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Ruben van Beesten (University of Groningen) - Integer recourse models with distributional uncertainty: a pragmatic approach
Supervisor: Kees Jan Roodbergen
Recorded full presentation

In stochastic linear programming (SLP), we deal with linear programs that contain some random parameters. One class of models within SLP are recourse models, in which we introduce recourse actions to solve infeasibilities that arise as a result of adverse realizations of the random parameters. The objective is to minimize the cost of the initial decisions plus the expected cost of these recourse actions, given the distribution of the random parameters. In practice, however, this distribution is often not known exactly. For instance, we may only have a data set of past realizations of the distribution, while not knowing the distribution itself. A popular way to deal with this distributional uncertainty is to consider distributionally robust recourse models. In these models we define a so-called uncertainty set of potential distributions and optimize under the worst-case distribution from this set. This approach is often surprisingly tractable if the underlying recourse model is convex. In this presentation, however, we make our lives more difficult by putting integer restrictions on the recourse actions, yielding distributionally robust integer recourse models. As a result, the underlying problem is non-convex, which makes the distributionally robust problem generally intractable. To solve this issue, we propose a pragmatic approach, in which we restrict the uncertainty set in such a way that the resulting problem is convex. We do this for the special case with a simple integer recourse structure (i.e., integer newsvendor-type problems). It turns out that in some cases, our approach is equivalent to solving a continuous model under a known distribution, hence both difficulties (integrality and distributional uncertainty) vanish.