The robust bilevel continuous knapsack problem

03/07/2019

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by   Christoph Buchheim, et al.

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We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower's profits are uncertain. Adopting the robust optimization approach and assuming that the follower's profits belong to a given uncertainty set, our aim is to compute a worst case optimal solution for the leader. We show that this problem can be solved in polynomial time for both discrete and interval uncertainty. In the latter case, we make use of an algorithm by Woeginger for a class of precedence constraint knapsack problems.