Note---Comments on "A Quantity Discount Pricing Model to Increase Vendor Profits"

Monahan (Monahan, J. P. 1984. A quantity discount pricing model to increase vendor profits. Management Sci. (June) 720--726.) adapted the quantity discount model of inventory theory to the problem of determining an optimal quantity discount schedule from a vendor's point of view, and opened up an important direction of research. However, his one-item, one-customer, one-vendor model is based on several implicit assumptions that must be judged unreasonable. Monahan must account for the vendor's inventory carrying charges and redefine his variable S₂. It is shown that a rational vendor's manufacturing frequency would not be identical to the buyer's ordering frequency if the vendor's manufacturing setup costs are substantially larger than the buyer's ordering costs. A numerical example presented in this note also questions the practical usefulness of Monahan's model even after its theoretical inaccuracies axe corrected. Monahan's model may explain discounts that are a fraction of 1% of the price of an item, but it fails to explain commonly observed magnitudes of quantity discounts, such as 10% of the unit price.