The Decisions to be Made
Economic Order
Quantity
The Definition of EOQ
EOQ, or Economic Order
Quantity, is defined as the
optimal quantity of orders that
minimizes total variable costs
required to order and hold
inventory.
One of the most frequent decisions
faced by operations managers is
“how much” or “how many” of
something to make or buy in order to
satisfy external or internal
requirements for some item.
Many times, this decision is made with
little or no thought about its cost
consequences.
The basic model makes the
following assumptions:

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Demand is uniform, constant and
continuous over time;
The leadtime is constant;
There is no limit on order size due either
to stores capacity;
The cost of placing an order is
independent of size of order;
The cost of holding a unit of stock does
not depend on the quantity in stock;
Exactly the same quantity is ordered
each time that a purchase is made.
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How to use EOQ in your
organization
Costs

How much inventory
should we order each
month?
EOQ accounts for 3 types of costs:



The EOQ tool can be used to model the
amount of inventory that we should order.
Inventory Holding Costs
Reasonably Typical Profile
Category
% of
Inventory Value
Housing (building) cost
6%
Material handling costs
3%
Labor cost
3%
Inventory investment costs
11%
Pilferage, scrap, & obsolescence 3%
Total holding cost
26%
Unit Cost: the cost of the units
themselves, assumed to be fixed,
regardless of the number of units
ordered
Inventory-Holding Cost: the cost of
holding units in inventory
Fixed order cost: represents all the
costs associated with placing an order
excluding the cost of the units
themselves (any administrative costs of
placing and/or receiving an order)
EOQ Model
Annual Cost
Holding Cost
Order Quantity
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Why Order Cost Decreases

EOQ Model
Cost is spread over more units
Example: You need 1000 microwave ovens
1 Order (Postage $ 0.35)
Annual Cost
1000 Orders (Postage $350)
Purchase Order
Description Qty.
Microwave 1000
Holding Cost
Purchase Order
Purchase
Order
Purchase
Order
Description
Qty.
Purchase
Order
Description
Qty.
Description
Qty.
Microwave
Description
Qty.11
Microwave
Microwave
Microwave
11
Order Cost
Order
quantity
Order Quantity
How EOQ Works
EOQ Model
The Total Cost Formula
Annual Cost
Total Cost Curve
Total Cost = Purchase Cost
Holding Cost
Order Cost
Optimal
Order Quantity (Q*)
+ Order Cost
+ Holding Cost
Order Quantity
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How EOQ Works
The Total Cost Formula
How EOQ Works
The Total Cost Formula
This represents the
unchanging fixed costs
This represents the
variable order costs
P = Purchase cost per unit
R = Annual usage in units
C = Cost per order event (not per unit)
Q = The number of units ordered
P = Purchase cost per unit
R = Annual usage in units
How EOQ Works
How EOQ Works
The EOQ Formula
The Total Cost Formula
Total
Cost
Formula
This represents the
variable holding costs
Taking the derivative of both sides of the equation and
setting equal to zero to find the minimum value of the
function, one obtains:
P = Purchase cost per unit
R = Annual usage in units
C = Cost per order event (not per unit)
Q = The number of units ordered
F = Holding cost factor
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How EOQ Works
How EOQ Works
The result of differentiation
The Economic Order Quantity
How EOQ Works
P = Purchase cost per unit
R = Annual usage in units
C = Cost per order event (not per unit)
F = Holding cost factor
How EOQ Works
The graphic representation of the EOQ equation
Expected Number Orders = N = R/Q*
Expected time between orders:
T=
Working days / Year
N
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Real Life Example:
Real Life Example:
Real Life Example:
Real Life Example:
Next let’s identify the correct
variables…
First, Recall
the EOQ
Equation:
P = Purchase cost per unit
R = Annual usage in units
C = Cost per order event
F = Holding cost factor
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Real Life Example:
Forecasted
Amount
Real Life Example:
Cost per
Unit
Real Life Example:
Ordering
Costs
Real Life Example:
Holding
Cost Factor
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Real Life Example:
Real Life Example:
R = Annual demand
R = 5200
C = Fixed ordering cost
C = $10 per order
P = Cost per case
P = $2
F = Holding Cost Factor
F = 20% of value of inventory per year
Real Life Example:
Wrapping It Up
EOQ, or Economic Order Quantity,
is defined as the optimal quantity of
orders that minimizes total variable
costs required to order and hold
inventory.
EOQ =
2 (10) (5200)
(2 )(.20)
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Conclusion
EOQ Example
You’re a buyer for SaveMart.
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EOQ is useful for minor stock
items of low values with known
steady prices, demands and
supply lead times;
Where there is demand variability,
such as seasonality, EOQ can still
be calculated but using shorter
time period.
SaveMart EOQ
R=
C=
P=
F=
H=
H=
1000
$100
$ 78
40%
PxF
$31.20
EOQ 
SaveMart needs 1000 coffee makers
per year. The cost of each coffee
maker is $78. Ordering cost is $100
per order. Carrying cost is 40% of per
unit cost. Lead time is 5 days.
SaveMart is open 365 days/yr.
What is the optimal order quantity?
Homework
2 1000  $100
$31.20
Calculate the EOQ of „A” materials if:
 The quartal demand for material "A" is
1.500 pieces
 The purchase price per unit is $80
 The rate of storage cost is of 20% of the
purchase price per unit
 Fixed costs are $50 per order
How many times should we order to meet
the annual demand for material "A"?
EOQ = 80 coffeemakers
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