Spatial Optimization of Hospital Bed Allocation with Bimodal Demand: Flow Modeling and Resilience Analysis

Hospital bed management is a critical challenge in healthcare systems under capacity constraints and demand spikes. This work proposes a network flow model for intermunicipal patient allocation, incorporating bimodal demand composed of observed and predictive components. The model is formulated as an Integer Linear Programming problem and applied to real data from the health network of Minas Gerais (853 municipalities). In a hyper-saturation scenario with a deficit of approximately 68,000 beds, the model was solved to the global optimum (1.45 million variables in 221 seconds), reducing the logistical effort by 96.3% compared to a policy based on proximity. In addition, state-level and multi-scale analyses show the robustness of the approach. Asymmetric penalties induce a prioritization mechanism, ensuring preferential allocation of observed demand and directing predictive demand to slack variables.