Decomposition algorithms for an integrated Home Health Care Planning Problem

P. Cappanera, T. Aldinucci

The growing demand for home-based care, driven by an aging population and chronic diseases, increases pressure on providers, making effective service delivery design essential to ensure high-quality care while controlling costs. In this work, we address an integrated home health care planning problem that jointly considers assignment, scheduling, routing, and rostering decisions in the medium term. The proposed mixed-integer formulation incorporates time window constraints, operator synchronization, labor, and skill compatibility. The objective function minimizes routing, overtime, and idle-time costs while penalizing unserved requests. To address the problem complexity, we propose alternative cluster-based decomposition methods that efficiently exploit the problem's structure. Computational experiments on real-world instances demonstrate that the proposed methods yield high-quality solutions and significantly improve scalability compared to the monolithic formulation.

Palabras clave: Home Health Care, Clustering, Planning, Logic-Based Benders Decomposition

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