A survey of adjustable robust optimization

Abstract

Static robust optimization (RO) is a methodology to solve mathematical optimization problems with uncertain data. The objective of static RO is to find solutions that are immune to all perturbations of the data in a so-called uncertainty set. RO is popular because it is a computationally tractable methodology and has a wide range of applications in practice. Adjustable robust optimization (ARO), on the other hand, is a branch of RO where some of the decision variables can be adjusted after some portion of the uncertain data reveals itself. ARO generally yields a better objective function value than that in static robust optimization because it gives rise to more flexible adjustable (or wait-and-see) decisions. Additionally, ARO also has many real life applications and is a computationally tractable methodology for many parameterized adjustable decision variables and uncertainty sets. This paper surveys the state-of-the-art literature on applications and theoretical/methodological aspects of ARO. Moreover, it provides a tutorial and a road map to guide researchers and practitioners on how to apply ARO methods, as well as, the advantages and limitations of the associated methods.