Network Design for Reliability and Resilience to Attack

We de ne and solve two network-design problems. In the first, 1 a defender uses limited resources to select a portfolio of paths or design a sub-network 2 an attacker then uses limited attack resources to destroy network arcs, and then 3 the defender operates the damaged network optimally by finding a shortest path. The solution identfies a network design that minimizes post-attack path length. We show how the tri-level problem is equivalent to a single-level mixed integer program MIP with an exponential number of rows and columns, and solve that MIP using simultaneous row and column generation. Methods extend to network operations defined through general flow constructs. The second problem considers a stochastic logistics network where arcs are present randomly and independently. Shipping from a source to a destination may be delayed until a path connecting the two is available. In the presence of storage capacity, cargo can be shipped partway. The problems solution identifies the storage locations that minimize the cargos waiting time for shipment. We develop and demonstrate practical methods to solve this P-complete problem on a model instance derived from a Department of Defense humanitarian shipping network.