Groupe d’études et de recherche en analyse des décisions

G-2016-69

Linearized robust counterparts of two-stage robust optimization problems with applications in operations management

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In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that this generalized method mainly relies on a linearization scheme employed in bilinear optimization problems, we will say that it gives rise to the "linearized robust counterpart" model. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe a simple way of modifying both types of models in order to make these approximations less conservative. We finally demonstrate how to employ this new scheme in a set of operations management problems in order to improve the performance and guarantees of robust optimization.

, 26 pages