In the quantity discount model in Example 12.2, the minimum total annual cost is region 3 is clearly the best. Evidently, the larger unit purchase costs in the other two regions make these two regions unattractive. When would a switch take place? To answer this question, change the model slightly. First, change the fixed cost of ordering to $40. Second, keep the unit cost in region 3 at $26, but change the unit costs in regions 1 and 2 to $26 + 2k and $26 + k, where you can let k vary. (Currently, k is $2.) Use Solver Table with k varied over some appropriate range to see how small k must be before it is optimal to order from region 1 or 2. What region is the optimal ordering quantity in if there is no price break at all (k = 0). How do you reconcile this with your Solver Table findings?

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.