Nested logic-based Benders decomposition for an integrated home healthcare problem
针对挪威居家医疗的人员配置、任务分配、路径与排班集成问题，提出嵌套逻辑型Benders分解方法，将问题分解为三个层次子问题，在40个测试实例中比直接求解混合整数线性规划模型获得更多最优解和可行解。
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.