Reservation planning for elective surgery under uncertain demand for emergency surgery

This work concerns the advance scheduling of elective surgery when the operating rooms' capacity utilization by emergency surgery, as well as by elective procedures, is uncertain. New requests for bookings of elective surgery arrive each day. Such procedures preferably would be performed as soon as possible, but admitting too many patients may result in exceeding a day's capacity, possibly necessitating turning away some emergency cases. So the problem facing the hospital at the start of each day is how many of the additional requests for elective surgery to assign for that day. We provide a stochastic dynamic programming model for this aggregate advance scheduling problem. The model has some novel mathematical features. We analyze it and characterize the nature of the optimal policy, which is not necessarily of a control-limit type. Plausible numerical examples which confirm our theoretical results and provide additional insights are reported.