New Models for Home Health Care under Uncertainty with Consideration of the Coordinated Development of Economy and Environment

With the aggravation of population aging, home health care (HHC) services are paid more and more attention by the elderly. Previous studies aim at improving service quality and reducing cost, ignoring the coordinated and sustainable development of the economy and environment. From the perspective of sustainable development, this paper first establishes a linear optimization (LO) model considering transportation, time, and carbon emission costs. However, the uncertainty of service demand is a very difficult problem for HHC research. Most of the previous studies only consider the deterministic model, which has difficulty dealing with the uncertain situation. Therefore, a robust optimization (RO) model is proposed to resist uncertain disturbances by introducing a robust uncertain set response. The experimental results show that the increase of low-carbon transition cost only increases the total cost of the LO model but has a significant positive impact on the RO model. With the increase of uncertainty, the robust model will pay the cost of robustness, but it can obtain a higher service level (93.20% to 93.38%). In addition, when the carbon tax increases, the total transportation cost does not increase but decreases, thus obtaining environmental benefits. When the carbon tax increases by 25%, the average total cost of using the RO model is reduced by 8.274%. The research results of this paper can provide enlightenment and reference for the low-carbon transformation of HHC enterprises.