Multi-objective home healthcare routing and scheduling problem based on sustainability and “physician–patient” satisfaction

Home healthcare is a product of an aging population, increased awareness of health management and growing demand for medical services. Home healthcare providers need to rationally and efficiently route caregivers to visit their customers. This paper investigates the green home healthcare routing and scheduling problem with simultaneous consideration of physician–patient satisfaction and sustainability based on prospect theory, which simultaneously optimizes four objectives including minimizing total cost, carbon emission, maximizing customer satisfaction, and caregiver satisfaction. Practicalities such as maximum working hours, load balancing, physician–patient skill level matching, customer prioritization, and time windows are also considered. In addition, an improved adaptive reference point-based third generation non-dominated sorting genetic algorithm is proposed to solve the problem. Finally, numerical experiments on various scales were conducted to verify the effectiveness of the algorithm, and the results show that the algorithm can provide decision makers with a larger number of feasible no dominated solutions, and can effectively solve the home healthcare path planning problem. It is also compared with three algorithms, second generation of non-dominated sorting genetic algorithm, third generation non-dominated sorting genetic algorithm, and adaptive reference point-based third generation non-dominated sorting genetic algorithm, to further verify that the proposed improved adaptive reference point-based third generation non-dominated sorting genetic algorithm performs better in terms of solution speed, distribution of Pareto-optimal solutions, convergence, and diversity in various instances. The problem proposed in this study synthesizes the goals of multiple stakeholders in home healthcare and is more conducive to the sustainable forward development of the enterprise.