Recoverable robust representatives selection problems with discrete budgeted uncertainty

Recoverable robust optimization is a multi-stage approach, in which it possible to adjust first-stage solution after the uncertain cost scenario revealed. We analyze this approach for class of selection problems. The aim choose fixed number items from several disjoint sets, such that worst-case costs taking recovery action are as small possible. uncertainty modeled discrete budgeted set, where adversary can increase items. While special cases problem have been studied before, its complexity has remained open. In work we make contributions towards closing gap. show NP-hard and identify case remains solvable polynomial time. provide compact mixed-integer programming formulation two additional extended formulations. Finally, computational results provided compare efficiency different exact approaches.