Question

Company A is selling packing material to the consumer products company B. Company B needs 1.021 km of a certain carton per year. The costs structure is as follows.

q	unit	Price (?) per km
10	km	310.00
50	km	243.00
100	km	230.00
150	km	227.00
200	km	223.00
300	km	222.40

Orders below 10,000 m are not allowed.

The company uses a holding cost rate of 30% per year. An economist has determined the fixed ordering costs at company B and he has arrived at a value of 8 euro per order. Assuming the lowest price (222,4 euro / 1000 m), calculate the optimal order quantity using the EOQ model. Is the assumed price valid under this quantity? Next, determine the optimal order quantity while taking the discount price structure into account.

Answer 1

Part A: Considering lowest cost:

Monthly Demand	A	1021.00	Km
Ordering cost	S	8.00	Euro/order
Holding cost per month	I	30%
Unit price	C	222.4	Euro/km
EOQ	?(2*A*S/C*I)	?(2*1021*8/(0.3*222.4)) = 15.647	Km/order

The Optimal order quantity is 15.647 km, but to purchase at the lowest price of 222.4 per km it is required to purchase at least 300 km per order.

Thus, assumed price is not valid under EOQ quantity.

Part B

For the given problem quantity discount or price-volume range model is applied.

Quantity Discount Model

1. For each price range (C), compute EOQ

2. If EOQ < Minimum quantity for price range, adjust the quantity to Q = Minimum for discount. If the EOQ > Maximum quantity for discount, adjust the quantity to Q = Maximum for discount. If the EOQ is within the range, then adjust Q = EOQ.

3. For each EOQ or adjusted Q, compute Total cost

4. Choose the lowest-cost quantity.

Monthly Demand		A	1021.00	Km
Ordering cost		S	8.00	Euro/order
Holding cost per month		I	30%
Quantity (km)	Unit Price (C) Euro/km	EOQ	Optimal order quantity	Annual Material Cost	Annual Ordering Cost (AOC)	Annual Carrying Cost (ACC)	Annual Inventory cost (AOC + ACC)	Total ($)
		?(2*A*S/C*I)	(Q)	A*C	(A/Q)*S	(Q/2)*H
10 - 49	310	13.254	13.254	$316,510	$616	$616	$1,233	$317,743
50 - 99	243	14.970	50	$248,103	$163	$1,823	$1,986	$250,089
100 - 149	230	15.387	100	$234,830	$82	$3,450	$3,532	$238,362
150 - 199	227	15.488	150	$231,767	$54	$5,108	$5,162	$236,929
200 - 299	223	15.626	200	$227,683	$41	$6,690	$6,731	$234,414
<300	222.4	15.647	300	227070.4	$27	$10,008	$10,035	$237,106

The lowest price is $234,414 for the order quantity of 200 km. thus, discount price for quantity of 200 km provides optimal quantity.