Solving Real-World Nurse Scheduling Problem with Simulated Annealing and Automated Parameter Optimization

Abstract

The nurse scheduling problem (NSP) is a complex operational challenge in healthcare, with direct implications for hospital costs, staff well-being, and quality of patient care. Although many methods have been proposed, generating feasible schedules remains challenging due to the diverse and complex constraints. This study addresses a real-world NSP by formulating it as a single quadratic unconstrained binary optimization (QUBO) model, incorporating more than 15 intricate constraints derived from an active hospital ward. To rigorously enforce numerical constraints―such as total working hours―we introduce a novel slack variable method using logarithmic encoding. In addition, preprocessing nurse availability and skill data reduces problem size by eliminating infeasible assignments. A key contribution of this study is the development of a hierarchical hyperparameter optimization framework using Bayesian optimization (Optuna), which addresses the manual and critical task of parameter tuning in metaheuristics. This methodology was applied to a 32-nurse ward, generating an error-free schedule that satisfied all the hard constraints. The schedule was validated by a head nurse, confirming its practical utility. This research demonstrates the feasibility and potential of applying simulated annealing to a real-world NSP. It also establishes a practical QUBO formulation and an automated tuning pipeline, paving the way for future deployment on next-generation annealing hardware.