Adjustable robust optimization via Fourier-Motzkin elimination

We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broader class of ARO problems. A scheme based on a blending of classical FME and a simple Linear Programming technique, that can efficiently remove redundant constraints, is used to reformulate ARO problems. This generic reformulation technique, contrasts with the classical approximation scheme via linear decision rules, enables us to solve adjustable optimization problems to optimality. We show via numerical experiments that, under limited computational resources, for small-size ARO problems our novel approach finds the optimal solution, and for moderate or large-size instances, we successively improve the solutions from linear decision rule type of approximations.