Stochastic surgery selection and sequencing under dynamic emergency break-ins

Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.