Application of Integer Programming to Nurse Scheduling at a General Hospital in Plateau State

Equitable and operationally efficient nurse scheduling is a persistent challenge in Nigerian public hospitals, where staff shortages and high patient loads create difficult rostering environments. This study applies binary integer programming to develop an optimal nurse scheduling model for the general ward of a government hospital in Plateau State, North Central Nigeria. Data were obtained from hospital administration records and structured interviews with the nursing management team, covering shift preferences, mandatory rest periods, skill mix requirements across three daily shifts, and weekly staffing targets. A binary decision variable is defined for each nurse-shift-day combination, and constraints are formulated to enforce minimum staffing levels, maximum consecutive working days, mandated rest intervals, and fair weekend duty distribution. The model is solved using a branch-and-bound algorithm implemented in a spreadsheet optimization environment. Results demonstrate that the optimized schedule reduces instances of understaffing by 60 percent compared to the manually prepared roster and achieves a more equitable distribution of weekend duties. Nurse satisfaction with the proposed schedule, assessed via a brief questionnaire, is significantly higher than with current arrangements. The study identifies computational tractability as an advantage of the model for hospital sizes comparable to the study site. Recommendations include adoption of the scheduling tool on a quarterly basis with input from nursing staff. This research underscores the potential of integer programming to improve healthcare workforce management across North Central Nigeria. Keywords: integer programming, nurse scheduling, hospital management, Plateau State, branch-and-bound