Niels van der Laan We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more
We propose a new solution method for two-stage mixed-integer recourse models. In contrast to existing approaches, we can handle general mixed-integer variables in both stages, and thus, e.g., do not require that the first-stage variables are binary. Our solution method is a Benders’ decomposition, in which we iteratively construct tighter approximations of the expected second-stage … Read more
We propose a novel way of applying cutting plane techniques to two-stage mixed-integer stochastic programs. Instead of using cutting planes that are always valid, our idea is to apply inexact cutting planes to the second-stage feasible regions that may cut away feasible integer second-stage solutions for some scenarios and may be overly conservative for others. … Read more