An optimization and simulation approach for Operating room scheduling under stochastic durations

Several variants of the Operating room scheduling problem are provided in literature for different contexts. In Tunisia, especially in Habib Bourguiba Hospital in Sfax, Open scheduling policy is considered to schedule elective surgeries. In the orthopedic service, operating room scheduling is carried out weekly. Three operating rooms are available and one of them is assigned to a special kind of surgeries called septic. At the tactical level, elective operations are assigned to weeks so that the workload (average) by week is approximately equal to the weekly capacity. In the selection of surgeries the variation of surgery duration is not taken into account. The average of the operations durations are considered for planning and scheduling. This situation can lead to either an overtime which is unwelcome by surgeons and surgical team. Or an underutilization of OR resources which generate an additional cost for hospital. To deal with this problem, we propose two stochastic MILP models that take into account the stochastic aspect of the surgery duration. Once the set of operations to be carried out in a week are selected, we choose at the operational level to which day and which room the operations are assigned and in which order. As patients are asked to come to the hospital in the morning, the best scheduling is the one that minimizes the patients waiting time. In this paper, we provide two MILP to model this problem. In the first one an additive slack is given to the total duration of surgery to deal with any possible overtime. The other one try to equilibrate the total charge between room/day and the total surgery variations during the week. The two models are solved using Cplex and then a simulation model is used to evaluate the robustness of the provided solutions.