A stochastic model for scheduling elective surgeries in a cyclic Master Surgical Schedule

In this study we propose a stochastic model that determines the number and type of surgeries to schedule in a two-week planning horizon where each operating session is assigned to a surgical specialty according to a fixed grid (Master Surgical Schedule). Our model considers surgery times, intensive care unit times and post-surgery lengths of stays stochastic and accounts for the availability of both intensive care unit beds and post-surgery beds. It aims to maximise the expected operating theatre's throughput. The assignment problem, modelled as a stochastic problem, is solved via a sample average approximation. It gets an estimate of the optimum expected throughput for each specialty and of the operating theatre. We illustrate the application of the model on a real case study with real data from a leading European Children's Hospital, study the sensitivity of obtained results to the two-week planned grid, and highlight the importance of considering the stochastic nature of the problem.