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.

我们考虑一类新的最大流量网络拦截问题，其中防御者能够在攻击者做出拦截决定后向网络引入新的弧线。我们证明了这种重组何时不会增加最小切割值的性质，这对破坏贩毒网络的问题具有重要的实践解释。特别是，它表明在替换被破坏的参与者很容易的情况下，破坏这些网络的较低级别不会影响它们的操作。对于这个问题的双层混合整数线性规划公式，我们设计了一个列和约束生成 (C&CG) 算法来解决它。我们的方法使用部分信息关于重组计划的可行性，并显示比以前的 C&CG 方法快几个数量级。我们证明，应用来自标准最大流量网络拦截问题的决策可以导致流量明显高于解释重组的拦截。