Leveraging decision diagrams to solve two-stage stochastic programs with binary recourse and logical linking constraints

Abstract

We generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (MP, 2022) to solve a special class of two-stage stochastic programs (2SPs) with binary recourse, where the first-stage decisions impact the second-stage constraints. First, we extend the second-stage problem to a more general setting where logical expressions of the first-stage solutions enforce constraints in the second stage. Then, as our primary contribution, we introduce a complementary problem, that appears more naturally for many of the same applications of the former approach, and a distinct BDD-based solution method, that is more efficient than the existing BDD-based approach on commonly applicable problem classes. In the novel problem, second-stage costs, rather than constraints, are impacted by expressions of the first-stage decisions. In both settings, we convexify the second-stage problems using BDDs and parameterize either the BDD arc costs or capacities with first-stage solutions. We extend this work by incorporating conditional value-at-risk and propose the first decomposition method for 2SP with binary recourse and a risk measure. We apply these methods to a novel stochastic problem, namely stochastic minimum dominating set problem, and present numerical results to support their effectiveness.