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We consider a new class of max flow network interdiction problems, where thedefender is able to introduce new arcs to the network after the attacker hasmade their interdiction decisions. We prove properties of when thisrestructuring will not increase the value of the minimum cut, which hasimportant practical interpretations for problems of disrupting drug traffickingnetworks. In particular, it demonstrates that disrupting lower levels of thesenetworks will not impact their operations when replacing the disruptedparticipants is easy. For the bilevel mixed integer linear programmingformulation of this problem, we devise a column-and-constraint generation(C&CG) algorithm to solve it. Our approach uses partial information on thefeasibility of restructuring plans and is shown to be orders of magnitudefaster than previous C&CG methods. We demonstrate that applying decisions fromstandard max flow network interdiction problems can result in significantlyhigher flows than interdictions that account for the restructuring.

Interdicting Restructuring Networks with Applications in Illicit Trafficking