A bi-objective stochastic model for operating room scheduling considering surgeons' preferences and collaborative surgeries

Operating Rooms (ORs) are pivotal hospital resources, significantly impacting expenses and revenue. This paper introduces a stochastic bi-objective model for OR allocation and scheduling of elective surgeries, considering surgeons' preferences for specific ORs and preferred start times, as well as the integration of collaborative surgeries (CSs)-where multiple surgeons collaborate to perform a procedure. The proposed stochastic model, which accounts for the inherent uncertainty in surgery durations, seeks to minimize operating costs while maximizing surgeons' preferences, thus offering a balanced solution for hospital management and medical staff. The model is formulated as a Mixed-Integer Linear Programming (MILP) problem and solved using the Sample Average Approximation (SAA) method. A comprehensive sensitivity analysis was conducted to precisely determine the optimal sample size, defined as the number of scenarios used to model the uncertain surgery durations, to ensure the robustness of the proposed approach. This is essential for approximating the probability distribution of surgery durations, for which a lognormal distribution was employed. This analysis enables stable results concerning the variability in surgery durations. Subsequently, the model was applied to a synthesized dataset, which mirrors real hospital operations. The results demonstrated that the model generates optimal OR and surgeon schedules robust enough to accommodate the inherent variability in surgery durations. Additionally, a Pareto-front analysis was employed to examine the trade-off between minimizing operating costs and maximizing surgeons' preferences. Implementing a bi-objective optimization algorithm using the ɛ-constraint method identified a set of optimal schedules, offering valuable insights into balancing cost efficiency and surgeon satisfaction, thereby enabling hospital administrators to make informed scheduling decisions. Extensive numerical experiments were conducted to test the model's scalability and effectiveness in generating optimal schedules under various operational conditions. The results of these experiments suggest that future work could focus on leveraging heuristic techniques to enhance computational efficiency. In conclusion, the proposed stochastic bi-objective model represents a comprehensive and flexible strategy for enhancing operational efficiency and improving surgeon satisfaction in the allocation and scheduling of ORs.