609 eng preprint 0 2025-10-28 -- -- 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. publish Creative Commons - CC BY - Namensnennung 4.0 International Daniela Bernhard Frauke Liers Michael Stingl B06 https://opus4.kobv.de/opus4-trr154/files/609/paper_integer.pdf