Orateur
Description
We propose a decomposition algorithm to approximately solve two-stage distributionally robust optimization problems with mixed-integer ambiguity sets. Such settings are particularly relevant in non-cooperative contexts, such as unplanned disruptions or interdictions, where an adversary reacts to the defender's decisions. DRO is a natural fit, but resulting problems are difficult to reformulate as solvable MILPs unless the ambiguity set follows a specific structure. Therefore, we propose a data-driven approach to find an upper bound to the original problem. The ambiguity set is split into integer and continuous sets, so that the recourse model is easily reformulated into a tractable form by relying on known strong duality results. The resulting problem is solved using a traditional decomposition approach combining Benders’ decomposition and column-and-constraint generation. We demonstrate our approach on a network design problem with interdiction constraints.
