A network flow-based model for operations planning in home health care delivery

Purpose: To solve the problem, a mathematical model is proposed; it relies on a directed acyclic graph (DAG), in which arcs are used to indicate whether a pair of appointments can be assigned to the same route or not (and so to the same care worker). The proposed model aims at minimizing the personnel required to meet daily demand and balancing workloads among the workers while considering the varying traffic patterns derived from traffic congestion. Design/methodology/approach: This paper aims at providing solution approaches for addressing the problem of assigning care workers to deliver home health-care (HHC) services, demanding different skills each. First, a capacity planning problem is considered, where it is necessary to define the number of workers required to satisfy patients' requests and then, patients are assigned to the care workers along with the sequence followed to visit them, thus solving a scheduling problem. The benefits obtained by permitting patients to propose multiple time slots where they can be served are also explored. Findings: The results indicate that the problem can be efficiently solved for medium-sized instances, that is, up to 100 daily patient requests. It is also indicated that asking patients to propose several moments when they can receive services helps to minimize the need for care workers through more efficient route allocations without affecting significantly the balance of the workloads. Originality/value: This article provides a new framework for modeling and solving a HHC routing problem with multiskilled personnel. The proposed model can be used to identify efficient daily plans and can handle realistic characteristics such as time-dependent travel times or be extended to other real-life applications such as maintenance scheduling problems.