Operations research: a comprehensive literature review on nurse rostering optimisation

Abstract This comprehensive review aims to address a complex part of operations research, the nurse rostering problem. It is a critical piece of healthcare management, which affects the operational efficiency of hospitals and, at the same time, the quality of patient care. Given the dynamics of the diversity in the healthcare settings and needs, optimising the nurse staff schedule not only improves the care delivery, but also affects staff satisfaction. This review covers a wide range of techniques, including heuristics, meta-heuristics, such as simulated annealing, variable neighborhood search, genetic algorithms, population-based meta-heuristics, such as plant propagation algorithm, bee colony optimisation, and differential evolution, and advanced approaches, like hyper-heuristics, stochastic programming, and hybrid approaches. Additionally, the study explores mathematical optimisation techniques, including integer programming, mixed integer programming, and branch-and-price algorithms, with a special focus on hybrid methods, which combine meta-heuristics with exact optimisation approaches. By analysing key and recent studies, the review shows that hybrid approaches, particularly those integrating meta-heuristics with mathematical models, appear to be the most effective in addressing the complexities of nurse rostering (NR). Future directions, on the other hand, indicate that the growing integration of machine learning and real-time scheduling systems can provide further adaptability and scalability for NR solutions.