Dynamic allocation of post-earthquake emergency housing: a physically constrained lexicographic model

Following major earthquakes, emergency housing allocation becomes a critical humanitarian logistics problem because shelter demand rises rapidly while transport networks may experience severe disruption. Unlike immediately consumable relief supplies, emergency housing provides effective shelter service only after transportation and post-arrival deployment have been completed. To address these challenges, this study develops a Physically Constrained Lexicographic Dynamic Allocation (PCLDA) model for post-earthquake emergency housing over a 72-h scenario-based acute allocation horizon following rapid assessment and initial route-serviceability assessment. The model integrates demand urgency, milestone-based minimum service protection, route availability, degraded travel time, period-specific dispatch capacity, vehicle loading capacity, and deployment delay, while distinguishing physical arrival from effective occupancy. A two-stage customized simulated annealing algorithm first maximizes 72-h effective coverage and then minimizes urgency-weighted cumulative unmet demand while preserving the best-found coverage. The model is evaluated using a Wenchuan-based scenario rather than an exact reconstruction of the historical relief process. Under the baseline setting, the best-found schedule provides 18,768 effectively occupiable housing units, corresponding to 90.746% of total demand, while satisfying the prescribed 5%, 30%, and 60% site-level service floors at 24, 48, and 72 h. Benchmark analysis shows that terminal-only protection can preserve final coverage while allowing substantial early service deprivation, whereas neglecting deployment delay can overestimate actual shelter availability. Route-disruption analysis further shows that moderate disruption reduces 72-h effective coverage to 87.612%, while under severe disruption no schedule satisfying all milestone requirements was identified. Sensitivity and housing-type analyses confirm that loading capacity and deployment delay materially affect short-horizon effective occupancy. The proposed PCLDA framework provides a physically grounded decision-support approach for emergency housing allocation over assessed and partially serviceable post-earthquake transport networks.