Georeferenced synthetic populations are essential inputs for agent-based simulations in epidemiology, transportation, and urban planning, yet existing methods for spatial allocation of households to residences lack formal optimality guarantees. We present a two-stage mathematical framework for generating such populations from publicly available census data. The first stage combines Iterative Proportional Fitting (IPF) with a mixed-integer linear program (MILP) to synthesize households that preserve observed demographic correlations from census microdata. The second stage formulates the household-to-residence allocation as a MILP that maximizes a composite objective balancing allocation volume, housing-quality matching, and adherence to census tract targets Our numerical experiments for the state of Santa Catarina(SC) show a realistic demographic distribution, demonstrating the practical applicability and effectiveness of our approach.