  Intensively studied in theory as a promising data-driven tool for
decision-making under ambiguity, two-stage distributionally robust optimization
(DRO) problems over Wasserstein balls are not necessarily easy to solve in
practice. This is partly due to large sample size. In this article, we study a
generic two-stage distributionally robust linear program (2-DRLP) over a
1-Wasserstein ball using an affine policy. The 2-DRLP has right-hand-side
uncertainty with a rectangular support. Our main contribution is to show that
the 2-DRLP problem has a tractable reformulation with a scale independent of
sample size. The reformulated problem can be solved within a pre-defined
optimality tolerance using robust optimization techniques. To reduce the
inevitable conservativeness of the affine policy while preserving independence
of sample size, we further develop a method for constructing an uncertainty set
with a probabilistic guarantee over which the Wasserstein ball is re-defined.
As an application, we present a novel unit commitment model for power systems
under uncertainty of renewable energy generation to examine the effectiveness
of the proposed 2-DRLP technique. Extensive numerical experiments demonstrate
that our model leads to better out-of-sample performance on average than other
state-of-the-art distributionally robust unit commitment models while staying
computationally competent.
