Supplementary file 1_Multi-resource operating room scheduling: a three-stage heuristic for efficiency and patient safety.docx

Introduction<p>Operating room (OR) scheduling remains a critical healthcare operations challenge, yet existing approaches suffer from three fundamental limitations: they either oversimplify the multi-resource synchronization requirements, lack provable performance guarantees for clinical decision-making, or fail to adequately integrate emergency responsiveness with elective efficiency.</p>Methods<p> To address these gaps, we formulate the multi-resource OR scheduling problem as a parallel machine scheduling problem with multi-machine joint processing and propose a three-stage heuristic algorithm (TSA) that achieves a worst-case 4/3 approximation ratio for makespan while integrating four objectives: minimizing makespan, reducing resource costs, maximizing high-priority patient satisfaction, and minimizing emergency waiting times.</p>Results<p> Validated on 12,864 surgical records from the MIMIC-IV database, the TSA achieves a 15.79% increase in monthly surgical throughput, a 10.34% reduction in total resource costs, an 18.53% improvement in high-priority patient satisfaction, and a 50.00% reduction in critical surgery waiting time, all within 3.2 s for large-scale instances.</p>Discussion<p> The TSA provides a computationally efficient, empirically validated decision support tool that bridges the gap between academic optimization theory and practical OR management requirements.</p>