Random-key algorithms for optimizing integrated Operating Room Scheduling

Efficient surgery room scheduling is essential for hospital efficiency, patient satisfaction, and resource utilization. This study addresses the challenge as a combinatorial optimization problem that incorporates multi-room scheduling, equipment scheduling, and complex availability constraints for rooms, patients, and surgeons, facilitating rescheduling and enhancing operational flexibility. To solve such a problem, we introduce multiple algorithms based on a Random-Key Optimizer (RKO), coupled with relaxed formulations to compute lower bounds efficiently, rigorously tested on literature and new, real-world-based instances. The RKO approach decouples the problem from the solving algorithms through an encoding/decoding layer, making it possible to use the same solving algorithms to multiple room scheduling problems case studies from multiple hospitals, given the particularities of each place, even other optimization problems. Among the possible RKO algorithms, we design the heuristics Biased Random-Key Genetic Algorithm with $Q$-Learning, Simulated Annealing, and Iterated Local Search for use within an RKO framework, employing a single decoder function. The proposed heuristics, complemented by the lower-bound formulations, provided optimal gaps for evaluating the effectiveness of the heuristic results. Our results demonstrate significant lower- and upper-bound improvements for the literature instances, notably in proving one optimal result. Our strong statistical analysis shows the effectiveness of our implemented heuristic search mechanisms. Furthermore, the best-proposed heuristic efficiently generates schedules for the newly introduced instances, even in highly constrained scenarios. This research offers valuable insights and practical solutions for improving surgery scheduling processes, delivering tangible benefits to hospitals by optimizing resource allocation, reducing patient wait times, and enhancing overall operational efficiency.