The single quantity-discount problem under ROI maximization

This paper extends the all-units quantity-discount pricing model to consider both parties, the buyer and the seller, as maximizers of their respective returns on their investment in inventory. Such characterization reflects more accurately the reality of some business concerns, such as retailers, with a small investment base, but with inventories as a large fractions of total assets. The model produces an upper limit on the quantity the buyer may be willing to purchase and a lower limit on the amount the vendor is willing to sell, for a given discount rate and an upper limit on the possible discount rate. The end result is a range of feasibility within which the parties may negotiate as to the desired order quantity and discount levels and still be both better off than under the pre-discount policy. A numerical example is included to illustrate the computational procedure.