Integrated super-efficiency models for network systems: from slack-based measure to unified analysis framework

Abstract As an extension beyond the conventional Data Envelopment Analysis (DEA), non-radial efficiency assessment methods, particularly the Slack-based Measure (SBM) model, have garnered significant attention for their enhanced discriminant power in evaluating black-box systems. Building on this, the Super-SBM (Sup-SBM) model has emerged to rigorously assess the performance of efficient Decision-Making Units (DMUs). While recent extensions of SBM have addressed two-stage or network structures, a systematic framework for Super-SBM in general network systems remains unexplored. This study presents the first comprehensive methodology for Sup-SBM analysis within network systems, introducing innovative models to compute overall and division-specific super efficiency across diverse configurations, including parallel, series, and general networks. To overcome critical challenges in non-radial Super-efficiency measurement, such as reliance on two-stage computational processes and non-Pareto efficient projection points, we develop a Mixed Integer Linear Programming (MILP) model that streamlines efficiency evaluation. Additionally, by integrating a multiplicative analysis framework with the unified super-efficiency approach, we resolve computational complexities arising from ratio-based data and unbounded efficiency scores. The practical applicability and robustness of our models are rigorously validated through numerical experiments and a case study of the European railway industry, demonstrating their effectiveness in real-world settings. This research not only advances the theoretical foundations of efficiency analysis in network systems but also provides actionable insights for policymakers and industry practitioners seeking to optimise complex operational structures.