Beyond Opacity: Interpretable Machine Learning for Hospital Efficiency Assessment

Hospital efficiency optimization remains a critical challenge as healthcare systems worldwide face mounting economic pressures. Traditional efficiency assessment methods often lack predictive capability, while machine learning approaches frequently operate as opaque "black boxes" unsuitable for high-stakes healthcare decisions. This study presents an integrated interpretable machine learning and multi-objective optimization framework for hospital resource allocation, bridging Data Envelopment Analysis (DEA) with explainable artificial intelligence and prescriptive analytics. The methodology comprises a four-stage analytical pipeline: (1) DEA-based efficiency scoring through Principal Component Analysis, (2) Agglomerative Hierarchical Clustering with Ward linkage for hospital stratification into efficiency tiers, (3) Decision Tree classification with SHAP (SHapley Additive exPlanations) interpretability analysis, and (4) NSGA-II bi-objective optimization with data-driven grid search for context-specific resource allocation strategies. Validated on 127 public hospitals across five institutional typologies, the framework achieved 94.87% classification accuracy (AUC = 0.993). SHAP analysis revealed that energy costs (mean |SHAP| = 0.2416) and medical staffing levels (0.2257) constitute the primary efficiency determinants, while equipment showed negligible contribution. Multi-objective optimization demonstrated substantial strategic heterogeneity: optimal weight configurations ranged from balanced (0.5/0.5) to energy-focused (0.9/0.1), with personnel ratios spanning 51%-77% across hospital types. Critically, 47% of hospitals require clinical staff reductions while 16% require increases, demonstrating that uniform resource allocation guidelines are inadequate for heterogeneous healthcare systems. By integrating explanatory analysis with prescriptive optimization, this framework transforms black-box predictions into transparent, context-specific, evidence-based recommendations for sustainable healthcare resource management.