  We study piecewise affine policies for multi-stage adjustable robust
optimization (ARO) problems with non-negative right-hand side uncertainty.
First, we construct new dominating uncertainty sets and show how a multi-stage
ARO problem can be solved efficiently with a linear program when uncertainty is
replaced by these new sets. We then demonstrate how solutions for this
alternative problem can be transformed into solutions for the original problem.
By carefully choosing the dominating sets, we prove strong approximation bounds
for our policies and extend many previously best-known bounds for the
two-staged problem variant to its multi-stage counterpart. Moreover, the new
bounds are - to the best of our knowledge - the first bounds shown for the
general multi-stage ARO problem considered. We extensively compare our policies
to other policies from the literature and prove relative performance
guarantees. In two numerical experiments, we identify beneficial and
disadvantageous properties for different policies and present effective
adjustments to tackle the most critical disadvantages of our policies. Overall,
the experiments show that our piecewise affine policies can be computed by
orders of magnitude faster than affine policies, while often yielding
comparable or even better results.
