We consider in this paper the coordinated replenishment dynamic lot-sizing problem when quantity discounts are offered. In addition to the coordination required due to the presence of major and minor setup costs, a separate element of coordination made possible by the offer of quantity discounts needs to be considered as well. The mathematical programming formulation for the incremental discount version of the extended problem and a tighter reformulation of the problem based on variable redefinition are provided. These then serve as the basis for the development of a primal-dual based approach that yields a strong lower bound for our problem. This lower bound is then used in a branch and bound scheme to find an optimal solution to the problem. Computational results for this optimal solution procedure are reported in the paper. (C) 2000 John Wiley & Sons, Inc.