Robust Network Flow Interdiction Problems with Applications to Counter-Narcotics

Abstract

Interdiction problems arise in a number of application areas, including global security, supply chains, and critical infrastructure protection - the goal is inhibit the movement of goods, people or information. An area of particular interest is counter-narcotics, where nodes or edges in a network are placed under surveillance or blocked to minimize the flow of illicit drugs from source to the destination. A fundamental challenge in this narco-traffic interdiction is data scarcity: available datasets are limited by the very nature of the problem and provide only partial and uncertain views of trafficking networks. Thus, developing robust interdiction methods that take this inherent lack of information is critical. In this paper we initiate the study of network flow interdiction problems under network uncertainty. First, using a limited real-world dataset, we generate an ensemble of plausible network realizations representing alternative trafficking scenarios. The method combines simulations with mathematical programming techniques to generate network ensembles that are consistent with the observed data. Second, we formulate the robust network flow interdiction problem and develop an integer linear program to solve the problem. We evaluate the optimal interdiction strategy and obtain the residual flows over the scenarios. Our analysis reveals that even modest budgets can yield significant flow reductions. However, optimal solutions vary substantially across scenarios, motivating the need for robust solutions. We show that the robust strategy achieves near-optimal performance across all near-real world realizations while remaining stable under structural uncertainty. This simulation-driven approach provides a principled basis for policy analysis and supports maximizing the return on interdiction investments in uncertain, data-limited environments.