Continuity-first approach improves home-care resource scheduling outcomes
Continuity-First Lexicographic Optimization for Home-Care Resource Allocation
Logic in Computer Science
Summary
Scheduling home-care workers involves balancing the need for consistent caregiver visits, avoiding too much overtime, and matching caregivers well to client needs. The authors propose a new method, called LEX-COS, that prioritizes continuity first, then reduces overtime, and finally considers compatibility. Compared to a common weighted approach, LEX-COS better reduces continuity issues and overtime without making these worse in any case, though it sacrifices some compatibility. They also provide tools and test cases to compare these approaches systematically.
What this means in practice
- •For home-care operations managers: Improve staff scheduling to prioritize consistent caregiver visits and minimize overtime, enhancing care quality and staff working conditions.
- •For facility scheduling software developers: Incorporate lexicographic optimization into scheduling tools to better balance care continuity and overtime constraints in home-care planning.
- •For healthcare workforce management vendors: Develop scheduling products that explicitly prioritize continuity and overtime reduction in home-care resource allocation for competitive advantage.$Commercial implications: This paper enables building products that offer improved scheduling solutions prioritizing care consistency and staff workload, attractive to home-care providers.
Authors
Tuyen Van Kieu, Khanh Ngoc Do, Khanh Van To
Abstract
Home-care allocation must balance continuity of care, caregiver overtime, and caregiver-service compatibility. The published formulation of the Home-Care Optimal Resource Allocation Problem (HCORAP) uses a weighted policy (Weighted) to combine these outcomes, allowing compatibility gains to offset poorer continuity or additional overtime. We introduce LEX-COS, a lexicographic objective for HCORAP that first minimizes continuity violations, then overtime, and finally maximizes compatibility. We give an exact MaxSAT implementation and construct HCORAP-LC, a reproducible 48-instance synthetic evaluation suite with limited caregiver capacity. Compared with Weighted, LEX-COS reduces both continuity violations and overtime in 42 of 48 instances, without increasing either measure in any instance, while yielding lower compatibility. In 36 instances, LEX-COS achieves better continuity and lower overtime than every Weighted-optimal allocation. On the separate 48-instance Original benchmark, Gurobi and CPLEX, two leading commercial MIP solvers, resolve every instance under both policies and are substantially faster than EvalMaxSAT. EvalMaxSAT also resolves the full benchmark under LEX-COS. Within EvalMaxSAT, replacing sorting networks with Totalizer improves runtime under Weighted, with no clear gain under LEX-COS. These results characterize the effects of giving continuity and overtime explicit priority in home-care allocation.