Flow-Based Robustness in Consistent Home Care Service Delivery

We address the Consistent Robust Home Care Problem. Home Care refers to medical, paramedical, and social services that may be delivered to patients’ homes, by considering aspects such as caregiver-to-patient assignment, scheduling of patient requests, and caregiver routing. Managing the uncertainty of some parameters in Home Care, such as patient demand, is of paramount importance in limiting service disruptions that might occur when such events are realized. In addition, service regularity, also known as consistency, is very important. Both aspects are indeed managed in the Consistent Robust Home Care, which addresses the patient demand uncertainty, in a consistent way, when assignment, scheduling, and routing decisions are taken simultaneously in a multiple-day time horizon. In this paper, we present an exact mathematical formulation to the problem, by proposing a non-standard cardinality-constrained model which is based on a flow formulation of the uncertainty aspects. The results of a preliminary experimentation are then presented, by performing a comparison with a robust approach from the literature which is however based on an approximation of the considered uncertainty paradigm.