We propose a definition of infrastructure resilience that is tied to the operation (or function) of an infrastructure as a system of interacting components and that can be objectively evaluated using quantitative models. Specifically, for any particular system, we use quantitative models of system operation to represent the decisions of an infrastructure operator who guides the behavior of the system as a whole, even in the presence of disruptions. Modeling infrastructure operation in this way makes it possible to systematically evaluate the consequences associated with the loss of infrastructure components, and leads to a precise notion of "operational resilience" that facilitates model verification, validation, and reproducible results. Using a simple example of a notional infrastructure, we demonstrate how to use these models for (1) assessing the operational resilience of an infrastructure system, (2) identifying critical vulnerabilities that threaten its continued function, and (3) advising policymakers on investments to improve resilience.

We describe new bilevel programming models to (1) help make the country's critical infrastructure more resilient to attacks by terrorists, (2) help governments and businesses plan those improvements, and (3) help influence related public policy on investment incentives, regulations, etc. An intelligent attacker (terrorists) and defender (us) are key features of all these models, along with information transparency: These are Stackelberg games, as opposed to two-person, zero-sum games. We illustrate these models with applications to electric power grids, subways, airports, and other critical infrastructure. For instance, one model identifies locations for a given set of electronic sensors that minimize the worst-case time to detection of a chemical, biological, or radiological contaminant introduced into the Washington, D.C. subway system. The paper concludes by reporting insights we have gained through forming "red teams," each of which gathers open-source data on a real-world system, develops an appropriate attacker-defender or defender-attacker model, and solves the model to identify vulnerabilities in the system or to plan an optimal defense.

The constrained shortest-path problem (CSPP) generalizes the standard shortest-path problem by adding one or more path-weight side constraints. We present a new algorithm for CSPP that Lagrangianizes those constraints, optimizes the resulting Lagrangian function, identifies a feasible solution, and then closes any optimality gap by enumerating nearshortest paths, measured with respect to the Lagrangianized length. "Near-shortest" implies -optimal, with a varying that equals the current optimality gap. The algorithm exploits a new path-enumeration method, aggregate constraints, preprocessing to eliminate edges that cannot form part of an optimal solution, "reprocessing" that reapplies preprocessing steps as improved solutions are found and, when needed, a "phase-I procedure" to identify a feasible solution before searching for an optimal one.The new algorithm is often an order of magnitude faster than a state-of-the-art labelsetting algorithm on singly constrained randomly-generated grid networks. On multi-constrained grid networks, road networks, and networks for aircraft routing the advantage varies, but, overall, the new algorithm is competitive with the label-setting algorithm.

A "proliferator" seeks to complete a first small batch of fission weapons as quickly as possible, whereas an "interdictor" wishes to delay that completion for as long as possible. We develop and solve a max-min model that identifies resourcelimited interdiction actions that maximally delay completion time of the proliferator's weapons project, given that the proliferator will observe any such actions and adjust his plans to minimize that time. The model incorporates a detailed project-management (critical path method) submodel, and standard optimization software solves the model in a few minutes on a personal computer. We exploit off-the-shelf project-management software to manage a database, control the optimization, and display results. Using a range of levels for interdiction effort, we analyze a published case study that models three alternate uranium-enrichment technologies. The task of "cascade loading" appears in all technologies and turns out to be an inherent fragility for the proliferator at all levels of interdiction effort. Such insights enable policy makers to quantify the effects of interdiction options at their disposal, be they diplomatic, economic, or military.

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