Prioritizing Network Interdiction of Nuclear Smuggling

We develop a stochastic network interdiction model for prioritizing locations for installing radiation detectors along a nation's border. In this one-country model, we characterize the smuggler population by a set of possible threat scenarios, where the identity of the smuggler is unknown at the time we install detectors. Detector performance depends on the threat scenario, as well as a number of additional factors such as terrestrial background radiation, geometric attenuation, and exposure time. Furthermore, the budget for installing detectors is unknown at the time the installation plan must be proposed. We model the budget as having a known probability distribution, and consequently, the solution to the problem is a rank-ordered priority list of installation locations, where one or more locations are assigned to each priority level. Upon its realization, we exhaust the budget by installing detectors at locations ranked from highest to lowest priority. The identity of the smuggler is subsequently revealed. Having full knowledge of the interdictor’s actions, the smuggler then selects an origin-destination path, which maximizes his evasion probability. Modeling the problem as a bilevel stochastic mixed-integer program, we present methods for strengthening the resulting formulation, exact and heuristic solution algorithms, and computational results. We also introduce a performance measure that quantifies the value of our prioritization model.