Transportation systems are critical lifelines for society, but are at risk from natural or human-caused hazards. To prevent significant loss from disaster events caused by such hazards, the transportation system must be resilient, and thus able to cope with disaster impact. It is impractical to reinforce or harden these systems to all types of events. However, options that support quick recovery of these systems and increase the system's resilience to such events may be helpful.

To address these challenges, this dissertation provides a general mathematical framework to protect transportation infrastructure systems in the presence of uncertain events with the potential to reduce system capacity/performance. A single, general decision-support optimization model is formulated as a multi-stage stochastic program. The program seeks an optimal sequence of decisions over time based upon the realization of random events in each time stage. This dissertation addresses three problems to demonstrate the application of the proposed mathematical model in different transportation environments with emphasis on system-level resilience: Airport Resilience Problem (ARP), Building Evacuation Design Problem (BEDP), and Travel Time Resilience in Roadways (TTR). These problems aim to measure system performance given the system's topological and operational characteristics and support operational decision-making, mitigation and preparedness planning, and post-event immediate response. Mathematical optimization techniques including, bi-level programming, nonlinear programming, stochastic programming and robust optimization, are employed in the formulation of each problem. Exact (or approximate) solution methodologies based on concepts of primal and dual decomposition (integer L-shaped decomposition, Generalized Benders decomposition, and progressive hedging), disjunctive optimization, scenario simulation, and piecewise linearization methods are presented. Numerical experiments were conducted on network representations of a United States rail-based intermodal container network, the LaGuardia Airport taxiway and runway pavement network, a single-story office building, and a small roadway network.