Program Arrives Home Smoothly: Uncertainty-Based Routing Scheduling of Home-Based Elderly Care Programs

Abstract

In China, the home-based elderly care program system plays an important role in meeting the needs of elderly individuals. The routing scheduling of home-based elderly care (RSHEC) programs is closely related to the quality of the home-based elderly care programs. The structural supply problem faced by home-based elderly care programs is a prominent problem, and the RSHEC programs are an important aspect that has rarely been studied. This paper explores RSHEC programs under uncertainty by comprehensively considering the costs of home-based elderly care, such as the fixed costs, time, and transportation costs. First, a deterministic mixed integer programming (MIP) model was constructed to solve the general routing scheduling problem. In addition, to effectively cope with the uncertainty and risk of the modern market, the robust optimization theory and algorithm model are introduced, namely, the mixed integer box set robust optimization (MIBRO) model and the mixed integer ellipsoid set robust optimization (MIERO) model. Finally, MATLAB and the Gurobi package are applied to obtain the solutions of the models. The case verification shows that the MIP model has the lowest total cost under deterministic conditions. However, the MIERO and MIBRO models can achieve more robust RSHEC programs under uncertain conditions. The results prove the effectiveness and feasibility of the optimization model and algorithm, which provides reference value for management decisions regarding home-based elderly care programs.