J Glob Optim (2007) 38:181–199 DOI 10.1007/s10898-006-9067-3 ORIGINAL PAPER Survivable network design under optimal and heuristic interdiction scenarios J. Cole Smith · Churlzu Lim · Fransisca Sudargho Received: 3 January 2006 / Accepted: 1 July 2006 / Published online: 9 August 2006 © Springer Science+Business Media B.V. 2006 Abstract We examine the problem of building or fortifying a network to defend against enemy attacks in various scenarios. In particular, we examine the case in which an enemy can destroy any portion of any arc that a designer constructs on the network, subject to some interdiction budget. This problem takes the form of a three-level, two-player game, in which the designer acts first to construct a network and transmit an initial set of flows through the network. The enemy acts next to destroy a set of constructed arcs in the designer’s network, and the designer acts last to transmit a final set of flows in the network. Most studies of this nature assume that the enemy will act optimally; however, in real-world scenarios one cannot necessarily assume rationality on the part of the enemy. Hence, we prescribe optimal network design algorithms for three different profiles of enemy action: an enemy destroying arcs based on capacities, based on initial flows, or acting optimally to minimize our maximum profits obtained from transmitting flows. Keywords Network design · Integer programming · Network interdiction · Game theory 1 Introduction The continuous increase of telecommunications and transportation needs has made the design of cost-efficient networks that meet requirements concerning flexibility and survivability a major challenge. Many traditional network design algorithms do not take into account the survivability aspect of a network, which can perhaps leave the network susceptible to failures of small subsets of its arcs. It is important to J. C. Smith (B ) · C. Lim Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA e-mail: cole@ise.ufl.edu F. Sudargho Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ, USA