A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, … Read more

A Framework for Generalized Benders’ Decomposition and Its Application to Multilevel Optimization

We describe an algorithmic framework generalizing the well-known framework originally introduced by Benders. We apply this framework to several classes of optimization problems that fall under the broad umbrella of multilevel/multistage mixed integer linear optimization problems. The development of the abstract framework and its application to this broad class of problems provides new insights and … Read more