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Finding robust solutions of an optimization problem is an important issue inpractice, and various concepts on how to define the robustness of a solutionhave been suggested. The idea of recoverable robustness requires that asolution can be recovered to a feasible one as soon as the realized scenariobecomes known. The usual approach in the literature is to minimize theobjective function value of the recovered solution in the nominal or in theworst case.  As the recovery itself is also costly, there is a trade-off between therecovery costs and the solution value obtained; we study both, the recoverycosts and the solution value in the worst case in a biobjective setting.  To this end, we assume that the recovery costs can be described by a metric.We demonstrate that this leads to a location planning problem, bringingtogether two fields of research which have been considered separate so far.  We show how weakly Pareto efficient solutions to this biobjective problem canbe computed by minimizing the recovery costs for a fixed worst-case objectivefunction value and present approaches for the case of linear and quasiconvexproblems for finite uncertainty sets. We furthermore derive cases in which thesize of the uncertainty set can be reduced without changing the set of Paretoefficient solutions.

A biobjective approach to robustness based on location planning