Nested logic-based benders decomposition for an integrated home healthcare problem

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Abdalrahman Algendi, Sebastián Urrutia, Lars Magnus Hvattum, Rafael A. Melo
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引用次数: 0

Abstract

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.
用于集成家庭医疗保健问题的基于嵌套逻辑的弯曲器分解
在本研究中,我们应用基于嵌套逻辑的Benders分解来解决挪威应用的综合家庭医疗保健人员配置、分配、路由和调度问题。所提出的方法在两个分解层次上运行。因此,整个问题被分解为三个层次子问题:人员配置问题、分配问题和路由和调度问题。这些子问题通过基于逻辑的两个层次的Benders切割相互关联。40个测试实例的计算实验表明,与直接求解文献中可用的混合整数线性规划模型相比,基于嵌套逻辑的Benders分解具有优越的性能。具体而言,所提出的求解方法在28个实例中实现了已证明的最优性,并为其余12个实例提供了可行的解。相比之下,直接求解混合整数线性规划模型在16个实例中证明了最优性,在20个实例中提供了可行解,在相同的计算时限内未能找到4个实例的可行解。
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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