As a new service model, home health care can provide effective health care by adopting door-to-door service. The reasonable arrangements for nurses and their routes not only can reduce medical expenses, but also can enhance patient satisfaction. This research focuses on the home health care scheduling optimization problem with known demands and service capabilities. Aimed at minimizing the total cost, an integer programming model was built in this study, which took both the priorities of

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... s and constraints of time windows into consideration. The genetic algorithm with local search was used to solve the proposed model. Finally, a case study of Shanghai, China, was conducted for the empirical analysis. The comparison results verify the effectiveness of the proposed model and methodology, which can provide the decision support for medical administrators of home health care. Sustainability 2017, 9, 253 2 of 22 world population as of 25 January 2017, based on the latest United Nations estimates. However, according to the report from China Daily, the medical resources of China only accounted for about three percent of the world's medical resources. In recent decades, China's demographic landscape has been thoroughly redrawn by unprecedented population changes, and the problem of a rapidly aging population has become more severe. The elderly population has grown substantially, and its share has reached about 10.5% of the total population in China. In particular, 80%-90% of the elderly population suffered from various chronic diseases, which has brought about the tremendous pressure on pension funds. According to China's elderly population and the aging career statistics in 2015, the elderly aged 60 years and older increased to 212 million, accounting for 15.5% of China's total population, which was significantly higher than the ratio in the traditional standard aging society (10%). Meanwhile, the pension services have been comprehensively increased, including pension beds, day care institutions and meal-aid services. It can be seen that these kind of medical and pension services serving the community and family would play important roles in health care in the aspects of relieving pension pressure, easing the tension between limited medical resources and increasing medical needs and improving the quality of pension and health care services. Most studies in China focused on the qualitative description of home health care services while paying little attention to resource management or scheduling optimization in family medical care. Actually, despite a vast range of prospects in home health care services, as well as its application and development in China, relevant management optimization methods designed to make the operation of home health care more reasonable and effective are still scarce. Compared with the traditional service industry, home health care service has its own features, as well as troubles in scheduling management. In the resource management and scheduling of home health care service, we should take various uncertain factors such as the uncertain demand, stochastic traveling time and high randomness of service time into account. In addition, there are many real constraints (time windows limit, care service priority, service consistency, workload balance, and so on). The factors mentioned above bring difficulties and challenges to home health care service management and scheduling compared with the traditional hospitalization. Therefore, it is necessary to explore research on scientific management and scheduling optimization methods to solve the problems of high randomness and a dynamic environment by taking the features of a structural network into consideration. According to the existing research of home health care, combined with practical difficulties and features, this paper focuses on the scheduling optimization of home health care service by considering patients' priorities and time windows. The rest of this paper will be organized as follows. A literature review is presented in Section 2. Section 3 describes the scheduling optimization model. The genetic algorithm with local search is provided in Section 4. Section 5 provides the empirical analysis and relevant results. Finally, the conclusion will be given in Section 6. Literature Review Many scholars have conducted research in the application of home health care. Chahed et al. [1] pointed out that resource planning is very important in the operation of home care organizations by properly managing human and physical resources so as to avoid the flow or the progress from poor efficiency, medical delay and low-quality service. Eveborn et al. [2, 3] , Bertels and Fahle [4], Thomsen [5] and Bennett and Erera [6] studied a program of human resources in home care, but they did not consider the consistency of medical service requirement. Bard and Purnomo [7, 8] developed an integer programming model for the problem of scheduling nurses by using the branch and bound algorithm, the column generation method and the Lagrangian relaxation technique. Belien and Demeulemeester [9] integrated the scheduling of nurses and the operating room and solved it by the column generation method. Punnakitikashem et al. [10] established a scheduling model that involves nurses' favor and medical contraction. Hertz and Lahrichi [11] proposed a two-stage mixed programming model to distribute medical resources. Brunner et al. [12, 13] made a plan of physicians'