Optimization of relief networks in humanitarian logistics often exemplifies the need for solutions that are feasible given a hard constraint on time. For instance, the distribution of medical countermeasures immediately following a biological disaster event must be completed within a short time-frame. When these supplies are not distributed within the maximum time allowed, the severity of the disaster is quickly exacerbated. Therefore emergency response plans that fail to facilitate the transportation of these supplies in the time allowed are simply not acceptable. As a result, all optimization solutions that fail to satisfy this criterion would be deemed infeasible. This creates a conflict with the priority optimization objective in most variants of the generic vehicle routing problem (VRP). Instead of efficiently maximizing usage of vehicle resources available to construct a feasible solution, these variants ordinarily prioritize the construction of a minimum cost set of vehicle routes. Research presented in this dissertation focuses on the design and analysis of efficient computational methods for optimizing high-consequence variants of the VRP for relief networks. The conflict between prioritizing the minimization of the number of vehicles required or the minimization of total travel time is demonstrated. The optimization of the time and capacity constraints in the context of minimizing the required vehicles are independently examined. An efficient meta-heuristic algorithm based on a continuous spatial partitioning scheme is presented for constructing a minimized set of vehicle routes in practical instances of the VRP that include critically high-cost penalties. Multiple optimization priority strategies that extend this algorithm are examined and compared in a large-scale bio-emergency case study. The algorithms designed from this research are implemented and integrated into an existing computational framework that is currently used by public health officials. These computational tools enhance an emergency response planner's ability to derive a set of vehicle routes specifically optimized for the delivery of resources to dispensing facilities in the event of a bio-emergency.