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In this paper we studied combinatorial problems with parameterized locallybudgeted uncertainty. We are looking for a solutions set such that for anyparameters vector there exists a solution in the set with robustness nearoptimal. The algorithm consists of applying a multiparametric algorithm toobtain a near optimal multiparametric solution relative to the objectivefunction for a combinatorial problem defined to find a robust solution forparameters fixed. As far as we know this is the first algorithm presented to dothat task. Computational experience is presented to shortest path and$p$-medians problems

Multiparametric robust solutions for combinatorial problems with parameterized locally budgeted uncertainty