1. EOQ Model Cost Curves Q* D 2 D Co EOQ, Q* = Ch
Annual
cost ($)
Total Cost
curve
Slope = 0
D = Demand/year
Co= cost per order
Ch = Holding
(carrying) cost
Minimum
total cost
Carrying Cost = ChQ/2
Ordering Cost = CoD/Q
Optimal order Q*
(EOQ)
Order Quantity, Q
Average inventory = Q/2
Expected Number of Orders = N D Q*
EOQ, Q* =
2 D Co Ch
Expected Time Between Orders Q* = D
Total Costs = Carrying Cost + Ordering Cost
Ct = ChQ/ 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* C o D h = 2
(8,000) (30) 3
400 units
D = 8,000 units
CO = € 30
Ch = € 3
Number of
orders per
year = D Q *
8,000
400
20 orders
Total Costs = 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 = € 1,200. #

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, tons per order
EOQ = 2(5,750,000)(595)/9.00 #

8. Example: Basic EOQ Total Annual Stocking Cost (TSC)
+ (5,750,000/27, )(595)
= 124, ,079.11
= $248,158.22 #

9. Example: Basic EOQ Number of Orders Per Year = D/Q
= 5,750,000/27,
= orders/year
Time Between Orders
= Q/D
= 1/208.5
= years/order
= (365 days/year) = 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 = √(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 = √(2(4860)(4)(30) = $1080/year
TC = √(2(4 860)(5)(30) = $ /year
Increase = – = $127.48/year
It will affect the total inventory cost to increase by $127.48/year. #