On the performance of affine policies for two-stage adaptive optimization: a geometric perspective
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Author(s)
Bidkhori, Hoda
Bertsimas, Dimitris J
Date Issued
September 2014
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Bertsimas, Dimitris, and Hoda Bidkhori. “On the Performance of Affine Policies for Two-Stage Adaptive Optimization: a Geometric Perspective.” Math. Program. 153, no. 2 (September 26, 2014): 577–594.
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Author's final manuscript
Abstract
We consider two-stage adjustable robust linear optimization problems with uncertain right hand side b belonging to a convex and compact uncertainty set U. We provide an a priori approximation bound on the ratio of the optimal affine (in b) solution to the optimal adjustable solution that depends on two fundamental geometric properties of U: (a) the “symmetry” and (b) the “simplex dilation factor” of the uncertainty set 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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-014-0818-5
