Applying historical hurricane data to model storm related uncertainty, this paper develops a stochastic optimization model to determine the stockpile location and capacities of medical supplies for improved disaster preparedness in the event of a hurricane. Our models incorporate facility damage and casualty losses, based upon their severity levels and remaining survivability time, as a function of time variant changes in hurricane conditions. To determine the optimal deployment time, we use an optimal stopping time framework to model the trade-offs between increasing costs and reduced uncertainty as the hurricane approaches landfall. Finally, aided by an innovative mixed integer programming model, we develop an evolutionary optimization heuristic that yields time efficient high quality solutions for solving large-scale problems, and we demonstrate the applicability of the approach via illustrative numeric examples.