Bicriteria Vehicle Routing Problem with Preferences and Timing Constraints in Home Health Care Services

Home Healthcare (HHC) is an emerging and fast-expanding service sector that gives rise to challenging vehicle routing and scheduling problems. Each day, HHC structures must schedule the visits of caregivers to patients requiring specific medical and paramedical services at home. These operations have the potential to be unsuitable if the visits are not planned correctly, leading hence to high logistics costs and/or deteriorated service level. In this article, this issue is modeled as a vehicle routing problem where a set of routes has to be built to visit patients asking for one or more specific service within a given time window and during a fixed service time. Each patient has a preference value associated with each available caregiver. The problem addressed in this paper considers two objectives to optimize simultaneously: minimize the caregivers’ travel costs and maximize the patients’ preferences. In this paper, different methods based on the bi-objective non-dominated sorting algorithm are proposed to solve the vehicle routing problem with time windows, preferences, and timing constraints. Numerical results are presented for instances with up to 73 clients. Metrics such as the distance measure, hyper-volume, and the number of non-dominated solutions in the Pareto front are used to assess the quality of the proposed approaches.