Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by many researchers. Considering the quantity discount in goods’ purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In this study, stochastic dynamic lot sizing problem with considering the quantity discount is defined and formulated. Since the considered model is mixed integer non-linear programing, piecewise linear approximation is also presented. In order to solve the mixed integer non-linear programing, two approaches are presented. The main solving approach is using a branch and bound algorithm (B am). Each node in the branch and bound algorithm, is a mixed integer non-linear programming roblem which is solved based on dynamic programming (DP). In each stage in this dynamic programming, there is a sub-problem which can be solved with two methods: lagrangian relaxation (LR) and active set method (AS). The numeric results found in this study indicate that the proposed algorithms, B am_DP_AS and B am_DP_LR solve the problem faster than the mathematical solution using the commercial software GAMS. Between the two algorithms, B am_DP_AS algorithm can reach the optimal solution with less time. Moreover, the proposed algorithms for the two discount levels are also compared with the approximate solution in mentioned software. The results indicate that B am_DP_AS algorithm for 16 periods not only can reach to the exact solution, it consumes less time in contrast to the approximate model.