Two-stage robust optimisation for surgery scheduling considering surgeon collaboration

Operating rooms (ORs) account for a significant proportion of the costs of maintaining a hospital. Surgery scheduling is optimised to reduce the costs in ORs. However, an important issue that directly affects surgery scheduling is often neglected, i.e. surgeon collaboration. In reality, a surgery requires two surgeons: the main surgeon and an assistant. The surgeon of one surgery might be assigned as the assistant of another surgery. Thus, this paper proposes a two-stage robust model that considers such collaborations. In Stage 1, it determines surgery allocations and surgeon assignments, while in Stage 2, the start time of each surgery is decided. The properties of the solutions are detected, based on which we develop a simple algorithm to solve the two-stage model. In addition, the column-and-constraint generation algorithm is applied to solve the model with a large number of surgeries. The numerical experimentation shows the good performances of the proposed models and algorithms.