Optimization via Benders' Decomposition

In a period when optimization has entered almost every facet of our lives, this thesis is designed to establish an understanding about the rather contemporary optimization technique: Benders' Decomposition. It can be roughly stated as a method that handles problems with complicating variables, which when temporarily fixed, yield a problem much easier to solve. We examine the classical Benders' Decomposition algorithm in greater depth followed by a mathematical defense to verify the correctness, state how the convergence of the algorithm depends on the formulation of the problem, identify its correlation to other well-known decomposition methods for Linear Programming problems, and discuss some real-world examples. We introduce present extensions of the method that allow its application to a wider range of problems. We also present a classification of acceleration strategies which is centered round the key sections of the algorithm. We conclude by illustrating the shortcomings, trends, and potential research directions