A stochastic programming approach to surgery scheduling under parallel processing principle

Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to IRs at the second stage of the model. We show that an optimal myopic policy can be used for IR assignment decisions due to the special structure of the model. We minimize the expected total cost of patient waiting time, OR idle time and IR idle time in the objective function. We enhance the model formulation using bounds on variables and symmetry-breaking constraints. We implement a novel progressive hedging algorithm by proposing a penalty update method and a variable fixing mechanism. Based on real data of a large academic hospital, we compare our solution approach with several scheduling heuristics from the literature. We assess the additional benefits and costs associated with the implementation of parallel processing using near-optimal schedules. We examine how the benefits are inflated by increasing the number of IRs. Finally, we estimate the value of stochastic solution to underline the importance of considering uncertainty in durations.