Quantitative Analysis for Management, 13/e

6.6 Quantity Discount Models

In developing the EOQ model, we assumed that quantity discounts were not available. However, many companies do offer quantity discounts. If such a discount is possible, and all of the other EOQ assumptions are met, it is possible to find the quantity that minimizes the total inventory cost by using the EOQ model and making some adjustments.

When quantity discounts are available, the purchase cost or material cost becomes a relevant cost, as it changes based on the order quantity. The total relevant costs are as follows:

$$\begin{array}{lll}\text{Total}\text{cost}\hfill & =\hfill & \text{Material cost + Ordering cost + Carrying cost}\hfill \\ \text{Total}\text{cost}\hfill & =\hfill & DC+\frac{D}{Q}{C}_o+\frac{Q}{2}{C}_h\hfill \end{array}$$ (6-14)

where

$$\begin{array}{lll}D\hfill & =\hfill & \text{annual demand in units}\hfill \\ C_o\hfill & =\hfill & \text{ordering cost of each order}\hfill \\ C\hfill & =\hfill & \text{cost per unit}\hfill \\ C_h\hfill & =\hfill & \text{holding or carrying cost per unit per year ...}\hfill \end{array}$$