Benders Decomposition

Benders decomposition is a solution method for solving certain large-scale optimization problems. Instead of considering all decision variables and constraints of a large-scale problem simultaneously, Benders decomposition partitions the problem into multiple smaller problems. Since computational difficulty of optimization problems increases significantly with the number of variables and constraints, solving these smaller prob-lems iteratively can be more efficient than solving a single large problem. In this chap-ter, we first formally describe Benders decomposition. We then briefly describe some extensions and generalizations of Benders decomposition. We conclude our chapter by illustrating how the decomposition decomposition works on a problem encountered in Intensity Modulated Radiation Therapy (IMRT) treatment planning and giving a numerical example