Asymmetric stochastic shortest-path interdiction under conditional value-at-risk

Abstract

We study a two-stage shortest-path interdiction problem between an interdictor and an evader, in which the cost for an evader to use each arc is given by the arc’s base cost plus an additional cost if the arc is attacked by the interdictor. The interdictor acts first to attack a subset of arcs, and then the evader traverses the network using a shortest path. In the problem we study, the interdictor does not know the exact value of each base cost, but instead only knows the (non-negative uniform) distribution of each arc’s base cost. The evader observes both the subset of arcs attacked by the interdictor and the true base cost values before traversing the network. The interdictor seeks to maximize the conditional value-at-risk of the evader’s shortest-path costs, given some specified risk parameter. We provide an exact method for this problem that utilizes row generation, partitioning, and bounding strategies, and demonstrate the efficacy of our approach on a set of randomly generated instances.