Decision Programming for Mixed-Integer Multi-Stage Optimization under Uncertainty

• Mixed-integer linear programming formulations for influence diagrams are presented. Even problems in which the no-forgetting assumption does not hold can be solved. Many kinds of resource, logical and risk constraints accommodated. All non-dominated strategies computed with multiple objectives. Support project porfolio selection under endogenous uncertainties is given. Influence widely employed to represent multi-stage decision each a choice from discrete set alternative courses action, uncertain chance events have outcomes, prior decisions may probability distributions endogenously. In this paper, we develop Decision Programming framework extends applicability by developing mixed-integer such problems. particular, makes it possible (i) solve earlier cannot necessarily recalled later, instance, when taken agents who communicate other; (ii) accommodate broad range deterministic constraints, including those based on resource consumption, dependencies or measures as Conditional Value-at-Risk; (iii) determine all value portfolio problems, allows scenario probabilities depend endogenously thus viewed generalization Contingent Portfolio (Gustafsson & Salo, 2005). We present several illustrative examples, evidence computational performance formulations, directions further development.