In the quantity discount model in Example 12.2, the minimum total annual cost is obtained by ordering enough to achieve the smallest unit purchasing cost. Evidently, the larger unit purchasing costs...

In the quantity discount model in Example 12.2, the minimum total annual cost is obtained by ordering enough to achieve the smallest unit purchasing cost. Evidently, the larger unit purchasing costs for smaller order quantities make them unattractive. Could an order quantity below 400 ever be best? Could an order quantity between 500 and 800 ever be best? To answer these questions, assume that there is no price break at all. Specifically, assume that the unit purchase cost is always $26. What is the optimal order quantity with this assumption? How does this help answer the preceding questions?

EXAMPLE 12.2 ORDERING THUMB DRIVES WITH QUANTITY DISCOUNTS AT AJ TAYLOR

The accounting firm of AJ Taylor buys USB thumb drives from a distributor of PC supplies. The firm uses approximately 5000 drives per year at a fairly constant rate. The distributor offers the following quantity discount. If fewer than 500 drives are ordered, the cost per drive is $30. If at least 500 but fewer than 800 drives are ordered, the cost per drive is $28. If at least 800 drives are ordered, the cost per drive is $26. The fixed cost of placing an order is $100. The company’s cost of capital is 10% per year, and there is no storage cost. The firm wants to find the optimal order quantity and the corresponding total annual cost.

Objective To find the order quantity that minimizes the total annual cost of ordering in the face of quantity discounts.