Realization‑based robust assignments for a nurse‑to‑patient assignment problem in home health care services

A major challenge in home health care services is to ensure continuity of care despite uncertain patients’ evolutions. Providers must face the trade-off between reassigning patients to balance workloads and keeping the assignments to guarantee continuity of care. In practice, patients with weaker continuity requirements are reassigned. However, this reassignment strategy has not yet been formalized in the literature. We consider a nurse-to-patient assignment problem in which patients require different continuity of care levels. We propose an approach that includes realization-based reassignments along with uncertain and time-correlated service times, in which the problem is solved on a long planning horizon, to provide the assignments of nurses to all patients, and the assignments of patients with weaker continuity of care requirement are periodically rediscussed when the actual service times are known. The long-term assignments are provided by solving a robust model using the implementor-adversary approach, to include time-correlation in the uncertainty set of patients’ service times. We provide two objective functions for the problem, with either constant or increasing overtime cost. The adversarial problem aims to build the service time realizations that maximize the cost, provided that the patients with a weaker continuity requirement are assigned to guarantee the minimum overtime cost. As this is a challenging problem, we also provide three heuristic approaches. The framework is applied to realistic instances, and the results confirm the effectiveness of the approach.