A Nurse Staffing and Scheduling Problem with Bounded Flexibility and Demand Uncertainty

Nurse staffing and scheduling are persistent challenges in healthcare due to demand fluctuations and individual nurse preferences. This study introduces the concept of bounded flexibility, balancing nurse satisfaction with strict rostering rules, particularly a real-world time regularity policy from a major hospital in Singapore. We model the problem as a multi-stage stochastic program to address evolving demand, optimizing both aggregate staffing and detailed scheduling decisions. A reformulation into a two-stage structure using block-separable recourse reduces computational burden without loss of accuracy. To solve the problem efficiently, we develop a Generative AI-guided algorithm. Numerical experiments with real hospital data show substantial cost savings and improved nurse flexibility with minimal compromise to schedule regularity. Numerical experiments based on real-world nurse profiles, nurse preferences, and patient demand data are conducted to evaluate the performance of the proposed methods. Our results demonstrate that the stochastic model achieves significant cost savings compared to the deterministic model. Notably, a slight reduction in the regularity level can remarkably enhance nurse flexibility.