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We investigate methods to solve the maximum-reliability stochastic networkinterdiction problem (SNIP). In this problem, a defender interdicts arcs on adirected graph to minimize an attacker's probability of undetected traversalthrough the network. The attacker's origin and destination are unknown to thedefender and assumed to be random. SNIP can be formulated as a stochasticmixed-integer program via a deterministic equivalent formulation (DEF). As thesize of this DEF makes it impractical for solving large instances, currentapproaches to solving SNIP rely on modifications of Benders decomposition. Wepresent two new approaches to solve SNIP. First, we introduce a new DEF that issignificantly more compact than the standard DEF. Second, we propose a newpath-based formulation of SNIP. The number of constraints required to definethis formulation grows exponentially with the size of the network, but themodel can be solved via delayed constraint generation. We present validinequalities for this path-based formulation which are dependent on thestructure of the interdicted arc probabilities. We propose a branch-and-cut(BC) algorithm to solve this new SNIP formulation. Computational resultsdemonstrate that directly solving the more compact SNIP formulation and this BCalgorithm both provide an improvement over a state-of-the-art implementation ofBenders decomposition for this problem.

New solution approaches for the maximum-reliability stochastic network interdiction problem