Calculate Economic Order
Quantity
Intermediate Cost Analysis
and Management
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What do you think?
Corporal O’Reilly, the supply clerk, knows that it
costs the Army money to generate a purchase
order. To save money he proposes ordering the
five years’ worth of ammunition at once.
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Terminal Learning Objective
• Action: Calculate Economic Order Quantity for
Various Situations
• Condition: You are training to become an ACE
with access to ICAM course handouts, readings,
and spreadsheet tools and awareness of
Operational Environment (OE)/Contemporary
Operational Environment (COE) variables and
actors
• Standard: With at least 80% accuracy:
• Describe the concept of economic order quantity
• Identify the key variables in the EOQ calculation
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Batch Quantity Concepts
• Certain costs are fixed on a per-batch basis
• Setting up machinery to run a particular product
• Purchasing cost
• Training cost
• We call these “Batch Costs”
• More units in a batch means lower batch cost
per unit
$Batch Cost
Batch cost per unit =
#Units in batch
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Batch Cost Assumptions
• Annual demand for units produced in batches
is known
• Every batch is the same size
• i.e. same quantity of units produced
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Batch Costs
• Batch Cost =
Batch Cost per Unit * # Units Demanded
-or-
$Batch Cost
* #Units Demanded
#Units in batch
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Batch Costs
• Another way of thinking of Batch costs is:
# of Batches * Cost per Batch
-or#Units Demanded
* Batch $Cost
#Units in Batch
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Batch Costs
• The full equation is:
# Units Demanded ∗ Batch $ Cost
# Units in Batch
• First divide # units demanded by # units in
batch to get # of batches, then multiply by
Batch $ Cost
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Batch Costs
• The full equation is:
# Units Demanded ∗ Batch $ Cost
# Units in Batch
• First divide # units demanded by # units in
batch to get # of batches, then multiply by
Batch $ Cost
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Batch Costs
• The full equation is:
# Units Demanded ∗ Batch $ Cost
# Units in Batch
• Or, first divide Batch $ Cost by # Units in batch
to get Batch cost per unit, then multiply by #
units demanded
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Batch Costs
• The full equation is:
# Units Demanded ∗ Batch $ Cost
# Units in Batch
• Or, first divide Batch $ Cost by # Units in batch
to get Batch cost per unit, then multiply by #
units demanded
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Batch Costs
• Regardless of how you look at it:
• More units in a batch mean fewer batches
• Fewer batches mean lower Batch costs
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Learning Check
• How does batch cost per unit change as batch
size increases?
• What are the key assumptions in batch
quantity tradeoffs?
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Batch Cost Example
• Purchasing supplies is a common example of a
Batch cost
• Each purchase order issued costs the
organization $250
• Demand for supplies is 200 units
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Batch Cost Example
• How much is purchasing cost if a separate
purchase order is issued for each unit of
supplies?
200 purchase orders * $250/ purchase order =
$50,000
• How much is purchasing cost if all 200 units
are purchased using a single purchase order?
1 purchase order * $250/ purchase order = $250
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Batch Cost Example
• How much is purchasing cost if a separate
purchase order is issued for each unit of
supplies?
$250
200 purchase orders *
= $50,000
purchase order
• How much is purchasing cost if all 200 units
are purchased using a single purchase order?
1 purchase order * $250/ purchase order = $250
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Batch Cost Example
• How much is purchasing cost if a separate
purchase order is issued for each unit of
supplies?
$250
200 purchase orders *
= $50,000
purchase order
• How much is purchasing cost if all 200 units
are purchased using a single purchase order?
$250
1 purchase order *
= $250
purchase order
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Graph of Purchasing Cost
Purchasing Cost
$ 5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
5000
When quantity per purchase order is 10,
twenty purchase orders are issued and
purchasing cost is $5000
When quantity per purchase order is 100,
two purchase orders are issued and
purchasing cost is $500
500
0 10
50
100
150
X-Axis = Number of units per purchase order or batch
As number of units per PO or batch increases, purchasing cost decreases
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Questions to Consider
• Using only this information for your decision,
how many units should be ordered per
purchase order?
• Similarly, what savings might be achieved by
training all of the soldiers needed for a
particular task in one large group?
• What else should be considered?
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Learning Check
• How would you describe the graph of batch
cost?
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Batch Quantity Concepts
• Certain costs increase as quantity per
purchase order increases
• Inventory ties up cash and must be stored and
maintained
• Spoilage and obsolescence can occur
• Time value of money – cash paid now is worth
more than cash paid later
• “Just in Time” ordering minimizes these
“Holding Costs”
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Questions to Consider
• What might be the “holding costs” involved
with training all of the soldiers required for a
particular task in one large group or “batch”?
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Holding Cost Assumptions
• Annual Holding Cost is linear or variable on a
per-unit basis
• Units produced or purchased in batches are
consumed or sold uniformly throughout the
period
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Holding Costs
• Holding cost =
$Holding Cost/Unit * Avg. #Units in Inventory
• Average #Units in Inventory =
#Units per Purchase Order/2
• Assumes Inventory is consumed uniformly
throughout the year
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Graph of Inventory Assumption
50 Units produced or
60.00
purchased
per batch
Inventory Level
50.00
40.00
30.00
20.00
10.00
0.00
X axis represents time
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Graph of Inventory Assumption
60.00
Inventory Level
50.00
40.00
30.00
25.00
20.00
10.00
0.00
Units Consumed or Sold
uniformly until all
Inventory is gone
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Graph of Inventory Assumption
60.00
Inventory Level
50.00
Average Inventory
is 50/2 or 25 Units
40.00
30.00
25.00
Average Inventory
20.00
10.00
0.00
X axis represents time
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Learning Check
• What are the underlying assumptions related
to holding costs?
• How is average inventory calculated?
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Holding Cost Example
• Annual holding cost for supplies is $50 per unit
• What is holding cost if each unit of supplies is
purchased on its own purchase order?
• Average inventory = 1 unit/2 or ½ unit
• ½ unit * $50/unit = $25
• What is holding cost if all 200 units of supplies
are purchased on one purchase order?
• Average inventory = 200 units/ 2 or 100 units
• 100 units * $50/unit = $5,000
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Holding Cost Example
• Annual holding cost for supplies is $50 per unit
• What is holding cost if each unit of supplies is
purchased on its own purchase order?
• Average inventory = 1 unit/2 or ½ unit
• ½ unit * $50/unit = $25
• What is holding cost if all 200 units of supplies
are purchased on one purchase order?
• Average inventory = 200 units/ 2 or 100 units
• 100 units * $50/unit = $5,000
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Holding Cost Example
• Annual holding cost for supplies is $50 per unit
• What is holding cost if each unit of supplies is
purchased on its own purchase order?
• Average inventory = 1 unit/2 or ½ unit
• ½ unit * $50/unit = $25
• What is holding cost if all 200 units of supplies
are purchased on one purchase order?
• Average inventory = 200 units/ 2 or 100 units
• 100 units * $50/unit = $5,000
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Graph of Holding Cost
Holding Cost
$ 5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
When quantity per purchase order is 10
Average Inventory = 5 and
holding cost is $250
When quantity per purchase order is 100
Average Inventory = 50 and
purchasing cost is $2,500
1
50
100
150
X-Axis = Number of units per purchase order
As number of units per purchase order increases, holding cost increases
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Learning Check
• How does holding cost change as batch
quantity changes?
• How is holding cost represented on the graph?
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Optimizing Order Quantity
• Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
• What is Total Cost when Quantity per order is
10 units?
5000 + 250 = 5250
• What is Total Cost when Quantity per order is
100 units?
500 + 2500 = 3000
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Optimizing Order Quantity
• Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
• What is Total Cost when Quantity per order is
10 units?
5000 + 250 = 5250
• What is Total Cost when Quantity per order is
100 units?
500 + 2500 = 3000
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Optimizing Order Quantity
• Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
• What is Total Cost when Quantity per order is
10 units?
5000 + 250 = 5250
• What is Total Cost when Quantity per order is
100 units?
500 + 2500 = 3000
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Graph of Total Costs
5000
4500
Total Cost is minimized where
Purchasing Cost = Holding Cost
4000
3500
3000
Purchasing Cost
2500
Holding Costs
2000
Total Cost
1500
1000
500
0
0
50
≈45
100
150
200
X-Axis = Order quantity in units
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Optimizing Order Quantity
• Total Cost is minimized at the order quantity
where Holding Cost = Purchasing Cost
• Computation of this “Indifference Point”
requires calculus beyond the scope of this
course
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Optimizing Order Quantity
• The relationship is well-documented and is
captured in the “Economic Order Quantity”
(EOQ) Formula:
2dp
EOQ =
h
d = Demand in units
p = cost per Purchase Order
h = Holding cost per unit
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Calculating EOQ
• Demand is 200 units
• Purchasing Cost is $250 per Order
• Holding Cost is $50 per Unit
2dp
EOQ =
h
2(200)(250)
EOQ =
= approx. 45 units
50
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Practical Exercise
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Batch Quantity Spreadsheet
Enter batch cost, holding cost, and
demand into the spreadsheet to
generate the graph of total cost
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Practical Exercise
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