Multi-Timescale and Multi-Agent Collaborative Allocation of Emergency Resources for Natural Disasters

The allocation of emergency resources serves as a critical lifeline in natural disaster relief, fundamentally determining survival rates, resources rescue efficacy, and the restoration of social order. There are two critical limitations in existing allocation models: 1) inadequate cross-agent coordination regarding fund and resource flows; 2) insufficient adaptability to dynamic uncertainties. To address these gaps, this study first proposes and models a multi-agent linkage mechanism to synchronize decision agent (fund), execution agent (procurement/transportation), and demand agent in disaster areas to holistically optimize economic costs, life-saving utility, and supply-demand balance. Multi-stage adaptive robust optimization is adopted to transform the above allocation model to a multi-timescale feedback model, integrating pre-disaster planning and post-disaster periodic adjustments under demand, procurement, and transportation uncertainties. For the convenience of solving, a linear reformulation technique is developed to convert the aforementioned nonlinear robust model into a tractable linear program using duality theory and semi-infinite constraint handling. A case study based on an earthquake scenario demonstrates the multi-timescale and multi-agent collaborative mechanisms significantly enhance resource allocation optimality, stability and robustness under multiple sources of uncertainty. Sensitivity analyses reveal optimal inflection points for key parameters such as time discretization and historical dependency depth, providing practical guidance for model deployment. Compared to deterministic, static robust, and rolling horizon methods, this study realizes notable improvements in allocation safety and a comprehensive rescue objective.