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Mathematical Programming

, Volume 153, Issue 2, pp 577–594 | Cite as

On the performance of affine policies for two-stage adaptive optimization: a geometric perspective

  • Dimitris BertsimasEmail author
  • Hoda Bidkhori
Full Length Paper Series A

Abstract

We consider two-stage adjustable robust linear optimization problems with uncertain right hand side \(\mathbf {b}\) belonging to a convex and compact uncertainty set \(\mathcal{U}\). We provide an a priori approximation bound on the ratio of the optimal affine (in \(\mathbf {b}\) ) solution to the optimal adjustable solution that depends on two fundamental geometric properties of \(\mathcal{U}\): (a) the “symmetry” and (b) the “simplex dilation factor” of the uncertainty set \(\mathcal{U}\) and provides deeper insight on the power of affine policies for this class of problems. The bound improves upon a priori bounds obtained for robust and affine policies proposed in the literature. We also find that the proposed a priori bound is quite close to a posteriori bounds computed in specific instances of an inventory control problem, illustrating that the proposed bound is informative.

Keywords

Robust optimization Adjustable optimization Affine policies 

Mathematics Subject Classification

90 Operations Research Mathematical Programming 

Notes

Acknowledgments

We would like to thank two anonymous referees for very thoughtful comments that have improved the paper and Dr. Angelos Georghiou for sharing with us his code and very helpful discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Sloan School of Management and Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA

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