On the performance of affine policies for two-stage adaptive optimization: a geometric perspective
Author(s)Bertsimas, Dimitris J.; Bidkhori, Hoda
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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.
DepartmentMassachusetts Institute of Technology. Operations Research Center; Sloan School of Management
Springer Berlin Heidelberg
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.
Author's final manuscript