We study the following questions related to wireless network security: Which jammer placement configuration during a jamming attack results in the largest degradation of network throughput? and Which network design strategies are most effective in mitigating a jamming attack? Although others have studied similar jammer placement problems, this article is the first to optimize network throughput subject to radio wave interference. We formulate this problem as a bi-level mixed-integer program, and solve it using a cutting plane approach that is able to solve networks with up to 81 transmitters, which is a typical size for studies in wireless network optimization. Experiments with the algorithm also yielded the following insights into wireless network jamming: (1) increasing the number of channels is the best strategy for designing a network that is robust against jamming attacks, and (2) increasing the range of the jammer is the best strategy for the attacker. (c) 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(2), 111-125 2016