Optimal staff assignment and routing in personalized home care

The increasing demand for labor intensive medical services such as personalized home care has contributed considerably to the rising cost of health care systems throughout the world. An efficient deployment of medical personnel has therefore become a priority for many medical service providers. In this paper, we address a real-world staff assignment and routing problem that was reported to us by a Swiss home care provider. The problem is to determine a multi-day visiting schedule that satisfies various constraints related to time windows, skill requirements, and the availability of personnel. Visiting schedules are evaluated based on service quality and deployment efficiency. We develop a novel mixed-binary linear programming formulation for this problem that is particularly efficient for long planning horizons. Our computational results demonstrate that the proposed formulation outperforms a recently-introduced formulation and is able to devise optimal or near-optimal solutions for real-world problem instances in short running times.