A single representative min-max-min robust selection problem with alternatives and budgeted uncertainty

A robust two -stage problem of selecting a single minimum cost representative out of n candidates is studied. Each candidate is associated with an uncertain cost that is described by a lower bound and a deviation from it. In the first stage, at most k representatives have to be selected. After that, an adversary distributes the worst costs to all representatives so that the sum of the cost deviation ratios (the uncertainty budget) does not exceed a given upper bound. In the second stage, the cost of the cheapest representative is paid. An O(n2 log n) time algorithm is proposed for this problem. (c) 2024 Elsevier B.V. All rights reserved.