A Logic-Based Benders Approach to Home Healthcare Delivery

We propose an exact optimization method for home healthcare delivery that relies on logic-based Benders decomposition (LBBD). The objective is to match patients with healthcare aides and schedule multiple home visits over a given time horizon, to maximize the number of patients served while taking into account patient requirements, travel time, and scheduling constraints. Unlike classical Benders methods, LBBD allows us to exploit a natural decomposition of the problem into a master problem, solved by mixed integer programming, and a subproblem that decouples into small scheduling problems, solved by constraint programming. We report computational results based on data obtained from a major home hospice care provider. We find that LBBD is far superior to mixed integer programming on all but a few instances with narrow time windows. It solves problems of realistic size to optimality if the aim is to conduct staff planning on a rolling basis, without temporal dependencies between visits. We also find that a version of LBBD known as branch and check usually outperforms standard LBBD on the instances tested.