A multi-time-window multi-objective hybrid fleet home health care routing optimization problem considering caregiver utilization and compatibility

Home healthcare plays a key role in the era of an aging population and limited healthcare resources in hospitals, and one of its important tasks is to develop optimal caregiver visit routines. In the context of sustainable development and dual carbon goals, home healthcare must also address carbon emissions during caregiver visits. One of the most effective initiatives is the use of electric vehicles to gradually replace fuel vehicles as an important means of transportation. Therefore, this paper investigates a multi-objective home healthcare path optimization problem based on a mixed fleet of vehicles. In this problem, the transportation of caregivers is either electric or fuel vehicles, and this paper considers the case of patients with different numbers of multiple time windows, defines compatibility, and optimizes five conflicting objectives under the constraints of time windows, doctor-patient skill matching, electric vehicle battery capacity, compatibility, and maximum working hours. To address this problem, we develop a mixed integer programming model to optimize five objectives: cost minimization, caregiver utilization maximization, workload deviation minimization, patient-caregiver compatibility maximization, and skill level deviation minimization. In addition, this paper proposes a hybrid algorithmic solution model with hybrid simulated annealing and a third-generation non-dominated sorting genetic algorithm and designs two neighborhood structures based on the problem characteristics as well as heuristics for charging station insertion. The results show that the improved hybrid algorithm solves the problem more comprehensively and effectively and can cover a wider solution space with good distribution and diversity.