Multi-stage robust and multi-role integrated allocation of emergency resources for hazard-induced disasters.

The allocation of emergency resources is a lifeline in hazard-induced disaster relief, directly determining survival rates, rescue efficiency, and the restoration of social order. Existing allocation models face two limitations: (1) insufficient cross-role integration of funds and resource flows, and (2) limited application of multi-stage robust optimization. To address these issues, this study proposes a tripartite multi-role integrated scheduling framework that jointly considers the objectives and constraints of decision-making (fund allocation), execution (procurement and transportation), and demand roles (affected populations) to optimize economic cost, life-saving utility, and supply-demand balance. We adopt multi-stage adaptive robust optimization to reformulate the allocation model into a feedback framework integrating pre-disaster planning with post-disaster periodic adjustments under demand, procurement, and transportation uncertainties. For model tractability and compatibility with off-the-shelf solvers, we develop a linear reformulation technique that converts the nonlinear robust model into a linear program using duality theory and semi-infinite constraint handling. A case study based on an earthquake scenario shows that multi-stage adjustment and multi-role integration improve allocation optimality, stability, and robustness under multiple uncertainty sources. Sensitivity analyses of key parameters, such as time discretization and historical dependency depth, provide practical guidance for model deployment. Compared with deterministic, static robust, and rolling-horizon methods, the proposed approach shows improvements in allocation safety and overall rescue performance.