665 / 2024-04-30 19:42:03

Study on Scheduling Problem of Single Period Home-health-care Staff for the Elderly Based on Priority

priority; home-health-care staff for the elderly; scheduling optimization; multi-objective optimization; NSGA-II

China is facing the challenge of the world's largest and fastest population aging. According to the latest data from the 7th National Population Census of the National Bureau of Statistics, as of November 2020, the population aged 60 and above in China is approximately 264 million, accounting for 18.7% of the total population. In the 14th Five Year Plan, home healthcare has been vigorously promoted by the state and local governments and has gradually become the mainstream model. As the service production carrier of home healthcare service centers, optimizing the allocation of home health caregivers is one of the effective measures to ensure that the elderly receive high-quality services. Therefore, it is necessary to introduce the service demand characteristics of the elderly and the service supply characteristics of home healthcare into the resource planning and scheduling of home health caregivers, in order to achieve high-quality matching between the participating parties and improve the allocation efficiency of caregivers.

Home health care routing and scheduling problem (HHCRSP) mainly includes two sub- problems: caregiver assignment problem and caregiver path planning. It is considered an extension of the vehicle routing problem with time window (VRPTW). Two goals are often considered in the traditional home health care routing and scheduling problem: one is the operating costs and the other is the perceived satisfaction of both service providers. However, with the acceleration of population aging in our country, it is often difficult for home healthcare service centers to respond the service needs of all elderly people timely. Therefore, it is of great significance to prioritize meeting the service needs of elderly people with poor health conditions and strong service timeliness, which will further improve the allocation efficiency of home health caregivers. By analyzing existing relevant studies, it can be found that most of the home health caregiver scheduling plans based on the above goals cannot reflect the priority differences among the elderly, making it difficult to ensure that elderly people with poor health conditions and strong service timeliness receive priority services. Therefore, this paper takes into account the health status and service timeliness of the elderly, and constructs a scheduling optimization model for home care caregivers that considers the priority of the elderly. The main contributions are as follows:

First, this paper comprehensively considers the impact of elderly health status and service timeliness on the scheduling plan, designs a two-dimensional priority table to reflect the scheduling priority, and converts it into the penalty cost of unresponsive demand. This problem is planned as a mixed- integer linear programming model to minimize the operating costs of home care service centers and minimize penalty cost for unresponsive demand. In addition, an improved NSGA-II algorithm is proposed to solve it.

Second, as an NP-hard problem, it is difficult to obtain the optimal solution of the problem in an effective time using precise algorithms. Therefore, it is necessary to choose an approximate algorithm to obtain the approximate solution of the problem. This paper improves the NSGA-II algorithm based on the characteristics of the problem: (1) A heuristic insertion algorithm is designed to obtain the initial population in order to improve the quality of the initial solution. The algorithm evaluates the possibility of each node inserting into the current path from two aspects: time window urgency and relative distance. (2) In order to enhance the algorithm's ability to jump out of local optima, this paper designs a damage repair strategy to replace the cross mutation process of NSGA-II algorithm, and introduces a local search strategy to expand the search width and depth of the algorithm.

Finally, this paper analyzes the problem characteristics and algorithm performance through numerical experiments. The results show that: (1) The model proposed in this paper can prioritize serving elderly people with poor health conditions and strong service timeliness in all scale examples. (2) When the demand scale is determined, the trend of operating costs varies with the number of caregivers in different solution states: when the demand response rate is less than 1, the operating costs increase with the increase of the number of caregivers; When the demand response rate remains constant and is 1, the operating cost shows a trend of first decreasing and then increasing. (3) The improved NSGA-II algorithm is competitive in terms of convergence, diversity, and distribution of solutions.

At present, there is a huge gap and serious turnover of home care caregivers in China. With the deepening of population aging, the demand for home healthcare has sharply increased. The model constructed in this paper aims to improve the allocation efficiency of home care caregivers, which has important guiding significance for the home healthcare industry. In the future, this paper will further optimize the evaluation indicators for elderly priority, including selecting more suitable evaluation indicators and adopting more reasonable indicator characterization forms.