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.

Optimal charging plan for electric bus considering time-of-day electricity tariff

Purpose–The purpose of this study is to develop an optimization method for charging plans with the implementation of time-of-day(TOD)electricity tariff,to reduce electricity bill.Design/methodology/approach–Two optimization models for charging plans respectively with fixed and stochastic trip travel times are developed,to minimize the electricity costs of daily operation of an electric bus.The charging time is taken as the optimization variable.The TOD electricity tariff is considered,and the energy consumption model is developed based on real operation data.An optimal charging plan provides charging times at bus idle times in operation hours during the whole day(charging time is 0 if the bus is not get charged at idle time)which ensure the regular operation of every trip served by this bus.Findings–The electricity costs of the bus route can be reduced by applying the optimal charging plans.Originality/value–This paper produces a viable option for transit agencies to reduce their operation costs.