Equity-Constrained, Demand-Responsive Shelter Location–Allocation for Sustainable Urban Earthquake Resilience: A GIS-Integrated Two-Stage Framework with a Fast Heuristic

Cities need emergency-shelter systems that are computationally efficient, socially fair, and consistent with long-term goals for sustainable urban development. This paper proposes a GIS-integrated, two-stage location–allocation framework for urban earthquakes that jointly optimizes shelter siting and evacuee assignment under time-varying demand. The model incorporates equity constraints that cap extreme travel burdens for vulnerable groups and robust capacity safeguards against demand uncertainty, helping prevent over- or under-investment in shelter infrastructure and promoting efficient use of land and public resources. A customized Phased Nested Local Search (PNLS) heuristic enables city-scale application and is benchmarked against a mixed-integer programming baseline solved by CPLEX. In a district-level case study of Chengdu, China, the framework reduces total assignment distance by 12.3% and the 95th-percentile travel burden by 15.8% while maintaining feasibility during the peak demand window. The results show that integrating equity, robustness, and spatial efficiency in shelter planning can strengthen urban resilience and directly support SDG 11 on sustainable cities and communities.