Orateur
Description
In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems with decisions. Instead of allowing all possible second-stage decisions, the k-adaptability approach aims at calculating a limited set of k such decisions already in the first-stage before the uncertainty reveals. The parameter k can be adjusted to control the quality of the approximation. However, not much is known on how many solutions k are needed to achieve an optimal solution for the two-stage robust problem. In this talk we answer this question by deriving bounds on k for objective and constraint uncertainty. Furthermore, we derive approximation guarantees the k-adaptability approach provides for small values of k. The results give new insights on how many solutions are needed for problems as the decision dependent information discovery problem or the capital budgeting problem with constraint uncertainty.
