Mathematical Scheduling of Nurse Workload in University College Hospital, Ibadan

Nurse scheduling in tertiary hospitals is a complex combinatorial optimisation problem with significant implications for patient safety, staff wellbeing, and operational cost. This study develops and implements an integer programming-based nurse scheduling model for the medical and surgical wards of the University College Hospital, Ibadan, Oyo State, South West Nigeria. The model assigns nurses across three daily shifts over a four-week scheduling horizon, satisfying constraints including minimum ward coverage requirements, maximum consecutive working days, contractual days off, skill-mix ratios, and individual preference requests. Data on ward census patterns, shift demand fluctuations, nurse qualifications, and existing schedule structure are collected over a 12-week observational period. The binary integer programming formulation is solved using the branch-and-bound algorithm implemented in Python-PuLP. The optimal schedule achieves a 21 percent reduction in overtime expenditure relative to the manually constructed reference schedule while satisfying all hard constraints. Nurse preference satisfaction rate improves from 54 percent in the manual schedule to 79 percent in the optimised schedule. Ward coverage deficits, a patient safety indicator, are eliminated under the optimised schedule. Sensitivity analysis shows that a 10 percent increase in ward census requires three additional full-time equivalent nursing positions to maintain coverage standards. Keywords: nurse scheduling, integer programming, University College Hospital Ibadan, workforce optimisation, healthcare management.