A scalable and high-accuracy computational framework for non-convex additive two-stage network data envelopment analysis in big data environments

Owing to the significantly nonlinear and non-convex objective function inherent in the additive two-stage network DEA model, obtaining high-accuracy and computationally efficient solutions remains challenging, particularly in large-scale settings where the number of DMUs and the associated benchmark constraints increase substantially. To mitigate these challenges, this study conducts a detailed analysis of the functional relationship between sub-stage efficiencies and overall efficiency, and develops a shadow-price interval-assisted extreme point search method for identifying candidate frontier segments more efficiently. Furthermore, this study introduces a network hierarchical decomposition preprocessing procedure to screen benchmark constraints satisfying the stated redundancy conditions and improve computational scalability. Numerical experiments on synthetic instances with increasing numbers of DMUs compare the proposed framework with a traditional heuristic method, a Gurobi-based non-convex numerical reference, and a McCormick-linearisation-based comparator. The results show that the proposed framework achieves high numerical consistency with the Gurobi-based non-convex reference, improves runtime performance as the number of DMUs increases, remains stable under different parameter settings, and supports rapid re-optimisation when stage-weight preferences change. These findings provide flexible and scalable support for decision-makers in performance evaluation problems involving two-stage network structures.