Robust nurse-to-patient assignment problem in Home Health Care with correlated time-correlated service times and random arrivals of patients

June 19, 2026

Home Health Care (HHC) systems face mounting pressure from demographic ageing, the rising prevalence of chronic conditions, and a persistent global shortage of nurses. In this setting, the assignment of nurses to patients over a multi-week planning horizon is a central tactical decision, shaped by continuity of care requirements and by two sources of uncertainty: variable and time-correlated service times, and new patient arrivals that are not known in advance. This work proposes a multi-period robust optimization model that jointly addresses admission and assignment decisions under both sources of uncertainty, while preserving three continuity of care regimes. The model extends the implementor-adversary approach of Carello and Lanzarone (2021) through a cardinality-constrained arrival uncertainty set, governed by a budget parameter that caps the number of weeks in which demand may deviate from its nominal value, and through a piecewise-linear overtime cost structure that represents contractual regimes with increasing penalties on workload excess. The formulation was applied to a case study inspired by an Italian HHC provider and evaluated on three representative instances spanning different team sizes, demand intensities, and uncertainty regimes. The results show that arrival uncertainty is absorbed primarily through admission control, while the overtime cost structure determines whether workload is concentrated on individual nurses or distributed across the team. A controlled comparison with the reference model confirms that the proposed framework generalizes it, matching its performance when arrivals are effectively deterministic and producing feasible plans in regimes where the reference model becomes infeasible.

Authors in the community:

• 

  F

  Francisca Maria Sanina do Espírito Santo e Silva

  ist193638

Supervisors of this institution:

• 

  I

  Inês Marques Proença

  ist427860

other-engineering-and-technologies - Other engineering and technologies

eng - English

Instituto Superior Técnico