From the uncertainty set to the solution and back: the two stage case

Robust optimization approaches compute solutions resilient to data uncertainty, represented by a given uncertainty set.
Instead, the problem of computing the largest uncertainty set that a given solution can support was, so far, quite neglected and the only results refer to the single stage framework.
For that setting, it was proved that this problem can be solved in polynomial time, when the uncertainty is modeled using the cardinality constrained set.
Here we study what happens if we consider a two stage framework.

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