Distributionally risk‐receptive and risk‐averse network interdiction problems with general ambiguity set

Abstract

AbstractWe introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk‐averse (or robust) network interdiction problem (DRA‐NIP) and a distributionally risk‐receptive network interdiction problem (DRR‐NIP) where a leader maximizes a follower's minimal expected objective value for either the worst‐case or the best‐case, respectively, probability distribution belonging to ambiguity set (a set of distributions). The DRA‐NIP arises in applications where a risk‐averse leader interdicts a follower to cause delays in their supply convoy. In contrast, the DRR‐NIP provides network vulnerability analysis where a network‐user seeks to identify vulnerabilities in the network against potential disruptions by an adversary (or leader) who is receptive to risk for improving the expected objective values. We present finitely convergent algorithms for solving DRA‐NIP and DRR‐NIP with a general ambiguity set. To evaluate their performance, we provide results of our extensive computational experiments performed on instances known for (risk‐neutral) stochastic NIP.