Treffer: Nested logic-based Benders decomposition for an integrated home healthcare problem.

In this study, we apply nested logic-based Benders decomposition to solve an integrated home healthcare staffing, assignment, routing, and scheduling problem with application in Norway. The proposed method operates at two decomposition levels. Consequently, the entire problem is decomposed into three hierarchical sub-problems: the staffing problem, the assignment problem, and the routing and scheduling problem. These sub-problems are interrelated through two levels of logic-based Benders cuts. Computational experiments on 40 test instances demonstrate the superior performance of nested logic-based Benders decomposition compared to directly solving a mixed-integer linear programming model available in the literature. Specifically, the proposed solution method achieved proven optimality in 28 instances and provided feasible solutions for the remaining 12 instances. In contrast, directly solving the mixed-integer linear programming model yielded proven optimality in 16 instances, provided feasible solutions for 20 instances, and failed to find feasible solutions for 4 instances within the same computational time limit. • Nested logic-based Benders' decomposition is employed to solve an integrated home healthcare problem. • The method jointly optimizes staffing, assignment, routing, and scheduling decisions. • The method enhances caregiver availability for emergencies while maintaining continuity of care. • Computational results show superior performance over directly solving a mixed-integer linear programming model. [ABSTRACT FROM AUTHOR]

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