Dynamic patient allocation in hospital systems during a pandemic
研究疫情期间如何在医院系统内动态分配ICU床位，通过滚动时域和贝叶斯方法实时调整决策，并采用分布鲁棒优化应对患者到达的不确定性，以减少死亡人数。
In this study, we address the problem of allocating Intensive Care Unit (ICU) beds among hospitals in a hospital system during a pandemic. The goal is to minimize the total costs associated with deaths, patient transfers, and bed setup by dynamically transferring patients among hospitals and admitting and discharging them from ICUs. The problem is initially formulated as a stochastic dynamic programming problem using Markov chains to model the evolution of patient health conditions. We propose a rolling horizon approach with estimation updating, integrating Bayesian methods to dynamically adjust ICU capacity and patient allocation decisions based on real-time data, thus enhancing responsiveness and accuracy in managing uncertainties in patient arrivals and optimizing resource allocation under varying healthcare demands. However, the traditional problem assumes exogenous uncertainty, whereas in reality, the availability of hospitals can influence patients’ decisions to seek medical services, and therefore, affect the number of patients arriving at hospitals. To address this issue, we propose a distributionally robust optimization (DRO) method that considers the dependence of the ambiguity set on decisions. We reformulate the decision-dependent DRO model as a mixed-integer programming problem. Using a real-world case study of a pandemic, we compare the DRO method with two benchmarks and show that the method is computationally scalable and results in a lower number of deaths.