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Despite methodological advances for modeling decision problems underuncertainty, faithfully representing endogenous uncertainty still proveschallenging, both in terms of modeling capabilities and computationalrequirements. A novel framework called Decision Programming provides anapproach for solving such decision problems using off-the-shelf mathematicaloptimization solvers. This is made possible by using influence diagrams torepresent a given decision problem, which is then formulated as a mixed-integerlinear programming problem.  In this paper, we focus on the type of endogenous uncertainty that receivedless attention in the introduction of Decision Programming: conditionallyobserved information. Multi-stage stochastic programming (MSSP) models useconditional non-anticipativity constraints (C-NACs) to represent suchuncertainties, and we show how such constraints can be incorporated intoDecision Programming models. This allows us to consider the two main types ofendogenous uncertainty simultaneously, namely decision-dependent informationstructure and decision-dependent probability distribution. Additionally, wepresent a decomposition approach that provides significant computationalsavings and also enables considering continuous decision variables in certainparts of the problem, whereas the original formulation was restricted todiscrete variables only.  The extended framework is illustrated with two example problems. The firstconsiders an illustrative multiperiod game and the second is a large-scalecost-benefit problem regarding climate change mitigation. Neither of theseexample problems could be solved with existing frameworks.

A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming