Interdicting layered networks : reformulations, algorithms and applications

Abstract

By using duality, we apply a multi-step reformulation technique to obtain a single-level formulation of this problem. We apply this technique to two applications and provide policy-driven analysis: law enforcement efforts against illegal drug trafficking networks and cyber vulnerability analysis of infrastructure and supply chain networks. Computational results demonstrate that our reformulation technique outperforms the traditional duality-based reformulation technique by orders of magnitude. We then extend this technique to develop algorithms to identify the damaged components in multiple interdependent infrastructures when we only have access to the outage reports from the service receivers. We present three computational approaches to develop inspection plans: (i) A Resource-constrained Damage Detection approach, (ii) A Replicate Damage Detection approach, and (iii) A Breadth-first Search approach. For the situation where the information supply arcs are capacitated, we apply a Benders decomposition technique to solve the problem. Last, we examine the law enforcement decisions against illegal drug trafficking from a non-deterministic perspective in which law enforcement does not have full knowledge of the criminal supply chain. We apply a discounted Markov Decision Process (MDP) approach and solve by using a linear programming model, a column generation approach and a heuristic method. Our solutions provide insights into which criminal types law enforcement should act on when multiple criminal types are present.

In this dissertation, we focus on interdependent physical and information flow networks which can help model the operations of criminal organizations, cyber-physical systems, and critical infrastructure systems. A component in the physical flow network is operational only if its information demand is met in the information flow network. We study a (bilevel) layered network interdiction problem on these networks in which there exist two players - a defender and an attacker. The objective of the defender is to maximize the amount of flow sent from the origin to the destination in the physical flow network, and the attacker then aims to minimize this maximum flow by interdicting the network components. Due to the interdependencies, the inner problem of this bilevel program has binary variables. We first assume that the supply arcs in the information flow network are uncapacitated.