A Review on Decomposition Methods in Engineering Problems

Article history: Received 16 November 2013 Received in revised form 18 Decomposition refers to the strategy of breaking up a large, difficult-to-solve problem into two or more smaller, easier-to-solve problems, such that the solution to the decomposed problems can be used to obtain the solution to the original problem. In the last years, decomposition techniques such as Benders decomposition are used efficiently and extensively to solve large scale optimization problems (particularly, in mixed integer variable optimization problems such as unit commitment and short term hydrothermal coordination). This paper reviews two basic decomposition methods (primal and dual decomposition) and used them to construct Dantzing-wolfe and Benders decomposition techniques.