Adjustable robust optimization: Theory, algorithm and applications

Adjustable robust optimization is a methodology to help decision makers make robust and resilient decisions that extend well into the future. In this thesis, we exploit Fourier-Motzkin elimination to investigate the theories and applications of adjustable robust optimization. As a result, a generic technique is developed to enhance the classical approximation scheme, and applied to several applications, e.g., medical appointment scheduling, lot-sizing on a network, wireless sensor networks, to demonstrate the efficiency and effectiveness of the proposed approach. We further show how to formulate two generic optimization problems, i.e., computing the maximum volume inscribed ellipsoid in a polytopic projection, and finding centered solutions for uncertain linear equations, as adjustable robust optimization problems, and investigate these two problems through the lens of Fourier-Motzkin elimination.