Stochastic Bi-level Programming Model for Home Healthcare Scheduling Problems Considering the Degree of Satisfaction with Visit Time

Home health care(HHC)includes a wide range of healthcare services that are performed in customers'homes to help them recover.With the constantly increasing demand for health care,HHC policymakers are eager to address routing and scheduling problems from the perspective of optimization.In this paper,a bi-level programming model for HHC routing and scheduling problems with stochastic travel times is proposed,in which the degree of satisfaction with the visit time is simultaneously considered.The upper-level model is formulated for customer assignment with the aim of minimizing the total operating cost,and the lower-level model is formulated as a routing problem to maximize the degree of satisfaction with the visit time.Consistent with Stackelberg game decision-making,the trade-off relationship between these two objectives can be achieved spontaneously so as to reach an equilibrium state.A three-stage hybrid algorithm combining an iterated local search framework,which uses a large neighborhood search procedure as a sub-heuristic,a set-partitioning model,and a post-optimization method is developed to solve the proposed model.Numerical experiments on a set of instances including 10 to 100 customers verify the effectiveness of the proposed model and algorithm.