Stochastic Network Interdiction Models for Homeland Security

University Of Texas At Austin, Austin TX

Investigators

Abstract

This research attempts to solve a stochastic network interdiction model for deterring and preventing smuggling of nuclear material. The interdiction model consists of two adversaries, a nuclear smuggler and an interdictor who installs sensors to detect the smuggler. The smuggler selects a path through a transportation network that maximizes the probability of avoiding detection. The interdictor installs sensors to minimize that maximum probability. This problem is formulated as a bi-level two-stage stochastic mixed-integer program. It is stochastic because the smuggler's origin and destination are unknown at the time the detectors are installed. The model is reformulated as a stochastic mixed-integer program that one can attempt to solve with commercial software. For larger instances of the problem, a decomposition procedure that exploits the model's special structure is proposed. The model's data requirements include the probability a smuggler can traverse an indigenous arc, an arc with an undetected sensor, and the probability distribution governing the smuggler's origin-destination pair. The efforts of terrorist organizations, such as al Qaeda, and rogue nations, such as Libya and Iraq, to obtain nuclear material and technology to produce a nuclear weapon have been well documented. Securing U.S. borders from the possible smuggling of nuclear/radiological weapons or precursor materials is an important step in minimizing the associated threat. Other U.S. organizations are focusing on issues needed to secure the border. For example, scientists at Los Alamos National Laboratory are developing radiation sensor equipment to detect minute quantities of nuclear material and data on terrorist groups. The Immigration and Naturalization Services, the Federal Bureau of Investigation, and the Customs Department are collecting data on potential smuggling routes. Significantly less effort is being devoted to developing methodology to use this data to determine where these detectors should be located. This grant supports research to help provide the technical basis for locating such detectors.