Document Type : Original Paper


Department of Mathematics, Faculty of Basic Science, University of Qom, Qom, Islamic Republic of Iran


In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum flow network interdiction problem is not bounded below by a constant, even when strengthened by the path inequalities. We show that this result is also  established for the nodal interdiction problem.