Mitigating Interdiction Risk with Fortification

We study a network fortification problem on a directed network that channels single-commodity resources to fulfill random demands delivered to a subset of the nodes. For given a realization of demands, the malicious interdictor would disrupt the network in a manner that would maximize the total demand shortfalls subject to the interdictor’s constraints. To mitigate the risk of such shortfalls, a network’s operator can fortify it by providing additional network capacity and/or protecting the nominal capacity. Given the stochastic nature of the demand uncertainty, the goal is to fortify the network, within the operator’s budget constraint, to minimize the expected disutility of the shortfalls in events of interdiction. We model this as a three-level, nonlinear stochastic optimization problem that can be solved via a robust stochastic approximation approach under which each iteration involves solving a linear mixed-integer program. We provide favorable computational results that demonstrate how our fortification strategy effectively mitigates interdiction risks. We also extend the model to multicommodity network with multiple sources and multiple sinks.