Home health care facility location problem under demand uncertainty

The demand for home health care services is rapidly increasing due to the growing number of older people. The uncertainty surrounding this demand affects the network design processes and the performance of the home health care system in the long term. This study aims to address the issue of demand uncertainty in a home health care location problem. While decisions regarding the location of home health care facilities must be made immediately, the determination of distribution can be postponed until actual demand is observed. In such situations, minimax/maximin robust optimization methods are commonly employed to address uncertainty and facilitate informed decision-making, even in cases where there is limited information about future demand. However, these methods are often too conservative and may lead to suboptimal solutions. To tackle this issue, we propose a regret minimization method, which is reformulated as a robust model to overcome its intractability. Additionally, we propose a column-and-constraint generation algorithm to solve the robust optimization and regret minimization models. Finally, we conduct a comprehensive set of numerical experiments to compare the performance of the models in terms of solution quality and computational time. The results demonstrate that the regret minimization model enhances solution quality and consumes less computational time when reformulated.