We propose an algorithm based on infeasible irreducible subsystems (IIS) to solve general binary chance-constrained problems. By leverag- ing on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete do- main is used to guide us eciently in the search of solutions. We apply our methodology to individual and joint binary chance-constrained prob- lems, demonstrating the ability of our approach to solve those problems. Extensive numerical experiments show that, in some cases, the number of nodes explored by our algorithm is drastically reduced when compared to a commercial solver.
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