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Parallel processing is a principle which enables simultaneous implementationof anesthesia induction and operating room (OR) turnover with the aim ofimproving OR utilization. In this article, we study the problem of schedulingsurgeries for multiple ORs and induction rooms (IR) that function based on theparallel processing principle under uncertainty. We propose a two-stagestochastic mixed-integer programming model considering the uncertainty ininduction, surgery and turnover durations. We sequence patients and setappointment times for surgeries in the first stage and assign patients to IRsat the second stage of the model. We show that an optimal myopic policy can beused for IR assignment decisions due to the special structure of the model. Weminimize the expected total cost of patient waiting time, OR idle time and IRidle time in the objective function. We enhance the model formulation usingbounds on variables and symmetry-breaking constraints. We implement a novelprogressive hedging algorithm by proposing a penalty update method and avariable fixing mechanism. Based on real data of a large academic hospital, wecompare our solution approach with several scheduling heuristics from theliterature. We assess the additional benefits and costs associated with theimplementation of parallel processing using near-optimal schedules. We examinehow the benefits are inflated by increasing the number of IRs. Finally, weestimate the value of stochastic solution to underline the importance ofconsidering uncertainty in durations.

A Stochastic Programming Approach to Surgery Scheduling under Parallel Processing Principle