This dissertation presents a speed up proposal for the Benders decomposition applied to a more general and compact version (less constraints and variables) of inventory management model, optimized via two-stage stochastic programming, which considers one layer, one item, uncertain demand and control policy (R, S). In order to be possible to consider large scale problems, the L-Shaped traditional method with single cuts and its extended form with multiple cuts were applied. Preliminary computational results showed a substantially better computational performance of the traditional L-Shaped method in comparison to the multi-cut L-Shaped method, even with the first requiring more iterations to converge on optimum solutions. This observation led to the development of a new technique to accelerate the decomposition of Benders and a set of valid inequalities. Numerical experiments show that the proposed approach of combining the elaborate acceleration technique with the developed valid inequalities, provide significant reduction in the computational time required to solve large scale instances.