Dynamic interdiction networks with applications in illicit supply chains

Abstract We study the interdiction of illegal product distribution in a network with multiple sources (origins) and sinks (destinations). This work contributes to the literature of dynamic maximum flow interdiction problems by addressing multiple commodities in a network of relationships. The related distribution network consists of (1) criminals, who are hierarchically connected, and seeking to maximize the total profit flow from origins to destinations, and (2) enforcement officers aiming to minimize criminals’ long-term success by monitoring and arresting them, using the limited resources at their disposal. Considering several real-world operational details, we first propose a mixed-integer programming model by reformulating a Min–Max bi-level mathematical model. We then propose a new formulation and discuss its efficiency compared with the traditional duality-based reformulation. This new formulation also has a higher compatibility with decomposition solution methods. Utilizing the new formulation, we design a solution method based on the Benders decomposition procedure and apply several accelerating strategies (e.g., Super Valid Inequalities) to solve larger instances for a better representation of reality. Lastly, we create a heuristic method based on real-world evidence, which is usually practiced by law enforcement officers. Our results show that the quality of the heuristic method declines quickly as the network size increases.