Question

Suppose that the annual demand for a component is approximately 56,000 units. The company orders the component from a supplier who has offered the following quantity discount schedule.

Order Quantity	0-999	1,000-1,499	1,500-3,499	3,500or more
Price Per Unit	$33	$31	$29	$27

If the company's carrying charge is 25% of the item's price and the cost per order is $330, determine the order quantity that would minimize the total related inventory costs for this component.

The company's decision would be to order ____ Units.

The total annualized ordering costs for this quantity is____

Answer 1

We have the following values:

DEMAND = 56000

HOLDING COST = 25%

ORDERING COST = 330

EOQ = SQRT(2DS/H)

Now to find the optimal order quantity, we need to adjust the EOQ value to fit the order quantity upon which the discounts are based:

If the EOQ value lies between the minimum and maximum quantity for a particular price, the value of the EOQ is used. If the EOQ is smaller than the quantity, the minimum quantity is used and if the value of the EOQ is higher than the quantity, the maximum quantity value for a particular price is used. Now. based on the above assumptions, we can calculate individual values for EOQ since the holding cost is variable and adjust them according to the quantity which represents the adjusted Q value

TOTAL COST OF INVENTORY = DEMAND * PRICE PER UNIT + ((ADJUSTED Q / 2) * HOLDING COST) + ((DEMAND / ADJUSTED Q) * ORDERING COST

The optimal order quantity is based on the lowest total inventory cost for a particular unit price:

The answer is as follows:

OPTIMAL ORDER QUANTITY = 3500

TOTAL COST OF INVENTORY = 1529093

Here are the intermediate calculations:

NO.	FROM QUAN	TO QUAN	PRICE	HOLDING	EOQ	ADJUSTED Q	TOTAL COST OF INVENTORY
1	0	999	33	8.25	2117	999	1870619.373
2	1000	1499	31	7.75	2184	1499	1754136.844
3	1500	3499	29	7.25	2258	2258	1640369.484
4	3500	MORE	27	6.75	2340	3500	1529092.5