Elective Surgery Sequencing and Scheduling Under Uncertainty

Problem definition: We consider a surgery sequencing and scheduling problem with uncertain durations of surgeries in the context of an operating theater. From real data collected from a hospital, we observe the common practice, namely, “to follow,” in which surgeries are conducted sequentially and immediately one after another, according to a specific schedule. Methodology/results: Based on this practice, we propose a mathematical framework to balance the risk of delay and idling using the punctuality index, which takes into consideration both the probability and intensity of delay and idle time. We develop a computationally efficient procedure based on Benders decomposition to derive exact solutions for the problem. The scheduling problem is solvable in polynomial time when the sequence is given. The framework can also accommodate a robust setting when the underlying probability distribution is not fully available. For practical use, we propose two effective heuristics for sequencing decisions by approximating the model. Using real data, we demonstrate that our framework is significantly better than the risk-neutral and probability-maximizing approaches in both performance and computational efficiency. Moreover, the robust setting can effectively lessen the risk of extremely long delay and idle time, and the heuristics are efficient with only a small sacrifice of performance. Managerial implications: With the to-follow policy, our sequencing and scheduling model describes the actual practice better. The two heuristics can be applied easily and directly to help managers of operating theaters to make decisions. Funding: J. Qi is supported by the Hong Kong Research Grants Council Grants 26202016, 16212419, and 16204521. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0029 .