ON THE BENEFITS OF DISTRIBUTIONAL INFORMATION IN ROBUST LINEAR OPTIMIZATION 1

Robust linear optimization techniques produce formulations (not necessarily linear) that guarantee the feasibility of a solution for all realizations of the uncertain data. A recent methodology developed by Bertsimas and Sim (2004) maintains the linearity of the formulation and is able to strike a balance between the conservatism and quality of a solution. In this work we adopt their robust model and demonstrate how to use distributional information on the uncertain data to improve solutions to the robust model. We obtain results when full distributions are available, as well as, when only first and second moments are known. We apply our methodology to a stochastic inventory control problem with quality of service constraints.