Abstract: 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 algorithmwas 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 algorithmwas illustrated with an example.