Emergency site location-allocation optimization with truck-drone cross-level substitution under facility disruptions and disaster risk assessment

This paper optimizes emergency site location-allocation under post-earthquake facility disruptions and heterogeneous vehicles. Earthquake, population, and social facility data are integrated through weighted overlay to quantify priority support levels. A two-stage stochastic programming model minimizes total system time and cost. The first stage determines distribution center locations and preliminary affected point allocations. The second stage incorporates a cross-level substitution mechanism combining truck delivery from available distribution centers with direct drone dispatch from the warehouse following disruptions. The epsilon-constraint method and CPLEX solve the mixed-integer linear programming problem to obtain the Pareto-optimal frontier. A multi-scenario case study using historical Sichuan earthquake data compares this framework with a truck-only strategy. The demand satisfaction rate in extreme disaster areas increases from 39.38% to 62.40%, while total system time decreases by 15.37 hours. Results suggest diminishing marginal returns of transport capacity and a trade-off between response efficiency and priority support for high-risk areas.