  We consider a new class of max flow network interdiction problems, where the
defender is able to introduce new arcs to the network after the attacker has
made their interdiction decisions. We prove properties of when this
restructuring will not increase the value of the minimum cut, which has
important practical interpretations for problems of disrupting drug trafficking
networks. In particular, it demonstrates that disrupting lower levels of these
networks will not impact their operations when replacing the disrupted
participants is easy. For the bilevel mixed integer linear programming
formulation of this problem, we devise a column-and-constraint generation
(C&CG) algorithm to solve it. Our approach uses partial information on the
feasibility of restructuring plans and is shown to be orders of magnitude
faster than previous C&CG methods. We demonstrate that applying decisions from
standard max flow network interdiction problems can result in significantly
higher flows than interdictions that account for the restructuring.
