Min–max–min robustness for combinatorial problems with discrete budgeted uncertainty

Robust combinatorial optimization with variable budgeted uncertainty

Abstract: We introduce a new model for robust combinatorial optimization where the uncertain parameters belong to the image of multifunctions of the problem variables. In particular, we study the variable budgeted uncertainty, an extension of the budgeted uncertainty introduced by Bertsimas and Sim. Variable budgeted uncertainty can provide the same probabilistic guarantee as the budgeted uncer...

Robust Combinatorial Optimization under Budgeted-Ellipsoidal Uncertainty∗

In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we introduce a new uncertainty class ...

Contributions to robust combinatorial optimization with budgeted uncertainty

Robust constrained shortest path problems under budgeted uncertainty

We study the robust constrained shortest path problem under resource uncertainty. After proving that the problem is NP-hard in the strong sense for arbitrary uncertainty sets, we focus on budgeted uncertainty sets introduced by Bertsimas and Sim (2003) and their extension to variable uncertainty by Poss (2013). We apply classical techniques to show that the problem with capacity constraints can...

Pareto Optimal Budgeted Combinatorial Auctions

This paper studies the possibility of implementing Pareto optimal outcomes in the combinatorial auction setting where bidders may have budget constraints. I show that when the setting involves a single good, or multiple goods but with single-minded bidders, there is a unique mechanism, called truncation VCG, that is individually rational, incentive compatible and Pareto optimal. Truncation VCG ...