Planning and scheduling operating rooms for elective and emergency surgeries with uncertain duration

In this paper we investigate the planning of operating rooms at Rigshospitalet, a large Danish hospital. Each operation must be assigned to a specific operating room and also be scheduled for a specific time while taking into account clinical guidelines. Both elective and emergency operations are included, such that the elective operations are planned while still taking potential emergency operations into consideration. Furthermore, the duration of each operation is uncertain. The aim is to construct robust operating room schedules that minimise overtime work and release unused capacity.

Due to the uncertainty associated with arrival of emergency patients and also the duration of each operation, a deterministic model is not suitable for this problem. Therefore, we develop a stochastic model where operation duration can vary and where the arrivals of emergency patients are unknown. The stochastic model is computationally heavy, so two mixed integer programming based heuristics denoted 2-Step Relax-and-Fix and All Open Relax-and-Fix are developed to solve the problem.

The computational study is based on an extensive dataset compromising 304 days. The heuristics give good results with half of the operating rooms having less than 8 min of overtime work. To test the robustness of the solutions we carry out a simulated implementation of the operation plans. The simulation shows that the heuristic solutions are fairly robust. In general, results show a clear potential for implementing the method for planning and scheduling of operating rooms at Rigshospitalet.