  Many discrete optimization problems are amenable to constrained shortest-path
reformulations in an extended network space, a technique that has been key in
convexification, bound strengthening, and search. In this paper, we propose a
constrained variant of these models for two challenging classes of discrete
two-stage optimization problems, where traditional methods (e.g.,
dualize-and-combine) are not applicable compared to their continuous
counterparts. Specifically, we propose a framework that models problems as
decision diagrams and introduces side constraints either as linear inequalities
in the underlying polyhedral representation, or as state variables in
shortest-path dynamic programming models. For our first structured class, we
investigate two-stage problems with interdiction constraints. We show that such
constraints can be formulated as indicator functions in the arcs of the
diagram, providing an alternative single-level reformulation of the problem via
a network-flow representation. Our second structured class is classical robust
optimization, where we leverage the decision diagram network to iteratively
identify label variables, akin to an L-shaped method. We evaluate these
strategies on a competitive project selection problem and the robust traveling
salesperson with time windows, observing considerable improvements in
computational efficiency as compared to general methods in the respective
areas.
