Ordered Weighted Averaging for Combinatorial Decision Problems with Interval Uncertainty

Abstract: This paper introduces a novel approach to applying the Ordered Weighted Averaging (OWA) operator for uncertain combinatorial problems characterized by interval uncertainty. In this setting, an interval of possible cost outcomes is known for each item, and we would like to minimize the sum of these item costs. By using a weighted integral over the Value-at-Risk, our method provides a more nuanced representation of uncertainty and the decision-maker's risk attitude than a previously proposed OWA aggregation method. We analyze fundamental properties of the OWA operator we propose, show that the classic discrete OWA operator converges to our framework when scenarios are sampled, and propose a 2-approximation algorithm. In computational experiments, we compare heuristic solution algorithms to alternative aggregation methods and demonstrate the improved flexibility of our setting.