A multi-objective approach for the nurse scheduling problem. A home health care delivery case study

Stress and job dissatisfaction among nurses pose serious challenges for healthcare managers, directly affecting staff retention. Developing schedules that accommodate nurse preferences is essential to mitigate dissatisfaction and turnover. Traditional scheduling approaches often overlook critical trade-offs between preferences and requirements, resulting in models that fail to capture staff motivations or effectively handle the complexity of real-world scenarios, such as home health care services. This paper presents a multi-objective optimization approach that integrates various nurse preference dimensions, including desired days off (even weekends) and balanced workload distribution. A Mixed-Integer Linear Programming (MILP) model, within an ε-constraint method, is proposed to evaluate and uncover inherent trade-offs in nurse preferences. The method was tested using both real and synthetic datasets derived from home healthcare units in Bogotá, Colombia. Results demonstrate its practical effectiveness in improving scheduling by incorporating nurse satisfaction and enhancing workload balance by an average of 60% during months with full nurse capacity. Furthermore, the approach provides decision-makers with a clear understanding of trade-off dynamics, illustrating how nurse availability and vacation requests significantly influence optimization strategies. This approach generates efficient schedules within seconds, substantially outperforming time-consuming manual processes. It also offers actionable insights for planning when constrained capacity leads to infeasible solutions, ultimately supporting staff well-being and operational efficiency.