Mastering uncertainty: Towards robust multistage optimization with decision dependent uncertainty

Abstract

We investigate, as a special case of robust optimization, integer linear programs with variables being either existentially or universally quantified. They can be interpreted as two-person zero-sum games between an existential and a universal player. In this setting the existential player must ensure the fulfillment of a system of linear constraints, while the universal variables can range within given intervals, trying to make the fulfillment impossible. We extend this approach by adding a linear constraint system the universal player must obey. Consequently, existential and universal variable assignments in early decision stages now can restrain possible universal variable assignments later on and vice versa resulting in a multistage optimization problem with decision dependent uncertainty. We present novel insights in structure and complexity.