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

• Main Authors: Bertsimas, Dimitris J. (Contributor), Bidkhori, Hoda (Contributor)
• Other Authors: Massachusetts Institute of Technology. Operations Research Center (Contributor), Sloan School of Management (Contributor)
• Format: Article
• Language: English
• Published: Springer Berlin Heidelberg, 2016-06-28T19:04:27Z.
• Subjects: Article
• Online Access: Get fulltext

 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.