Economic Order Quantity
EOQ is the optimal size of orders
needed to replenish _____________
Variables include:
Ch = per unit cost of Holding items in inventory
Co = cost of placing one Order
D = Demand per year
Holding or Carrying Cost
Holding (or Carrying) Costs consists of
the costs of keeping items in ____________
including interest as well as the costs
of maintaining a warehouse such as
rent, utilities, insurance, wages, etc.
Holding (or Carrying) Costs must be
expressed as a cost per unit, but often
textbook problems state Holding Costs
as a percentage of the purchase cost
THEN: Ch = % * Purchase Price Per Item
Inventory Costs
Order Costs is the cost of placing a
single ______________, such as paperwork
costs, material handling costs, shipping
and handling costs, etc.
Demand is the ___________ of units
that will be used during a year.
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Annual Holding Cost
Assume that new ________ arrive just as the
inventory runs out
Lowest level of inventory will be zero just
before the order is delivered
Highest level of inventory will be the order
quantity immediately after the order arrives
The average number of units in inventory =
(zero + order quantity) ÷ two
annual holding costs = Ch * (Q+0)÷2
any number + zero = just the number
annual holding costs = Ch * Q÷2
Annual Ordering Cost
Number of orders placed will equal the
demand divided by the ______ of the orders
Number of Orders = D ÷ Q
Annual Ordering Costs = C0 *(D ÷ Q)
Annual Holding Cost
Cost
When the size of each
order increases
then more items must
be kept in ____________
Total Annual Holding Costs
will increase
Order
Quantity
2
Annual Order Cost
Cost
When the size of each
order increases
then the number of orders decrease
So the Total Order Costs will
decrease with _________ quantities
Order
Quantity
Inventory Costs
Cost
Total Inventory Cost equals
Annual Holding Costs
plus Annual Ordering __________
Lowest Total Inventory Costs
is where the two lines cross
Holding Costs
Order Costs
Order
Quantity
Least Annual Inventory Costs
Annual Ordering Costs = C0 * D÷Q
Annual Holding Costs
= Ch * Q÷2
Lines cross when the two ___________ equal each other
Ch * Q÷2
=
C0 * D÷Q
3
EOQ is where the two costs
are equal (solve for Q)
Annual Holding Costs = Annual Order __________
Ch cancels out
Ch * Q
Ch * 2
=
C0 * D
Q * Ch
Divide both sides by Ch
2 cancels out
2*
Q = Co * D
*2
2
Q * Ch
Multiply both sides by 2
Q * Q = 2 * Co * D * Q
Q cancels out
Q * Ch
Multiply both sides by Q
Q2 = 2 * Co * D ÷ Ch
Then take the Square _______
of both sides of the equation
 Q2 =  2 * Co * D ÷ Ch
Square root of Q2 = Q
Q =
 2 * Co * D ÷ Ch
Q = Economic Order Quantity
Example
Demand equals 10,000 units per year
Annual Holding Costs equals $2 per unit
Order ________ equals $100 per order
√ 2 * D * C0 ÷ Ch = Q
√ 2 * 10,000 * 100 ÷ 2 = Q
√ 1,000,000 = Q
1,000 = Q
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Annual Inventory _________
EOQ = 1,000 units
Average Inventory = (0 + EOQ) ÷ 2
Average Inventory = (0 + 1,000) ÷ 2
Annual Holding Costs = Avg Inv * Ch
Annual Holding Costs = 500 * $2 per unit
Annual Holding Costs = $1,000
Annual number of orders = Demand ÷ EOQ
Annual Order Costs = # of orders * Order Cost
Annual Order Costs = 10,000÷1,000 * $100
Annual Order Costs = $1,000
Annual Inventory _________
EOQ = 1,000 units
Annual Holding Costs = $1,000
Annual Order Costs
= $1,000
Annual Holding Costs = Annual Order Costs
Economic Order Quantity
EOQ is the optimal size for ___________
EOQ = √ 2 * D * C0 ÷ Ch
Average Inventory = EOQ ÷ 2
Annual Holding Costs = Avg Inv * Unit Holding Cost
Annual number of orders = Demand ÷ EOQ
Annual Ordering Costs = # of Orders * Order Costs
Total Annual Inventory Costs =
Annual Holding Costs plus Annual Order Costs
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