An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts
研究了当供应商提供数量折扣时，企业如何协调多种产品的补货时间和批量，以最小化总成本。提出了一种基于原始-对偶方法的分支定界算法，能求得问题的最优解。
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. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 686–695, 2000