A matheuristic-based approach for the multi-depot home health care assignment, routing and scheduling problem

Home health care structures provide care for the elderly, people with disabilities as well as patients with chronic conditions. Since there has been an increase in demand, organizations providing home health care are eager to optimize their activities. In addition, the increase in patient numbers has led organizations to expand their geographical reach. As a result, home health care structures tend to be located in different offices to limit their travel time and, consequently, caregivers employed by these various structures must be assigned to one of the offices so they start and end their workday at their associated office. Unlike the existing literature where an upstream assignment of caregivers is performed to become a parameter of the model, the assignment of caregivers to offices is solved during the resolution of the problem in order to obtain the best possible combinations. Thus, we suggest a mixed-integer programming model of the multi-depot home health care assignment, routing, and scheduling problem without prior assignment of caregivers to the home health care offices. In addition, we propose an original matheuristic-based approach with different assignment strategies to assign visits and caregivers to the home health care offices in order to solve the problem. The experiments are conducted on a set of 56 heterogeneous instances of various sizes. Results are compared with best solutions obtained by a commercial solver, and with a lower bound obtained by Lagrangian relaxation. The results highlight the efficiency of the matheuristic-based approach since it provides a low deviation ratio with a faster computational time.