带折扣的多阶段库存系统的优化算法

针对供应商提供数量折扣、需求率随时间变化、周期性检查并补充库存的多阶段库存控制策略，提出一种优化算法．该算法以各时段的累计需求为根节点建立搜索树，从而将带折扣的库存问题转化为典型的动态批量问题，运用动态规划法即可求解．利用该算法可以找出在计划时段内总成本最小的补充策略．用算例说明了该算法的有效性．

Optimal Algorithm for Multi-period Inventory System with Quantity Discount

To optimize milti-period inventory systems, in which quantity discounts are available, demand rates change over time, and checking and replenishments are made periodically, an algorithm was proposed to search control rules. In the algorithm, a search tree with roots of the cumulative demands in the corresponding period is taken as the roots of the search tree, transforming the quantity discount problem into dynamic order quantity (DOQ) problem that is solvable with a dynamic programming algorithm. The proposed algorithm is capable to search the supplemental policy to minimize the cost of the concerned period. The validity of the algorithm was illustrated with an example.