Stochastic structural policies for solving the nurse assignment problem under continuity of care in home care

Home Care (HC) providers are complex organizations that manage a large number of patients, different categories of operators, support staff and material resources in a context affected by high variability. A robust resource planning is crucial for operating in HC organizations; in particular, under continuity of care, one of the main issues is the assignment of the reference nurse to the assisted patients, since this decision has an impact on the nurse workload for the whole duration of stay of the patient. At the same time, this topic is also challenging, since in the literature the high variability of patient demands is still neglected in the HC planning. We derive a set of structural policies for solving the assignment problem of the reference nurse under continuity of care, taking into account the randomness of patient demands and nurse workloads. The goal of the policies is the minimization of a stochastic cost function related to the visits that each nurse provides above his/her capacity. This is an innovative approach with respect to the usual practice of HC providers, where each new patient is assigned to the nurse with the highest expected available capacity, computed as the difference between the capacity and the expected workload. A numerical analysis based on a relevant study demonstrates the validity of the proposed policies.