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

TL;DR

This paper introduces a generalized framework for Benders' decomposition applicable to multilevel and multistage mixed integer linear optimization problems, offering new insights into duality and value functions.

Contribution

It extends Benders' decomposition to a broader class of multilevel optimization problems, providing a unified approach and deeper theoretical understanding.

Findings

Framework successfully reformulates complex multilevel problems

Application yields improved solution strategies

Provides new theoretical insights into duality and value functions

Abstract

We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of optimization problems that fall under the umbrella of multilevel/multistage mixed integer linear optimization problems. The application of this abstract framework to this broad class of problems provides new insights and a broader interpretation of the core ideas, especially as they relate to duality and the value functions of optimization problems that arise in this context.