Risk Averse Scheduling for a Single Operating Room with Uncertain Durations

We introduce stochastic programming models for scheduling a single operating room using the variance, value-at-risk (VaR), and conditional value-at-risk (CVaR) as criterions. These criterions express the risk-averse attitude of the scheduler to the risk event that the expected end time of a surgery presumed by a surgeon can be considerably delayed. One of the important advantages of the CVaR is that the stochastic programming problem can be treated as a linear programming problem. The CVaR is thus more practical than the variance, or VaR, as a measure of risk for single operating room scheduling. This paper evaluates the effectiveness of the proposed model by numerical experiments. The results are useful for the management of schedules for a single operating room. We recommend that the scheduler considers both the expected total delay and CVaR when he/she scheduling a single operating room. To avoid the risk of delayed surgery, the scheduler orders surgeries from small to big variances of duration.