Quantity Discount Model

Quantity Discounts

Whenever discounts are offered for bulk purchases, each case should be considered in items of its ultimate cost. A rough and ready formula for deciding such cases can be worked out if, to simplify matters, we assume that the ordering cost is negligible compared to the other factors involved. If one month’s usage of an item is added to the EOQ by bulk purchase, the average inventory cost of the item is increased by half a month’s usage i.e., by A/24 of a year’s usage where A is, as before, the annual consumption value of the item. If a month’s usage is added to the EOQ the average inventory will be increased by mA/24 rupees. The increase in inventory-carrying cost expressed as a fraction of the inventory cost. The reduction in cost offered by the discount must be more than this increase. If x is the reduction (expressed as a fraction) offered per rupee3-worth of material, the annual cost reduction due to bulk discount will be x A rupees.

XA      >          mA1/24

x          >          mI/24

If I is taken as 24 percent or 0.24

x          > m/100

or        100 x   > m

This indicated that bulk purchases can be profitably made if the percent discount offered is greater than the number of month’s usage added to the EOQ.

Example: The price and discount pattern for an item is as follows:

quantity-discount-model

If the monthly usage of the item is 150 and the EOQ is 500, would it be advisable to increase the order quantity to 1000 to take advantage of the bulk discount?

Percent discount if 1000 units are ordered at a time instead of

quantity-discount-model-01

Number of month’s usage added to the EOQ by purchasing 1000 instead of 500 at a

quantity-discount-model-02

As 10.5 are greater than 3.3, order quantity can be raised from 500 to 1000 to take advantage of the discount.

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