Robust optimization has become an important paradigm to deal with optimization under uncertainty. Adjustable robust optimization is an extension that deals with multistage problems. This thesis starts with a short but comprehensive introduction to adjustable robust optimization. Then the two approaches developed in this thesis are explained in detail: a primal and a dual approach. In the dual approach various duality aspects of adjustable robust optimization models are exploited which lead to new model formulations. Although these formulations are equivalent to the original models, they have a different structure which allows us to solve problems more efficiently. It even opens up the possibility to solve a type of nonlinear adjustable robust optimization models that were deemed intractable before. In the primal approach the so-called decision rules, that are used to find solutions to adjustable robust models, are improved by lifting the uncertainty set. Crucially, these richer decision rules require only little additional computational effort. Next, it is shown that there can be multiple optimal solutions for adjustable robust optimization models. Lastly, an extension to existing adjustable robust models is given in which the information used in decision rules is still inexact. Throughout the thesis the benefits of all approaches are illustrated with numerical experiments.
|Qualification||Doctor of Philosophy|
|Award date||19 Jan 2018|
|Place of Publication||Tilburg|
|Print ISBNs||978 90 5668 550 8|
|Publication status||Published - 2018|