  Catastrophic tornadoes cause severe damage and are a threat to human
wellbeing, making it critical to determine mitigation strategies to reduce
their impact. One such strategy, following recent research, is to retrofit
existing structures. To this end, in this article we propose a model that
considers a decision-maker (a government agency or a public-private consortium)
who seeks to allocate resources to retrofit and recover wood-frame residential
structures, to minimize the population dislocation due to an uncertain tornado.
In the first stage the decision-maker selects the retrofitting strategies, and
in the second stage the recovery decisions are made after observing the
tornado. As tornado paths cannot be forecast reliably, we take a worst-case
approach to uncertainty where paths are modeled as arbitrary line segments on
the plane. Under the assumption that an area is affected if it is sufficiently
close to the tornado path, the problem is framed as a two-stage robust
optimization problem with a mixed-integer non-linear uncertainty set. We solve
this problem by using a decomposition column-and-constraint generation
algorithm that solves a two-level integer problem at each iteration. This
problem, in turn, is solved by a decomposition branch-and-cut method that
exploits the geometry of the uncertainty set. To illustrate the model's
applicability, we present a case study based on Joplin, Missouri. Our results
show that there can be up to 20 percent reductions in worst-case population
dislocation by investing 15 million dollars in retrofitting and recovery; that
our approach outperforms other retrofitting policies, and that the model is not
over-conservative.
