An optimization tool to dimension innovative home health care services with devices and disposable materials

Home health care (HHC) consists of care services provided to patients at their domicile rather than in hospitals or other health facilities. HHC human resources are largely studied in the optimization literature, to improve service quality and efficiency. However, the growth of complex HHC services that include the delivery of devices and disposable materials makes it necessary to include them in the decision-making process together with human resources. In fact, they may represent a high cost item, and their release may affect the scheduling of HHC visits. Unfortunately, as far as our knowledge, devices and materials are not considered together with the technical staff required to support their utilization. In this paper, we address the dimensioning problem for new HHC services that also involve devices and materials, considering the joint dimensioning of human and material resources. We include three categories of staff (nurses, physicians and technicians), a set of devices and a set of materials; also, we assume that the requirements from patients are in terms of frequencies, i.e., the maximum number of days between two consecutive visits, two supplies of a material or two uses of a device. We propose a linear programming model and a matheuristic approach for solving instances of realistic dimension. The model allows determining the number of nurses, physicians, and technicians to be hired, as well as the number of devices to be acquired to meet the demand. As for the matheuristics, we combine a decomposition step and a heuristics inspired by the Local Branching idea. Results show the capability of the approach to solve the problem and provide good dimensioning solutions, which can be actually adopted in real-life problems. Moreover, the matheuristic approach performs well in a variety of instances.