Suppose that you are the manager of a production department that uses 1600 boxes of specific parts per year. The supplier quotes you a price of $8.50 per box for an order size of 499 boxes or less, a price of $8.00 per box for orders of 500 to 1499 boxes, and a price of $7.50 per box for an order of 1,500 or more boxes. You assign a holding cost of 25 percent of the price to this inventory. What order quantity would you use if the objective is to minimize total annual costs of holding, purchasing, and ordering? Assume ordering cost is $200/order.

1,500 or more boxes

Explanation:

To calculate which order quantity would minimize total cost, we will support the calculation by using the formulae of Economic Order Quantity (EOQ).

EOQ = √2 x Demand x Ordering Cost / Holding Cost

Order Size 499 or less

EOQ = √2 x 1,600 x 200 / 8.5 x 25%

EOQ = √640,000 / 2.125

EOQ = √301,176

EOQ = 549

Total Cost = 1,600 / 549 x 200 + (549 / 4) x (8.5 x 25%) + 1,600 x 8.5

Total Cost = 583 + 292 + 13,600

Total Cost = $14,475

Order Size 500 to 1,499

EOQ = √2 x 1,600 x 200 / 8 x 25%

EOQ = √640,000 / 2

EOQ = √320,000

EOQ = 566

Total Cost = 1,600 / 500 x 200 + (500 / 2) x (8 x 25%) + 1,600 x 8

Total Cost = 640 + 500 + 12,800

Total Cost = $13,940

Order Size 1,500 or more

EOQ = √2 x 1,600 x 200 / 7.5 x 25%

EOQ = √640,000 / 1.875

EOQ = √341,333

EOQ = 584

Total Cost = 1,600 / 1500 x 200 + (1500 / 2) x (7.5 x 25%) + 1,600 x 7.5

Total Cost = 213 + 1,406 + 12,000

Total Cost = $13,619

Hence, the total cost is minimized at the order quantity of 1,500 or more.