On Robust Optimization of Two-Stage Systems

Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context
of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to sub-optimal second-stage decisions. To overcome this drawback, we propose a sufficient condition on the variability measure to preserve second-stage optimality. Under this condition, a modification of the L-shaped decomposition method solves the robust formulation efficiently.