Solving a multi-period home health care routing and scheduling problem using an efficient matheuristic

This paper focuses on optimizing a multi-period home health care routing and scheduling problem (HHCRSP). The problem consists of assigning suitable caregivers to serve patients at their homes and designing a set of optimized visit routes for caregivers. Various practical constraints such as synchronized visits, lunch breaks, continuity of care, and workload balancing are concerned. There are three objectives considered in this study: the minimization of relevant operational costs, the maximization of the satisfaction of patients and the maximization of the satisfaction of caregivers. First, the target problem is formulated as a mixed-integer programming model, which can be solved directly by a commercial linear programming solver. Considering the NP-hard nature of the target problem, a matheuristic integrating a heuristic (adaptive large neighborhood search, ALNS) and a commercial solver (Gurobi) is proposed to solve large-scale instances efficiently. Two versions of the matheuristic, matheuristic1 and matheuristic2, are developed by combining ALNS and Gurobi in different ways. The experimental results highlight the excellent performance of the proposed matheuristic and the results are quite encouraging compared with those of the pure ALNS and Gurobi solver. In addition, matheuristic2 outperforms matheuristic1 in the majority of the instances. Furthermore, the sensitivities of a set of key characteristics in the model, such as the weight distribution of the objective function, prioritizing continuity of care, and departure rules for caregivers, are analyzed. This study has broad application prospects in the HHC field, and it provides home health care companies (HHCCs) an efficient approach to solve the multi-period HHCRSP and offers the managers managerial insights to achieve the objective they care about the most.