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Two-stage stochastic programs with binary recourse are challenging to solveand efficient solution methods for such problems have been limited. In thiswork, we generalize an existing binary decision diagram-based (BDD-based)approach of Lozano and Smith (Math. Program., 2018) to solve a special class oftwo-stage stochastic programs with binary recourse. In this setting, thefirst-stage decisions impact the second-stage constraints. Our modified problemextends the second-stage problem to a more general setting where logicalexpressions of the first-stage solutions enforce constraints in the secondstage. We also propose a complementary problem and solution method which can beused for many of the same applications. In the complementary problem we havesecond-stage costs impacted by expressions of the first-stage decisions. Inboth settings, we convexify the second-stage problems using BDDs andparametrize either the arc costs or capacities of these BDDs with first-stagesolutions depending on the problem. We further extend this work byincorporating conditional value-at-risk and we propose, to our knowledge, thefirst decomposition method for two-stage stochastic programs with binaryrecourse and a risk measure. We apply these methods to a novel stochasticdominating set problem and present numerical results to demonstrate theeffectiveness of the proposed methods.

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints