Approximate and exact convexification approaches for solving two-stage mixed-integer recourse models

Many practical decision-making problems are subject to uncertainty. A powerful class of mathematical models designed for these problems is the class of mixed-integer recourse models. Such models have a wide range of applications in, e.g., healthcare, energy, and finance. They permit integer decision variables to accurately model, e.g., on/off restrictions or natural indivisibilities. The additional modelling flexibility of integer decision variables, however, comes at the expense of models that are significantly harder to solve. The reason is that including integer decision variables introduces non-convexity in the model, which poses a significant challenge for state-of-the-art solvers.In this thesis, we contribute to better decision making under uncertainty by designing efficient solution methods for mixed-integer recourse models. Our approach is to address the non-convexity caused by integer decision variables by using convexification. That is, we construct convex approximating models that closely approximate the original model. In addition, we derive performance guarantees for the solution obtained by solving the approximating model. Finally, we extensively test the solution methods that we propose and we find that they consistently outperform traditional solution methods on a wide range of benchmark instances