A matheuristic for a multi-depot home health care problem

Abstract

Home health care structures provide cares for the elderly, people with disabilities or patients with chronic conditions. Since the increase in demand, organizations providing home health care are eager to optimize their activities. In addition, the growing number of patients is expanding their geographic reach. As a result, home health care structures tend to be located in different offices to get closer to their patients. As a result, caregivers employed by the 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, we suggest a mixed-integer programming model of the multi-depot home health care problem without pre-assignment of caregivers to offices. As a result, the assignment of caregivers to the offices is resolved during the resolution of the problem in order to obtain the best possible combinations. In addition, we propose an original matheuristic to solve the multi-depot home health care problem without pre-assignment of caregivers to offices. The experiments are conducted on a set of 56 heterogeneous instances. The results highlight the efficiency of the matheuristic since it provides a low deviation ratio compared to an optimization solver with a faster resolution.