Robust Adjustable Optimization with an Affine Linear Decision Rule - with Applications in Public Water Supply

Robust optimization deals with optimization problems under uncertainty. There are many different approaches including adjustable, recoverable, min-max-regret and inverse robustness. In this work, these robustness concepts are compared and combined.
For the first time, affine linear decision rules from adjustable robustness are combined with other robustness concepts to obtain the advantages of different robustness concepts. For solving the resulting optimization problems, an algorithm is presented and its convergence is proven. Furthermore, the applicability of these concepts is demonstrated through an example of optimizing a robust pump operation plan for a drinking water supply system.