The home health care location-routing problem with a mixed fleet and battery swapping stations using a competitive simulated annealing algorithm.

Population aging and a shortage of medical resources are driving the growth of home health care (HHC). Many HHC studies have focused on developing an optimal routing plan to reduce operation costs; however, few have addressed the attendant long-term sustainability concerns, such as HHC center locations and carbon emissions from transportation. This paper proposes a home health care location-routing problem with a mixed fleet of electric and conventional vehicles that considers battery swapping stations. It aims to simultaneously determine the locations of HHC centers, the scheduling of caregivers with respect to skill requirements, and a routing plan for a mixed fleet under specific time windows, load capacities, synchronized visits, and driving ranges. To address this problem, the paper proposes a novel competitive simulated annealing (CSA) algorithm in which a series of problem-specific effective local search operators expand the solution space of the CSA algorithm, with a competitive mechanism to adaptively adjust these operators to accelerate convergence speed and improve exploration ability. To enhance the exploitation ability, it employs a modified simulated annealing algorithm with a heating strategy and variable neighborhood descent. Comparison experiments are conducted to verify the superior performance of the CSA algorithm in comparison to existing algorithms and the Gurobi solver. Finally, sensitivity analyses are performed on key factors and provide some new managerial insights.