Strategically pre-positioning relief supplies before disasters can reduce both response times and supply costs. However, accurately estimating the probabilities of disaster occurrences is difficult due to limited historical data and cognitive biases in decision-making. Prior research has demonstrated the effectiveness of robust-modeling approaches to such problems. This paper expands the prior work by incorporating $$\phi $$-divergence uncertainty regions into decision-making models to account for uncertainty in scenario probability estimates. An extensive numerical study using Monte Carlo simulation studies applied to a real-world case study of hurricane preparedness in the Southeastern United States demonstrates that our models yield lower expected response costs, compared to traditional stochastic optimization approaches. Additionally, we show that explicitly incorporating knowledge of cognitive biases in probability estimation can significantly enhance decision-making effectiveness and cost efficiency.