  Despite methodological advances for modeling decision problems under
uncertainty, representing endogenous uncertainty still proves challenging both
in terms of modeling capabilities and computational requirements. A novel
reformulation based on rooted junction trees (RJTs) provides an approach for
solving such decision problems using off-the-shelf mathematical optimization
solvers. This is made possible by using an influence diagram to represent a
given decision problem and reformulating it as an RJT, which is then
represented as a mixed-integer linear programming model. In this paper, we
focus on the type of endogenous uncertainty that received less attention in the
rooted junction tree approach: conditionally observed information. Multi-stage
stochastic programming models use conditional non-anticipativity constraints to
represent such uncertainties, and we show how such constraints can be
incorporated into RJT formulations. This allows us to consider the two main
types of endogenous uncertainty simultaneously, namely decision-dependent
information structure and decision-dependent probability distribution. Finally,
the extended framework is illustrated with a large-scale cost-benefit problem
regarding climate change mitigation.
