@unpublished{BernhardLiersStingl2025, author = {Daniela Bernhard and Frauke Liers and Michael Stingl}, title = {Branch-and-cut for mixed-integer robust chance-constrained optimization with discrete distributions}, year = {2025}, abstract = {We study robust chance-constrained problems with mixed-integer design variables and ambiguity sets consisting of discrete probability distributions. Allowing general non-convex constraint functions, we develop a branch-and-cut framework using scenario-based cutting planes to generate lower bounds. The cutting planes are obtained by exploiting the classical big-M reformulation of the chance-constrained problem in the case of discrete distributions. Furthermore, we include the calculation of initial feasible solutions based on a bundle method applied to an approximation of the original problem into the branch-and-cut procedure. We conclude with a detailed discussion about the practical performance of the branch-and-cut framework with and without initial feasible solutions. In our experiments we focus on gas transport problems under uncertainty and provide a comparison of our method with solving the classical reformulation directly for various real-world sized instances.}, url = {https://opus4.kobv.de/opus4-trr154/609}, type = {Preprint}, institution = {TRR 154} }