Stochastic optimization methods for health care delivery: the home care example

Uncertainty is inherent in many health care optimization problems and cannot be neglected,
as it may have a significant impact on the problem solution.
For instance, uncertainty is associated to the availability of ambulances in
locating emergency vehicles, and related to the duration of surgery in planning and scheduling operating room theaters. Uncertainty also occurs in managing Home Care (HC) services: the most critical and frequent random event is a sudden variation in the amount of service required by
HC patients, which is in general highly variable. In this talk, I discuss how to manage uncertain demands while planning the activities of a HC provider, with particular reference to the nurse-to-patient assignment problem under continuity of care. I present three different optimization techniques that include demand uncertainty, i.e., a stochastic programming approach, a robust cardinality-constrained optimization model,
and an analytical policy. In addition, since all these approaches require an estimation of the future patients demands, I briefly discuss two possible stochastic models to predict a patient s care pathway and his/her demands for visits over time. Finally, the application to a relevant real case is described, and the benefits deriving
from implementing the proposed approaches are shown.