Latest Advances on Benders Decomposition

Operations research and mathematical programming together with information science and technology are tools used to solve various problems in the modern economic environment. This chapter addresses the Benders decomposition method, which is used for the solution of problems of operations research. This method, applied to certain large-scale mathematical problems, can make their solution feasible (if they cannot be solved with another procedure) or can accelerate the solution process in terms of CPU time. The authors provide a thorough presentation of how the decomposition of a problem is made and the Benders algorithm is applied for its solution. The main purpose of this chapter is to analyze the recent studies that address the method's weaknesses and accelerate its application for the faster solution of mathematical problems. A large number of papers is presented and the contribution of each one of them to the improvement of the method is described.