Abstract
We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to polytope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row generation or column-and-row generation algorithms. The novelty of our approach lies in formulating the separation problem as a feasibility problem instead of a max–min problem as done in recent works. Applying the Farkas lemma, we can reformulate the separation problem as a bilinear program, which is then linearized to obtained a mixed-integer linear programming formulation. We compare the two algorithms on a robust telecommunications network design under demand uncertainty and budgeted uncertainty polytope. Our results show that the relative performance of the algorithms depend on whether the budget is integer or fractional.
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Acknowledgments
We would like to thank Sara Mattia for fruitful discussions on the topic of this paper. We also thank the editors and the referees for useful remarks and suggestions that helped in improving the presentation and the content of the paper.
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Ayoub, J., Poss, M. Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Comput Manag Sci 13, 219–239 (2016). https://doi.org/10.1007/s10287-016-0249-2
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DOI: https://doi.org/10.1007/s10287-016-0249-2