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We propose a model for recoverable robust optimization with commitment. Givena combinatorial optimization problem and uncertainty about elements that mayfail, we ask for a robust solution that, after the failing elements arerevealed, can be augmented in a limited way. However, we commit to preserve theremaining elements of the initial solution. We consider differentpolynomial-time solvable combinatorial optimization problems and settle thecomputational complexity of their robust counterparts with commitment. We showfor the weighted matroid basis problem that an optimal solution to the nominalproblem is also optimal for its robust counterpart. Indeed, matroids areprovably the only structures with this strong property. Robust counterparts ofother problems are NP-hard such as the matching and the stable set problem,even in bipartite graphs. However, we establish polynomial-time algorithms forthe robust counterparts of the unweighted stable set problem in bipartitegraphs and the weighted stable set problem in interval graphs, also known asthe interval scheduling problem.

Recoverable Robust Optimization with Commitment