Multi-objective Robust Optimization for Home Health Care Routing and Scheduling Problem

To address the uncertainty surrounding travel and service times in home health care routing and scheduling problem, a budget uncertainty set was employed from the perspective of Robust Optimization. Considering time window and skill-level constraints, a multi-objective mixed-integer programming model was formulated with the objectives of minimizing costs, maximizing robustness and maximizing patient satisfaction. NSGA-Ⅲ was proposed to obtain the Pareto non-dominated solution set for this model. Research findings indicate that, compared with the exact model, the robust optimization model can indeed improve the robustness of the solution, and the lower the risk preference of the manager, the higher the robustness of the solution, however, this comes at the trade-off of higher total costs and diminished patient satisfaction. The number of caregivers significantly influences scheduling outcomes, with a constant number of caregivers showing a positive correlation between total costs and patient satisfaction, and a negative correlation between robustness and patient satisfaction.