EOQ Model Cost Curves

1
EOQ Model Cost Curves
Annual cost ()
Total Cost curve
D Demand/year Co cost per order Ch Holding
(carrying) cost
Slope 0
Minimum total cost
Carrying Cost ChQ/2
Ordering Cost CoD/Q
Optimal order Q (EOQ)
Order Quantity, Q
Total Costs Carrying Cost Ordering Cost Ct
ChQ/2 CoD/Q
2
Example Basic EOQ

• QUESTION
• The annual demand for a product is 8,000 units.
  The ordering cost is 30 per order. The cost of
  the item is 10 and the carrying cost has been
  calculated at 3 to carry out one item in stock
  for one year. Calculate
• What is the EOQ?
• The numbers of orders to be placed annually, and
• The overall costs.

3
Example Basic EOQ

• ANSWER

D 8,000 units CO 30 Ch 3
4
Example Basic EOQ
QUESTION A local distributor for a national tire
company expects to sell approximately 9,600
steelbelted radial tires of a certain size and
tread design next year. Annual carrying cost is
16 per tire, and ordering cost is 75. The
distributor operates 288 days a year. a. What is
the EOQ? b. How many times per year does the
store reorder? c. What is the length of an order
cycle? d. What is the total annual cost if the
EOQ quantity is ordered?
5
Example Basic EOQ
6
Example Basic EOQ

• Zartex Co. produces fertilizer to sell to
  wholesalers. One raw material calcium nitrate
  is purchased from a nearby supplier at 22.50
  per ton. Zartex estimates it will need 5,750,000
  tons of calcium nitrate next year.
• The annual carrying cost for this material is 40
  of the acquisition cost, and the ordering cost is
  595.
• a) What is the most economical order quantity?
• b) How many orders will be placed per year?
• c) How much time will elapse between orders?

7
Example Basic EOQ

• Economical Order Quantity (EOQ)
• D 5,750,000 tons/year
• Ch .40(22.50) 9.00/ton/year
• Co 595/order
• 27,573.135 tons per order

8
Example Basic EOQ

• Total Annual Stocking Cost (TSC)
• TSC (27,573.135/2)(9.00)
• (5,750,000/27,573.135)(595)
• 124,079.11 124,079.11
• 248,158.22

9
Example Basic EOQ

• Number of Orders Per Year
• D/Q
• 5,750,000/27,573.135
• 208.5 orders/year
• Time Between Orders
• Q/D
• 1/208.5
• .004796 years/order
• .004796(365 days/year) 1.75 days/order

Note This is the inverse of the formula above.
10
Example Basic EOQ
A large bakery buys flour in 25-kg bags. The
bakery uses an average of 4860 bags a year.
Preparing an order and receiving a shipment of
flour involves a cost of 4 per order. Annual
carrying costs are 30/bag.

• Determine the economic order quantity
• What is the average number of bags on hand?
• How many orders per year will there be?
• Compute the total cost of ordering and carrying
  flour
• If annual ordering cost were to increase by 1
  per
• order. How much would that affect the minimum
• total annual cost?

11
Example Basic EOQ

• EOQ v(2(4860)(4)/30 36 bags/order
• Average number of bags on hand 36/2 18
  bags/order
• No 4 860/36 135 orders/year
• TC v(2(4860)(4)(30) 1080/year
• TC v(2(4 860)(5)(30) 1207.48/year
• Increase 1207.48 1 080 127.48/year
• It will affect the total inventory cost to
  increase by 127.48/year.