Adjustable Robust Optimization via Fourier-Motzkin Elimination

AbstractWe demonstrate how adjustable robust optimization ARO problems with fixed recourse can be cast 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 broad 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 developed to reformulate ARO problems. This generic reformulation technique enhances the classical approximation scheme via decision rules, and it enables us to solve adjustable optimization problems to optimality. We show via numerical experiments that, for small-sized ARO problems, our novel approach finds the optimal solution. For moderate-or large-sized instances, we eliminate a subset of the adjustable variables, which improves the solutions obtained from linear decision rules.