A Reinforcement-learning-based Column Generation Algorithm for Integrated Operating Room Planning and Scheduling

Abstract: In this paper, we propose a novel mixed integer programming model to formulate integrated operating room planning and scheduling problems, where several mandatory and elective surgeries are to be assigned and scheduled in operating rooms on different days. We consider both overtime in operating rooms and surgeons' daily availability limits. We propose a column generation (CG) algorithm to solve large-scale instances. In order to enhance the CG, we integrate the Reinforcement Learning Algorithm and the Genetic Algorithm and develop a hybrid algorithm to generate initial columns for the CG algorithm. For our analysis, we employed two sets of test instances: one consisting of synthetic data and the other based on real-world cases from a local hospital in Naples, Italy. Computational experiments demonstrate that our proposed model and methodology yields an average optimality gap of 1.23% for synthetic instances and 1.49% on real-world scenarios, significantly outperforming previous solution methodologies in the literature. Additionally, we demonstrate that the developed CG algorithm provides a high-quality solution for large-scale instances where other models and methods fail to obtain even a feasible solution. To further evaluate robustness under uncertainty, we examined scenarios with 20% variability in surgery durations. The results indicate that incorporating a 120-minute buffer time minimizes the overall cost. Moreover, we investigated the impact of emergency surgeries by either introducing additional cases or escalating surgical priorities. For synthetic instances, the inclusion of emergency surgeries increased the total rescheduling cost by 4.13%, whereas in the real-world Naples cases, priority escalation led to only a 0.11% increase.