A combined optimization-simulation approach to the master surgical scheduling problem

This paper addresses the master surgical scheduling problem. First, we present a mixed integer programming model. The model assumes that the cases in a hospital's waiting list can be classified into homogeneous surgery groups based on the resources (e.g. operating room, post-surgical beds) that they are expected to require. Hence, it produces a solution that indicates, for each day of the month and for each time slot of the day, the number of cases to treat and the surgery group these cases must belong to. The model maximizes the patient throughput, takes into account the cases' due dates and allows for control of the waiting list. Secondly, we illustrate the results of a simulation study through which we test the model solution's robustness against the randomness of surgery duration and the length of stay. Finally, we present a combined optimization simulation approach that allows us to fine tune the optimization model to trade-off robustness and efficiency. Our study shows that, by planning surgery groups instead of individual cases and by combining optimization and simulation, it is possible to obtain schedules that are both robust and easy to implement. In addition, it shows that such a combined approach allows for the performance of more accurate scenario analyses. The results presented in this paper are based on real data from the Meyer University Children's Hospital in Florence, which is one of the most renowned children's hospitals in Italy.