Bilevel Network Interdiction Models: Formulations and Solutions

This definition is unnecessarily restrictive— for instance, it should also include ship-based firepower—but the essence is reasonable: interdiction connotes preemptive attacks that limit an enemy’s subsequent ability to wage war, or carry out other nefarious activities. The mathematical study of interdiction has focused primarily on network interdiction, in which an enemy’s activities are modeled using the constructs of network optimization (e.g., maximum flows, multicommodity flows, and shortest paths), and in which attacks target the network’s components to disrupt the network’s functionality. Depending on the type of network, targeted components can include bridges, road segments or interchanges, communications links or switches, and so on. This article focuses on the bilevel network interdiction problem (BNI), but the reader should note that much of the presentation extends to interdiction of more general systems. Examples of what we now call network interdiction date from antiquity. Herodotus [[2] 9.49–50] describes how the Persian cavalry (in 479 BC) cut Greek supply lines and routes to water sources in a battle near the