Slides calculate economic order quantity

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 © Dale R... Batch

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

© Dale R Geiger 2011 2

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.

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 per unit =

•  

© Dale R Geiger 2011 4

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

• 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

•  

© Dale R Geiger 2011 8

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

• The full equation is:

• Or, first divide Batch $ Cost by # Units in batch

to get Batch cost per unit, then multiply by # units demanded

•  

© Dale R Geiger 2011 10

Batch Costs

• The full equation is:

• 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

© Dale R Geiger 2011 12

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

© Dale R Geiger 2011 14

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?

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

•  

© Dale R Geiger 2011 16

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

•  

Graph of Purchasing Cost

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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particular task in one large group?

• What else should be considered?

Check on Learning

• How would you describe the graph of batch

cost?

© Dale R Geiger 2011 20

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

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”?

© Dale R Geiger 2011 22

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

© Dale R Geiger 2011 24

Graph of Inventory Assumption

Graph of Inventory Assumption

Units Consumed or Sold uniformly until all Inventory is gone

25.00

© Dale R Geiger 2011 26

Graph of Inventory Assumption

Average Inventory is 50/2 or 25 Units

Average Inventory

25.00

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?

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

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?

Graph of Holding Cost

X-Axis = Number of units per purchase order

As number of units per purchase order increases, holding cost increases

When quantity per purchase order is 10

Average Inventory = 5 and holding cost is $250

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

When quantity per purchase order is 100

Average Inventory = 50 and purchasing cost is $2,500

© Dale R Geiger 2011 32

Optimizing Order Quantity

• Total Costs Related to Order Quantity =

Purchasing Cost + Holding Cost

• What is Total Cost when Quantity per order is

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

Optimizing Order Quantity

• Total Costs Related to Order Quantity =

Purchasing Cost + Holding Cost

• What is Total Cost when Quantity per order is

Graph of Total Costs

Total Cost is minimized where Purchasing Cost = Holding Cost

Total Cost is minimized where Purchasing Cost = Holding Cost

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

© Dale R Geiger 2011 38

Optimizing Order Quantity

• The relationship is well-documented and is

captured in the “Economic Order Quantity”

Calculating EOQ

• Demand is 200 units

• Purchasing Cost is $250 per Order

• Holding Cost is $50 per Unit

EOQ = EOQ = = approx 45 units

•  

© Dale R Geiger 2011 40

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

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Batch Quantity Spreadsheet

Practical Exercise

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