A flexible mathematical model for Home Health Care Problems

In the health and social care sectors it is common for some specialized teams to travel to patients homes to provide care. These teams are typically made up of by a number of staff members with varying skills, starting locations and working hours. Patients require different types of care, during specific time windows, and may have special requirements, such as needing two staff members, or multiple visits with some sort of temporal dependency between them. Since teams need to decide which staff member will visit each patient, as well as the routes they will take to do so, this kind of planning problem is known in the literature as the Home Health Care Routing and Scheduling Problem (HHCRSP). We introduce a new mixed integer linear programming formulation for the HHCRSP that extends previous models. Our formulation can readily be adapted to address more specific variants in the scientific literature, proving a larger number of optimal solutions and stronger lower bounds on benchmark instances using the same computational framework. We further propose an instance generator for producing scenarios that closely resemble those of the National Health Service in the United Kingdom.