We apply new bilevel and trilevel optimization models to make critical infrastructure more resilient against terrorist attacks. Each model features an intelligent attacker (terrorists) and a defender (us), information transparency, and sequential actions by attacker and defender. We illustrate with examples of the US Strategic Petroleum Reserve, the US Border Patrol at Yuma, Arizona, and an electrical transmission system. We conclude by reporting insights gained from the modeling experience and many “red-team” exercises. Each exercise gathers open-source data on a real-world infrastructure system, develops an appropriate bilevel or trilevel model, and uses these to identify vulnerabilities in the system or to plan an optimal defense.

Digital Equipment Corporation evaluates global supply chain alternatives and determines worldwide manufacturing and distribution strategy, using the Global Supply Chain Model (GSCM) which recommends a production, distribution, and vendor network. GSCM minimizes cost or weighted cumulative production and distribution times or both subject to meeting estimated demand and restrictions on local content, offset trade, and joint capacity for multiple products, echelons, and time periods. Cost factors include fixed and variable production charges, inventory charges, distribution expenses via multiple modes, taxes, duties, and duty drawback. GSCM is a large mixed-integer linear program that incorporates a global, multi-product bill of materials for supply chains with arbitrary echelon structure and a comprehensive model of integrated global manufacturing and distribution decisions. The supply chain restructuring has saved over $100 million (US).

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.

Traditional probabilistic risk assessment (PRA), of the type originally developed for engineered systems, is still proposed for terrorism risk analysis. We show that such PRA applications are unjustified in general. The capacity of terrorists to seek and use information and to actively research different attack options before deciding what to do raises unique features of terrorism risk assessment that are not adequately addressed by conventional PRA for natural and engineered systems-in part because decisions based on such PRA estimates do not adequately hedge against the different probabilities that attackers may eventually act upon. These probabilities may differ from the defender's (even if the defender's experts are thoroughly trained, well calibrated, unbiased probability assessors) because they may be conditioned on different information. We illustrate the fundamental differences between PRA and terrorism risk analysis, and suggest use of robust decision analysis for risk management when attackers may know more about some attack options than we do.

A crude oil tanker scheduling problem faced by a major oil company is presented and solved using an elastic set partitioning model. The model takes into account all fleet cost components, including the opportunity cost of ship time, port and canal charges, and demurrage and bunker fuel. The model determines optimal speeds for the ships and the best routing of ballast (empty) legs, as well as which cargos to load on controlled ships and which to spot charter. All feasible schedules are generated, the cost of each is accurately determined and the best set of schedules is selected. For the problems encountered, optimal integer solutions to set partitioning problems with thousands of binary variables have been achieved in less than a minute.transportation: planning, set partitioning, enumerative methods