Marius Roland Explainability is a growing concern for optimization models used as decision-making tools. It aims to help a stakeholder understand why a model recommends a given outcome, typically by exhibiting the elements of the input that account for this outcome. We study this question for linear two-stage stochastic programs, and explain the returned decision by a … Read more
This paper investigates the a posteriori analysis of Branch-and-Bound (BB) trees to extract structural information about the feasible region of mixed-binary linear programs. Using only the branching decisions of a tree and one dual bound per node, we introduce three polyhedral outer approximations of the feasible region, namely a disjunctive, a network-flow-based, and a mixing-set-based … Read more
We consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bound and, by this, the overall performance of such methods. We introduce so-called multi-disjunctive valid … Read more
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem is constructed to yield a bound on the optimal value of the original problem. We show how to adapt the partitioning of the scenario set so … Read more