Recovery Beds and Blocking in Stochastic Operating Theatres

In health care systems, the operating theatre plays an important part in the creation of care, 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 impact on the actual working of a surgical unit. In this paper, we propose a complete analytical modelling of the operating theatre, aiming at giving insights on how to consider its stochastic reality, and based on the Markov theory. We consider various sources of randomness: stochastic operating times, unpredictable emergencies arrivals, and blocking due to recovery beds. From our model, various performance measures can be computed: the emergency disruption rate, the waiting time for an emergency, the probability of blocking, etc.