calculate economic order quantity © dale r. geiger 20111

© Dale R. Geiger 2011 1

Calculate Economic Order Quantity

Principles of Cost Analysis and Management


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.


Terminal Learning Objective

• Action: Calculate Economic Order Quantity For Various Situations

• Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors.

• Standard: With at least 80% accuracy:1. Describe the concept of economic order quantity2. Identify the key variables in the EOQ calculation


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 unitBatch cost per unit =


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


Batch Costs

• Batch Cost = Batch Cost per Unit * # Units Demanded

-or- * #Units Demanded


Batch Costs

• Another way of thinking of Batch costs is: # of Batches * Cost per Batch

-or-* Batch $Cost


Batch Costs

• The full equation is:

• First divide # units demanded by # units in batch to get # of batches, then multiply by Batch $ Cost


Batch Costs


• First divide # units demanded by # units in batch to get # of batches, then multiply by Batch $ Cost


Batch Costs


• Or, first divide Batch $ Cost by # Units in batch to get Batch cost per unit, then multiply by # units demanded


Batch Costs

• Regardless of how you look at it:• More units in a batch mean fewer batches• Fewer batches mean lower Batch costs


Check on Learning

• How does batch cost per unit change as batch size increases?

• What are the key assumptions in batch quantity tradeoffs?


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


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


Batch Cost Example

• How much is purchasing cost if a separate purchase order is issued for each unit of supplies?200 purchase orders * = $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


Batch Cost Example

• How much is purchasing cost if a separate purchase order is issued for each unit of supplies?200 purchase orders * = $50,000

• How much is purchasing cost if all 200 units are purchased using a single purchase order?1 purchase order * = $250

18

Graph of Purchasing Cost

0 20 40 60 80 100 120 140 160 180 2000

500100015002000250030003500400045005000 5000

500

Purchasing CostWhen 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

10

$

X-Axis = Number of units per purchase order or batchAs number of units per PO or batch increases, purchasing cost decreases

© Dale R. Geiger 2011


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?


Check on Learning

• How would you describe the graph of batch cost?


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”


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”?


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


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

25

Graph of Inventory Assumption

0.00

10.00

20.00

30.00

40.00

50.00

60.00Inventory Level

50 Units produced or purchased per batch

X axis represents time


26


0.00

10.00

20.00

30.00

40.00

50.00


Units Consumed or Sold uniformly until all Inventory is gone

25.00


27


0.00

10.00

20.00

30.00

40.00

50.00


Average Inventory is 50/2 or 25 Units

Average Inventory25.00

X axis represents time



Check on Learning

• What are the underlying assumptions related to holding costs?

• How is average inventory calculated?


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

32

Graph of Holding Cost

1 50 100 150 2000

500100015002000250030003500400045005000

Holding Cost$

X-Axis = Number of units per purchase orderAs number of units per purchase order increases, holding cost increases

When quantity per purchase order is 10Average Inventory = 5 and

holding cost is $250

When quantity per purchase order is 100 Average Inventory = 50 and

purchasing cost is $2,500



Check on Learning

• How does holding cost change as batch quantity changes?

• How is holding cost represented on the graph?


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






100 units?500 + 2500 = 3000


Graph of Total Costs

0 20 40 60 80 100 120 140 160 180 2000

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Purchasing CostHolding CostsTotal Cost

≈45 X-Axis = Order quantity in units

Total Cost is minimized wherePurchasing Cost = Holding Cost



• 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



• The relationship is well-documented and is captured in the “Economic Order Quantity” (EOQ) Formula:

EOQ = d = Demand in units

p = cost per Purchase Orderh = Holding cost per unit


Calculating EOQ

• Demand is 200 units• Purchasing Cost is $250 per Order• Holding Cost is $50 per Unit

EOQ = EOQ = = approx. 45 units


Check on Learning

• What are the three variables used in the Economic Order Quantity formula?

• How will EOQ change if holding cost per unit increases while all other variables remain the same?


Practical Exercise


Batch Quantity Spreadsheet

Enter batch cost, holding cost, and demand into the spreadsheet to generate the graph of total cost


Practical Exercise

calculate economic order quantity © dale r. geiger 20111

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