Integrated Emergency Medical Facility Location and Patient Dispatching Under Uncertainty

In the face of a sudden public health emergency caused by a new infectious disease, it is necessary to establish a multi-level emergency medical facility (including primary and superior facilities) to address the surge in medical needs. In this context, traditional hospitals are responsible for patient screening, primary emergency medical facilities are responsible for treating mild cases, and superior emergency medical facilities are responsible for treating severe cases. Against the backdrop of uncertainties such as patient self-referral and the autonomous progression of the disease, we address an important problem of integrated emergency medical facility location and patient dispatching under uncertainty and propose a multi-stage stochastic programming model to formulate the problem. For a deterministic model under a given set of scenarios, a Decomposition-based Dual-level Heuristic (DDH) algorithm is proposed to efficiently solve the problem, where the upper level employs tabu search to optimize the location scheme, and the lower level utilizes a patient allocation heuristic to provide an optimized patient dispatching solution. Numerical experiments are conducted using Wuhan, China, the epicenter of the COVID-19 outbreak, as an example. The results show that the DDH algorithm achieves high quality solutions close to those obtained by state-of-the-art solver CPLEX but with significantly reduced computational overload. The DDH algorithm is also compared with the progressive hedging algorithm and genetic algorithm, showing its superior performance in terms of solution quality and computational efficiency. Through extensive data analysis, valuable conclusions and managerial insights are obtained, providing useful references for emergency response in similar public health emergencies in the future.