A Scalable Multi-Objective Location-Allocation Optimization Framework for Mega-City Seismic Emergency Response: Application to the Metropolitan Area of the Valley of Mexico

Background: Seismic emergency response in densely populated megacities requires optimal relief shelter site selection and evacuee allocation under severe spatial scale constraints. Methods: Using empirical geostatistical data from the Metropolitan Area of the Valley of Mexico supplemented with calibrated synthetic spatial sampling, a bi-objective Mixed-Integer Linear Programming (MILP) model was formulated to minimize shelter adaptation costs (Z1) and evacuee travel distances (Z2) across 30,000 demand points and 307 candidate facilities. The flow allocation decision variables (yij) were computationally relaxed to continuous variables, yielding 307 binary selection variables (xj) and 9,209,693 continuous flow variables. A normalized weighted-sum scalarization was executed across various objective weight combinations (w1/w2). Results: In the baseline deterministic instance (Scenario I, w1=w2=0.5), the model selected 160 shelters with an optimality gap of 0.0025% in 2113 s. A weight sensitivity analysis demonstrates a Pareto trade-off, where prioritizing travel accessibility (w2=0.9) opens 255 shelters but increases adaptation costs. Under parametric demand and capacity variance stress-testing (Scenario II), 147 shelters were selected. Conclusions: The optimization framework demonstrates computational scalability for pre-disaster strategic planning at megacity dimensions. The results offer civil protection authorities structural trade-off insights between budgetary retrofitting limits and evacuee transit burdens, distinct from real-time post-disaster operational routing.