Research Outputs
Peer-reviewed research, working papers, and accompanying code
Working Papers (Under Review)
Integrating Regime-Switching Probabilistic Forecasts into Stochastic Optimization for Nurse Rostering in Mental Health Wards
Abstract
Mental health inpatient wards must deliver the most acute care under persistent demand uncertainty, yet approximately 65% of mental health service nurses already report chronic stress and exhaustion. When occupancy surges without warning, deterministic scheduling approaches fall short, leading to understaffing that harms patient safety and drives staff to leave in a cycle that current practice cannot break. Research has advanced forecasting and staffing optimization in parallel but rarely together, leaving unclear how improving forecast accuracy actually translates into better staffing decisions. We develop the Holistic Multi-Ward Nurse Rostering (HMNR) framework to close this gap, embedding a novel Autoregressive Markov-Switching Regression (AR-MSR) forecasting model, which captures abrupt regime shifts between high and low demand states, within a two-stage stochastic programming formulation that translates probabilistic forecasts into robust staffing decisions across multiple wards simultaneously. Evaluated on daily occupancy data from seven inpatient wards in a UK National Health Service spanning January 2018 to April 2025, HMNR reduces average understaffing by 58.7% and total operational costs by 13.6% compared to deterministic baselines, while raising the probability of maintaining full staff-to-patient ratios to approximately 28%. Critically, our systematic evaluation using the Value of the Stochastic Solution and Expected Value of Perfect Information reveals that forecast accuracy and operational utility are not always aligned, challenging the prevailing assumption that improving predictive performance automatically improves scheduling outcomes.