On the performance of affine policies for two-stage adaptive optimization: a geometric perspective
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...
| Main Authors: | , |
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| Other Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg,
2016-06-28T19:04:27Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. |
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