Pareto and decomposition based approaches for the multi-objective home health care routing and scheduling problem with lunch breaks

Home health care (HHC) is a fast-growing area of research that has received increasing attention in recent years due to the rise in life expectancy and the fall in birth rates. It is expected to reduce length of stay in hospital as well as to allow patients to receive care and assistance in their home. Several models and algorithms have been proposed to manage the various constraints and criteria. However, multi-objectives HHC routing and scheduling problems (HHCRSP) with practical and complicated constraints as well as Pareto dominance based approaches are still scarce in the literature. In this paper, we focus on modeling and solving the multi-objectives HHCRSP with lunch breaks, multiple time windows, duty length, skill requirement and a mix of soft and hard services. A mixed integer linear programming (MILP) model with three objectives is proposed, which aims to minimize tardiness of soft services and caregivers' waiting times and also to balance their workload. Two approaches, Pareto and decomposition based, with multi-objective evolutionary algorithms are proposed to solve the multi-objective HHCRSP. We developed a memetic algorithm (NSGA-LS), resulting from the hybridization of non-dominated sorting genetic algorithm II (NSGA-II) with multidirectional local search (MDLS), to trade-off between exploration and exploitation. Computational results and performance measures inferred that NSGA-LS has a better performance compared to other algorithms. According to the hyper-volume indicator, NSGA-LS obtained 93.75% better solutions for the tested instances in a pairwise comparison between algorithms while multiobjective evolutionary algorithm based on decomposition (MOEA/D) has better complexity. Sensitivity analysis of the percentage of soft/flexible services and the maximum allowed tardiness showed that increasing them significantly improved the quality and trade-off of solutions.