Multi-Objective Optimization in Short and Mid-term Home Health Care Planning

Summary : The Home Health Care (HHC) provides care to the elderly, disabled, and chronically ill, funded by social insurance and taxation. To meet the growing demand, HHC companies must plan effectively to maximize resource utilization and ensure quality care. In the HHC companies, managers accept a limited number of patients, assess their dependency level, and plan their weekly services. Caregivers, both internal and external, visit patients according to predefined routes and schedules.

For the weekly planning, our first goal is to optimally create routes and schedules considering multiple stakeholders’ needs. Secondly, we aim to provide the ideal number of each type of caregiver for hire, to effectively manage the fluctuating task volumes resulting from the varying demands of admitted patients. We propose a mixed-integer linear programming model and a large neighborhood search within an enhanced multi-directional local search framework to solve the problem. The results show superior performance compared to the augmented ε-constraint method, and management recommendations are provided.

Following weekly home care planning, uncertainties related to service times may arise on each day, affecting service quality. To address this, we introduce a bi-objective optimization problem under uncertain service times for daily planning. We propose deterministic and stochastic versions of an adaptive large neighborhood search integrated into an enhanced multi-directional local search framework, offering superior efficiency compared to the Gurobi Solver. The robustness of our model and method is verified by a sensitivity analysis. Finally, the practical application of this method is demonstrated through a real-life case, accompanied by managerial recommendations.