How Stochasticity and Emergencies Disrupt the Surgical Schedule

In health care system, the operating theatre is recognized as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity, and has been the subject of many studies. However, the stochasticity of the operating theatre environment is rarely considered while it has considerable effect on the actual working of a surgical unit. In practice, the planners keep a safety margin, let's say $15%$ of the capacity, in order to absorb the effect of unpredictable events. However, this safety margin is most often chosen subjectively, from experience. In this paper, our goal is to rationalize this process. We want to give insights to managers in order to deal with the stochasticity of their environment, at a tactical--strategic decision level. For this, we propose an analytical approach that takes account of the stochastic operating times as well as the disruptions caused by emergency arrivals. From our model, various performance measures can be computed: the emergency disruption rate, the waiting time for an emergency, the distribution of the working time, the probability of overtime, the average overtime, etc. In particular, our tool is able to tell how many operations can be scheduled per day in order to keep the overtime limited.