关键词: 家庭医护人员调度, 数字医疗, 车辆路径问题, 变邻域搜索算法

Abstract: Based on the era characteristics of digital healthcare service development and the personalized needs of patients, this study proposes a home doctor scheduling optimization problem that incorporates selectable service modes and time windows for patients. In this problem, patients can choose from three service modes: home visits, outpatient services and online consultations. The home healthcare team assigns doctors to patients based on their specific circumstances. Each doctor is capable of providing services to any type of patient but can only offer one type of service per day. During the daily schedule, doctors must provide services within the time windows set by the healthcare center. Doctors differ in terms of skill level and ability, and patients have individualized skill requirements. To ensure service quality, the doctors’ skill levels must meet the patients’ skill demands.
   For home visit services, the scheduling problem is a variant of the Vehicle Routing Problem (VRP). Doctors depart from the healthcare center, serve patients, and then return to the center after completing all visits. For online consultation services, the scheduling problem is also a VRP but includes a virtual start and end point. Doctors begin their services from the virtual start point and return to the virtual end point after finishing all consultations. In outpatient services, patients visit the healthcare center to receive care. This study uses queuing theory to quantify the outpatient services, where the set of doctors and their respective patients form independent queuing systems.
   To achieve a comprehensive optimization of the three service modes, while accounting for the distinct characteristics of each mode, a unified model is constructed. The model aims to optimize the following key objectives: the routing cost and waiting time associated with home visits, the waiting time generated during online consultations, the waiting time for patients in outpatient services and patient preference satisfaction. Patient preference satisfaction is represented by the sum of the skill gap between doctors and patients and the familiarity between them. The problem to be addressed involves determining the service mode for each doctor as well as their visit routes to patients. The objective is to minimize the weighted total cost, and the problem is formally described using a Mixed-Integer Nonlinear Programming (MINLP) model.
   Given the characteristics of the model, an Improved Adaptive General Variable Neighborhood Search (IAGVNS) algorithm is designed to solve the problem. The algorithm employs a list-based method for individual encoding. The first part of the list represents the doctor identification number, the second part denotes the service type assigned to the doctor, and the third part specifies the set of patients served by the doctor. The improvement strategies for the algorithm include: using the Forward Start Intervals Algorithm to handle multiple time windows; designing an initial solution construction heuristic based on the insertion algorithm; developing five local search operators, including four intra-service mode operators and one inter-service mode operator; applying a multi-neighborhood transformation strategy for local search; and improving the local search process using the Metropolis criterion from the simulated annealing algorithm. These improvements enhance the algorithm's adaptability across different solution spaces, effectively balancing the exploration and exploitation processes of the algorithm.
   The performance of the IAGVNS algorithm is tested using instances of varying scales and compared with the traditional General Variable Neighborhood Search (GVNS) algorithm and Tabu Search algorithm. The algorithm’s performance is evaluated using optimal values, worst-case values, mean values and standard deviations as criteria. The numerical experiments show that IAGVNS outperforms in most instances, particularly in terms of standard deviation, where it demonstrates superior performance over GVNS. The sensitivity analysis results indicate: (1)The weighting parameters have varying degrees of influence on the overall scheduling scheme and mutually constrain one another. Decision-makers can adjust parameter values according to decision preferences or actual conditions. (2)The matching between doctors and patients also requires a balanced consideration.

Key words: home health care scheduling, digital healthcare service, vehicle routing problem, variable neighborhood search algorithm