An optimal algorithm for the quantity discount problem

The quantity discount problem determines order quantities in a dynamic environment where demand rate changes over time, replenishments are made periodically, and discounts are available for quantity purchases. The undiscounted case, which is known as the dynamic lot-sizing problem, has been studied extensively in the literature. In particular, the algorithm of Wagner and Whitin gives an optimal order policy for the undiscounted problem. However, for the discounted problem, the only optimal algorithm that the authors know of in the literature is the mixed integer programming model presented by Callerman and Whybark, which requires excessive computation time even for problems with only twelve periods. The purpose of this article is to present an efficient algorithm to find an optimal order policy when all-units quantity discounts are available.