Network design for reliability and resilience to attack

Abstract

We define 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 ending a shortest path. The solution identifies 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 denied through general now 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 problem's solution identifies the storage locations that minimize the cargo's 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.