1. Calculate Economic Order Quantity
Principles of Cost Analysis and Management

2. 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.

3. Terminal Learning Objective
Action: Calculate Economic Order Quantity
Condition:  FM Leaders in a classroom environment working as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy, you must:
Determine Batch Quantity Concepts
Apply Batch Cost Example
Applying Holding Cost Example
Optimizing Order Quantity

4. Determine Batch Quantity Concepts

5. 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

6. Batch Costs

7. Batch Costs (Cont.)

8. Batch Costs (Cont.)

9. Batch Costs (Cont.)

10. Batch Costs (Cont.)

11. Batch Costs (Cont.)

12. Batch Costs (Cont.) Regardless of how you look at it:
More units in a batch mean fewer batches
Fewer batches mean lower Batch costs

13. LSA #1 Check on Learning
Q1. How does batch cost per unit change as batch size increases? A1. Q2. What are the key assumptions in batch quantity tradeoffs? A2.
Q1. How does batch cost per unit change as batch size increases?
A1. As batch size increases, batch cost per unit decreases. So does total batch cost.
Q2. What are the key assumptions in batch quantity tradeoffs?
A2. That annual demand is known and that all batches are the same size.

14. LSA #1 Summary
During this lesson, we first defined Batch Cost and then discussed the formula used in order to predict the Batch Cost per Unit.

15. Apply 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

16. Batch Cost Example (Cont.)
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

17. Batch Cost Example (Cont.)

18. Batch Cost Example (Cont.)

19. 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

20. 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?

21. LSA #2 Check on Learning
Q1. How would you describe the graph of batch cost? A1.
Q1. How would you describe the graph of batch cost?
A1. It is a concave, downward sloping curve. It is similar to the graph for fixed cost per unit.

22. LSA #2 Summary
In this block, we’ve discussed Batch Costs while providing an example.

23. Determine 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”

24. 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”?

25. 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

26. 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

27. Graph of Inventory Assumption (Cont.)
50 Units produced or purchased per batch
X axis represents time

28. Graph of Inventory Assumption (Cont.)
25.00
Units Consumed or Sold uniformly until all Inventory is gone

29. Graph of Inventory Assumption (Cont.)
Average Inventory is 50/2 or 25 Units
25.00
Average Inventory
X axis represents time

30. LSA #3 Check on Learning
Q1. What are the underlying assumptions related to holding costs? A1. Q2. How is average inventory calculated? A2.
Q1. What are the underlying assumptions related to holding costs?
A1. That holding costs are linear or variable on a per-unit basis, and that units produced in batches are consumed or sold uniformly throughout the period.
Q2. How is average inventory calculated?
A2. The maximum inventory is the batch quantity, and the minimum is zero. The average is batch quantity/2.

31. LSA #3 Summary
During this discussion, we spoke of Holding Costs and assumptions, as well as graphed it out for learning reinforcement.

32. Applying 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

33. 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

34. 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

35. Graph of Holding Cost $ X-Axis = Number of units per purchase order
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
X-Axis = Number of units per purchase order
As number of units per purchase order increases, holding cost increases

36. LSA #4 Check on Learning
Q1. How does holding cost change as batch quantity changes?
A1.
Q2. How is holding cost represented on the graph?
A2.
Q1. How does holding cost change as batch quantity changes?
A1. As batch quantity increases, holding cost increases, like a variable cost.
Q2. How is holding cost represented on the graph?
A2. As an upward sloping line.

37. LSA #4 Summary
Again, during this discussion, we spoke of Holding Costs examples, as well as a graphic representation for learning reinforcement.

38. Optimizing Order Quantity
Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
What is Total Cost when Quantity per order is 10 units?
= 5250
What is Total Cost when Quantity per order is 100 units?
= 3000

39. Optimizing Order Quantity (Cont.)
Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
What is Total Cost when Quantity per order is 10 units?
= 5250
What is Total Cost when Quantity per order is 100 units?
= 3000

40. Optimizing Order Quantity (Cont.)
Total Costs Related to Order Quantity =
Purchasing Cost + Holding Cost
What is Total Cost when Quantity per order is 10 units?
= 5250
What is Total Cost when Quantity per order is 100 units?
= 3000

41. Total Cost is minimized where Purchasing Cost = Holding Cost
Graph of Total Costs
Total Cost is minimized where
Purchasing Cost = Holding Cost
≈45
X-Axis = Order quantity in units

42. Optimizing Order Quantity (Cont.)
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

43. Optimizing Order Quantity (Cont.)

44. Calculating EOQ

45. LSA #5 Check on Learning
Q1. What are the three variables used in the Economic Order Quantity formula?
A1.
Q2. How will EOQ change if holding cost per unit increases while all other variables remain the same?
A2.
Q1. What are the three variables used in the Economic Order Quantity formula?
A1. Demand in units, cost per order, and holding cost per unit
Q2. How will EOQ change if holding cost per unit increases while all other variables remain the same?
A2. The EOQ will decrease

46. LSA #5 Summary
In this lesson, we spoke of Optimizing Order Quantity, provided a graphic representation, and solved for the EOQ.

47. TLO Summary Action: Calculate Economic Order Quantity
Condition:  FM Leaders in a classroom environment working as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy, you must:
Determine Batch Quantity Concepts
Apply Batch Cost Example
Applying Holding Cost Example
Optimizing Order Quantity

48. Practical Exercises

49. Batch Quantity Spreadsheet
Enter batch cost, holding cost, and demand into the spreadsheet to generate the graph of total cost
© Dale R. Geiger 2011