A stochastic optimization model and decomposition techniques for surgery scheduling with duration and emergency demand uncertainty

Abstract

A robust and reasonable ex-ante operating rooms (ORs) scheduling for the upcoming surgery day is important as it provides a fundamental reference for equipment management and a working plan for staff physicians. This study aims to develop effective initial OR schedules in the presence of stochastic duration and emergency demand where elective and emergency demand share open multi-functional ORs in a specialty. In addition, physicians’ precedence requirements are considered to ensure that the resulting schedule facilitates the smoothness of each physician’s work under any uncertainty realization. Through characterizing the duration and emergency demand uncertainties by a scenario set, a two-stage stochastic optimization model is formulated to minimize the total expected costs under uncertainties. An effective decomposition algorithm is developed, given that the simpler variant of this problem is known as NP-hard. Several enhancements were added based on the understanding of the proposed problem and the established model. Numerical results highlight the benefits of considering both uncertainties when curating initial OR schedules. The effectiveness of the proposed algorithm and its significant advantage over the commercial solver in terms of efficiency are demonstrated. Finally, to obtain good feasible schedules within a desirably short time, a Monte-Carlo sampling approximation based on our decomposition algorithm is also proposed and its effectiveness is briefly demonstrated.