Interdiction Models and Applications

Through interdiction models, we infer the vulnerabilities inherent in an operational system. This chapter presents four applications of interdiction modeling: (i) to delay an adversary’s development of a first nuclear weapon; (ii) to understand vulnerabilities in an electric power system; (iii) to locate sensors in a municipal water network; and (iv) to secure a border against a nuclear smuggler. In each case, we detail and interpret the mathematical model, and characterize insights gained from solving instances of the model. We point to special structures that sometimes arise in interdiction models and the associated implications for analyses. From these examples, themes emerge on how one should model, and defend against, an intelligent adversary. This chapter describes how to assess the vulnerabilities of operational systems by using interdiction models. We do so in the context of four applications from the literature: delaying an adversary’s development of a first nuclear weapon; understanding vulnerabilities in an electric power system; locating sensors to rapidly detect an illicit contaminant injected in a municipal water system; and locating radiation sensors to detect a nuclear smuggler. The key steps in this approach involve answering the following questions: (1) How is the system operated? and (2) What are the vulnerabilities of that system? Operations research has a rich history of developing mathematical models to answer question (1). Key to our approach is that we must be able to answer question (1) when any subset of the system’s components has been interdicted. We may be the operators of the system of interest, or an adversary may operate the system or be operating within a system we own. The former case arises when the system involves critical infrastructure, such as an electric power system or municipal water system. In such situations, a third question arises: (3) How can we invest to make the system more resilient? The latter case arises, for example, when an adversary is managing a project or attempting to transport illicit material across our transportation network. In answering question (1), we assume operation of the system optimally adapts after interdiction of a subset of system components. Here, interpret the term interdiction liberally. It can mean an action that removes or degrades one more more system components, e.g., damaging a generator, substation, or transmission line in an electric power system, or it can mean an action that delays completion of a task in a project. Interdiction can also mean detecting illicit operations on, or threats to, a system that we own. Interdiction models identify a set of system components to interdict, subject to resource limits, so that system performance is optimally degraded. The system components identified indicate the vulnerabilities of the system, answering question (2). Again, central to the analysis is the recognition that system operation will optimally adapt, post-interdiction, to the residual system. The sections that follow develop four applications of interdiction modeling. We motivate each application, describe a mathematical model, discuss important modeling choices, discuss computa-