A Bilevel Network Interdiction Problem to Minimize the Number of Active Special Arcs in the Maximum Flow

We consider a bilevel network interdiction problem where the follower aims to maximize the amount of flow from the source node to the sink node, and the leader aims to minimize the number of arcs from a critical set that have positive flow on them, that is, active arcs, in the maximum flow solution obtained by the follower. This problem is motivated by an application in human trafficking disruption. We consider both the optimistic and pessimistic variants of this bilevel optimization problem and develop their respective single-level reformulations. We present a tailored solution method to the pessimistic problem, which solves the problem to optimality for one practically important class of networks. Through computational experiments on randomly generated layered network instances, we show the effectiveness of the proposed methods and demonstrate that the tailored method is orders of magnitude faster than existing approaches in the literature. We also conduct computational experiments on randomly generated test instances inspired by domestic human trafficking networks and draw domain-specific insights.