  We introduce a unified framework for the study of multilevel mixed integer
linear optimization problems and multistage stochastic mixed integer linear
optimization problems with recourse. The framework highlights the common
mathematical structure of the two problems and allows for the development of a
common algorithmic framework. Focusing on the two-stage case, we investigate,
in particular, the nature of the value function of the second-stage problem,
highlighting its connection to dual functions and the theory of duality for
mixed integer linear optimization problems, and summarize different
reformulations. We then present two main solution techniques, one based on a
Benders-like decomposition to approximate either the risk function or the value
function, and the other one based on cutting plane generation.
