We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood's [19] integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally, we provide an approximation-factor-preserving reduction from the simpler R-Interdiction Covering Problem to MFNIP.
Altner et al. REF presented two polynomially separable valid inequalities for the network interdiction problem, and analyzed the integrality gaps and approximability of the bi-level mixed-integer program.
The maximum flow network interdiction problem: Valid inequalities, integrality gaps, and approximability
Operations Research Letters
Mathematics Computer Science