All‐Units Discounts for Standard Container Sizes

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Abstract
Some vendors offer their products to a purchaser in various container sizes. Normally, vendors will offer larger all‐units discounts on larger container sizes. Two algorithms have been developed in this paper to solve for the optimal number of each container size and the order quantity for the deterministic economic order quantity (EOQ) situation. The first algorithm, based in part on the dynamic programming solution to knapsack problems, solves the general case. The second algorithm, based in part on the dominance relations inherent in the pricing schedule, solves the more restricted case in which the purchaser is forced to accept the discount in the following manner. An order must be filled with containers of successively smaller sizes, beginning with the largest size. The purchaser is forced to accept the largest discount first, then the next largest, and so on.