Nurse-to-patient assignment in home care services with uncertain and temporally correlated patient demand

Assisting patients at home, rather than in hospital, offers many advantages, from the decrease in hospitalization costs to the improvement in the quality of life of patients. Home care services will, therefore, become more and more common in the next future, especially for dealing with the elderly population, who, most of all, benefits from home care treatment. However, home care services are expensive and must be carefully managed in order to make them efficient. A key problem in planning home care services is the assignment of patients to nurses. It is a medium term decision which heavily affects the workload of nurses for a long time horizon. However, when assigning patients to nurses, their demand, namely the number of weekly visits, is not fully known. Indeed, it depends on the patients’ conditions, and they may change along time. We consider the problem of assigning patients to nurses over a planning horizon of several weeks. Patients may require different kinds of continuity of care: they may require to be cared after by only one nurse, or they may accept to be assigned to different nurses in different weeks, but this should be discouraged, or they may be cared after by different nurses even in the same week. To deal with the uncertain temporal evolution of the patients’ demands a robust solution is generated through an implementor-adversarial-like approach. Two levels of flexibility are considered and compared: in the less flexible case the assignment of patients with no continuity requirement is independent from the demand realization, while in the more flexible one it is re-optimized based on the current patients’ conditions.