Cross-regional manpower scheduling and routing problem with stochastic service times in home health care

At present, home health care services supply is still insufficient and unbalanced in China, and the elderly nursing manpower is particularly scarce. Therefore, it is important to reasonably arrange the existing nursing personnel to make full use of the service capabilities. This paper proposes a mixed integer linear programming (MILP) model for a cross-regional scheduling and routing problem with stochastic service times in the one-day planning horizon. A range of possible realistic constraints are considered, including patient time windows, working time regulations, task importance, and skill matching. Due to the complexity of the problem, a hybrid Simulated Annealing algorithm is introduced to solve the model. Monte Carlo simulation method is used for the uncertainty cost evaluation. The numerical example tests verify the effectiveness of the algorithm proposed. This paper analyzes the advantages and disadvantages of cross-regional scheduling and routing by comparing the empirical experiment results of the cross-regional and independent scheduling of two regions. It is found that in the case of this paper, cross-regional scheduling is generally beneficial to reducing the cost of both care centers and improving the efficiency of resource utilization.