EOQ Model Cost Curves
Annual
cost ($)
Slope = 0
Minimum
total cost
Total Cost
curve
Carrying Cost = ChQ/2
D = Demand/year
Co= cost per order
Ch = Holding
(carrying) cost
Ordering Cost = CoD/Q
Optimal
order Q*
(EOQ)
EOQ, Q* =
2 D Co
Ch
Total Costs
Ct
Order Quantity, Q
Average inventory = Q/2
D
Expected Number of Orders = N = *
Q
Expected Time Between Orders
= Carrying Cost + Ordering Cost
=
ChQ/2
+
CoD/Q
=
Q*
D
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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:
a.What is the EOQ?
b.The numbers of orders to be placed annually, and
c.The overall costs.
2
Example: Basic EOQ
ANSWER
D = 8,000 units
CO = € 30
Ch = € 3
Q*
=
2CoD
Ch
=
2 (8,000) (30)
3
= 400 units
Number of orders per year =
Total Costs
D
Q*
=
8,000
= 20 orders
400
= Carrying Cost + Ordering Cost
Holding Costs = Average quantity in stock x Cost of holding item for 1 year
= 400/2 x 3 = € 600
Ordering Costs = Cost of ordering x Number of orders
= 30 x 20 = € 600
therefore Total Costs = € 600 + € 600 = € 1,200.
3
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?
4
Example: Basic EOQ
5
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?
6
Example: Basic EOQ
• Economical Order Quantity (EOQ)
D = 5,750,000 tons/year
Ch = .40(22.50) = $9.00/ton/year
Co = $595/order
EOQ =
2(5,750,000)(595)/9.00
= 27,573.135 tons per order
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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
8
Example: Basic EOQ
• Number of Orders Per Year
= D/Q
= 5,750,000/27,573.135
= 208.5 orders/year
• Time Between Orders Note: This is the inverse
of the formula above.
= Q/D
= 1/208.5
= .004796 years/order
= .004796(365 days/year) = 1.75 days/order
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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?
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Example: Basic EOQ
a. EOQ = √(2(4860)(4)/30 = 36 bags/order
b. Average number of bags on hand = 36/2 = 18
bags/order
c. No = 4 860/36 = 135 orders/year
d. TC = √(2(4860)(4)(30) = $1080/year
e. TC = √(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.
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