional value lies in combining this adjustment with the proposed parameter-independent first-stage model and in measuring the inefficiency of the initial projection through an SBM-type normalized fractional term incorporated into the final evaluation.