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We study the performance of linear and piecewise-linear decision rules for adaptive optimization problems based only on the geometry of uncertainty sets. In particular, we show that Minkowski Symmetry and Banach-Mazur distance play a signicant role in determining the power of linear and piecewise-linear decision rules in adaptive optimization problems. We discuss the effectiveness of the proposed decision rules in the context of two-stage inventory control problems. Finally, we introduce a method for evaluating the worst-case performance of a class of distributionally robust optimization problems. This is applied to evaluate the performance of general unbalanced process exibility structures in manufacturing. We derive a simple, tight lower bound for the expected sales for a process flexibility structure known as chaining. Based on two joint works with Dimitris Bertsimas, with David Simchi-Levi and Yehua Wei.
Hoda Bidkhori is a postdoctoral associate in Operations Research at MIT. She holds a Ph.D. degree in Applied Mathematics from MIT. Her current research interests lie in decision making under uncertain and data-rich environment, with applications in Flexibility in manufacturing, Logistics and Business analytics. She is a recipient of the Roger Family Prizes at MIT, and Second and Third Prizes in the 8th and 9th International Competition for University Students. She currently serves on the Editorial Board of the Journal of Research and Communications in Mathematics and Mathematical Sciences.