Scheduling Home Hospice Care with Logic-Based Benders Decomposition

We propose an exact optimization method for home hospice care staffing and scheduling, using logic-based Benders decomposition (LBBD). The objective is to match hospice care aides with patients and schedule visits to patient homes, so as to maximize the number of patients serviced by available staff, while meeting requirements of the patient plan of care and scheduling constraints imposed by the patients and the staff. The Benders master problem assigns aides to patients and days of the week and is solved by mixed integer programming (MIP). The routing and scheduling subproblem decouples by aide and day of the week and is solved by constraint programming. We report preliminary computational results for problem instances obtained from a major hospice care provider. We find that LBBD is superior to state-of-the-art MIP and solves problems of realistic size, if the aim is to conduct staff planning on a rolling basis while maintaining continuity of the care arrangement for patients currently receiving service.