1. Inventory Modeling for Independent Demand
MBA 570 Summer 2011

2. Learning Objectives Explain what inventory is
Describe how inventory is classified
Explain ABC analysis
Explain cycle counting
Compare inventory models
Use inventory models to find how much & when to order

3. What Is Inventory?
Stock of materials
Stored capacity

4. What Is Inventory? Stock of materials Stored capacity Examples
© 1995 Corel Corp.
© T/Maker Co.
© 1995 Corel Corp.
© T/Maker Co.

5. The Functions of Inventory
To ”decouple” or separate various parts of the production process
To provide a stock of goods that will provide a “selection” for customers
To take advantage of quantity discounts
To hedge against inflation and upward price changes

6. Types of Inventory Raw material Work-in-progress
Maintenance/repair/operating supply
Finished goods

7. Disadvantages of Inventory
Higher costs
Item cost (if purchased)
Ordering (or setup) cost
Costs of forms, clerks’ wages etc.
Holding (or carrying) cost
Building lease, insurance, taxes etc.
Difficult to control
Hides production problems

8. Inventory Holding Costs
% of Category 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%
Housing costs: building rent, depreciation, operating cost, taxes, insurance.
Material handling costs: equipment, lease, depreciation, power, operating
Labor: wages
Investment costs: borrowing, taxes, insurance on inventory
Pilferage, scrap & obsolescence

9. Inventory Classifications
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10. Inventory Management

11. ABC Analysis Divides on-hand inventory into 3 classes
A class, B class, C class
Basis is usually annual $ volume
$ volume = Annual demand x Unit cost
Policies based on ABC analysis
Develop class A suppliers more
Give tighter physical control of A items
Forecast A items more carefully

12. Classifying Items as ABC
% Annual $ Usage
% of Inventory Items

13. Classifying Items as ABC
% Annual $ Usage A B C
% of Inventory Items

14. ABC Classification Example
You’re a buyer for Auto Palace. Classify the following items as A, B, or C.
Note: Example is for illustration only; too few items.

15. ABC Classification Solution

16. ABC Classification Thinking Challenge
You’re an inventory control supervisor for USX. Classify the following items as A, B, or C.

17. ABC Classification Solution*

18. Cycle Counting
Physically counting a sample of total inventory on a regular basis
Used often with ABC classification
A items counted most often (e.g., daily)

19. Advantages of Cycle Counting
Eliminates shutdown and interruption of production necessary for annual physical inventories
Eliminates annual inventory adjustments
Provides trained personnel to audit the accuracy of inventory
Allows the cause of errors to be identified and remedial action to be taken
Maintains accurate inventory records

20. Basic Inventory Planning Questions
How much to order?
When to order?
Purchase Order
Description
Qty.
Microwave
1000

21. Inventory Models Fixed order quantity models Economic order quantity
Help answer the inventory planning questions!
Fixed order quantity models
Economic order quantity
Production order quantity
Quantity discount
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22. Economic Order Quantity (EOQ) Model

23. EOQ Assumptions Known & constant demand Known & constant lead time
Instantaneous receipt of material
No quantity discounts
Only order (setup) cost & holding cost
No stockouts

24. Goal of an Inventory System
Minimize Total Cost (TC)
TC = Holding + Order/Setup Cost
TC = H + S

25. EOQ Model: How Much to Order?
Annual Cost
Order Quantity

26. EOQ Model: How Much to Order?
Annual Cost
Holding Cost
Order Quantity

27. EOQ Model: How Much to Order?
Annual Cost
Holding Cost
Order (Setup) Cost
Order Quantity

28. EOQ Model: How Much to Order?
Annual Cost
Total Cost Curve
Holding Cost
Order (Setup) Cost
Order Quantity

29. EOQ Model: How Much to Order?
Annual Cost
Total Cost Curve
Holding Cost
Order (Setup) Cost
Order Quantity
Optimal Order Quantity (Q*)

30. Why Holding Cost Increases
More units must be stored if more ordered
Purchase Order
Purchase Order
Description
Qty.
Description
Qty.
Microwave 1
Microwave
1000
Order quantity
Order quantity

31. Why Order Cost Decreases
Cost is spread over more units
Example: You need 1000 microwave ovens
1 Order (Postage $ 0.32)
1000 Orders (Postage $320)
Purchase Order
Purchase Order
Purchase Order
Purchase Order
Description
Qty.
Purchase Order
Description
Qty.
Description
Qty.
Description
Qty.
Microwave
1000
Description
Microwave
Qty. 1
Microwave 1
Microwave 1
Microwave 1
Order quantity

32. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Time

33. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Decrease due to constant demand
Time

34. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Instantaneous receipt of optimal order quantity
Time

35. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Time

36. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Reorder Point (ROP)
Time
Lead Time

37. EOQ Model: When to Order?
Inventory Level
Optimal Order Quantity (Q*)
Average Inventory (Q*/2)
Reorder Point (ROP)
Time
Lead Time

38. EOQ Model Output Example
When the inventory of microwaves gets down to 15 units (reorder point), order 35 units (EOQ).
Purchase Order
Description
Qty.
15 left
Microwave 35

39. EOQ Model Equations D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days

40. EOQ Thinking Challenge
You’re a buyer for Wal-Mart. Wal-Mart 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. Wal-Mart is open 365 days/yr. What is the optimal order quantity & ROP?

41. EOQ Model Equations D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days

42. EOQ Solution* 2 X1000X100 Q * = = = 80 units H . 40 (78) D 1000 d = =
2 X D X S 2
X1000X100 Q * = = = 80
units H . 40
(78) D
1000 d = = = 2 . 74
units /
day
Working Da ys /
Year
365
ROP = d × L = 2 .
74 X 5 = 13 . 7
units

43. Production Order Quantity Model

44. Production Order Quantity Model
Answers how much to order & when to order
Allows partial receipt of material
Other EOQ assumptions apply
Suited for production environment
Material produced, used immediately
Provides production lot size
Lower holding cost than EOQ model

45. POQ Model: Inventory Levels
Time
Supply Begins

46. POQ Model: Inventory Levels
Time
Supply Begins
Supply Ends

47. POQ Model: Inventory Levels
Inventory level with NO demand during supply of optimum order quantity
Time
Supply Begins
Supply Ends

48. POQ Model: Inventory Levels
Inventory level with NO demand during supply of optimum order quantity Q*
Time
Supply Begins
Supply Ends
Q* is optimum order qty

49. POQ Model: Inventory Levels
Inventory level with CONSTANT demand during supply of optimum order quantity
Time
Supply Begins
Supply Ends
Q* is optimum order qty

50. POQ Model: Inventory Levels
Quantity used before becoming inventory
Time
Supply Begins
Supply Ends

51. POQ Model: Inventory Levels
Decrease due to no supply & constant demand
Time
Supply Begins
Supply Ends

52. POQ Model: Inventory Levels
Production portion of cycle
Demand portion of cycle with no supply
Time
Supply Begins
Supply Ends

53. POQ Model: Inventory Levels
Next Cycle
Time

54. POQ Model: Inventory Levels
Next Cycle
Time
Supply Begins

55. POQ Model: Inventory Levels
Time
Supply Begins
Supply Ends

56. POQ Model: Inventory Levels
Time
Supply Begins
Supply Ends

57. POQ Model: Inventory Levels
Max. Inventory Q*·(1- d/p)
Time

58. POQ Model: Inventory Levels
Inventory level with no demand
Max. Inventory Q·(1- d/p)
Production Portion of Cycle Q*
Time
Supply Begins
Supply Ends
Demand portion of cycle with no supply

59. POQ Model Equations d = Q - p D = S Q Max. Inventory Level Setup Cost
Optimal Order Quantity = Qp* =
2 x D x S
H x (1- d/p) d = Q
x 1 -
Max.
Inventory
Level p
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per day D = x
Setup Cost S Q
Holding Cost = Q
1 - (d/p) H

60. POQ Model Thinking Challenge
You’re a production planner for Stanley Tools. Stanley Tools makes 30,000 screw drivers per year. Demand is 100 screw drivers per day & production is 300 per day. Production setup cost is $150 per order. Carrying cost is $1.50 per screw driver. What is the optimal lot size?

61. POQ Model Equations d = Q - p D = S Q Max. Inventory Level Setup Cost
Optimal Order Quantity = Qp* =
2 x D x S
H x (1- d/p) d = Q
x 1 -
Max.
Inventory
Level p
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per day D = x
Setup Cost S Q
Holding Cost = Q
1 - (d/p) H

62. Production Order Quantity Model Solution*2 × D × S 2 ×
30000 ×
150 Q * = = =
3000 p d
100 H × 1 -
1.5 × 1 - p
300
100 =
3000 × 1 - =
Max.
Inventory
Level
2000
300
D = Demand Per Year
S = Setup Cost
H = Holding Cost
d = Demand Per Day
p = Production Per Day

63. Quantity Discount Model
Answers how much to order & when to order
Allows quantity discounts
Reduced price when item is purchased in larger quantities
Other EOQ assumptions apply
Trade-off is between lower price & increased holding cost

64. Quantity Discount Model: How Much to Order?
Total Cost
Order Quantity

65. Quantity Discount Model: How Much to Order?
Total Cost
Price 1
Order Quantity
Discount Quantity 1

66. Quantity Discount Model: How Much to Order?
Total Cost
Price 1
Price 2
Order Quantity
Discount Quantity 1
Discount Quantity 2

67. Quantity Discount Model: How Much to Order?
Total Cost
Price 1
Price 2
Price 3
Order Quantity
Discount Quantity 1
Discount Quantity 2

68. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
Order Quantity
Discount Quantity 1
Discount Quantity 2

69. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
Order Quantity Q*
Discount Quantity 1
Discount Quantity 2

70. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
Outside discount range
Order Quantity Q*
Discount Quantity 1
Discount Quantity 2

71. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
Order Quantity
Discount Quantity 1
Discount Quantity 2

72. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
Order Quantity Q*
Disc Qty 1
Discount Quantity 2

73. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
Outside discount range
Outside discount range
Order Quantity Q*
Disc Qty 1
Discount Quantity 2

74. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2 X
Order Quantity
Q* adjusted
Disc Qty 1
Discount Quantity 2

75. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
TC for Discount 3
Order Quantity
Discount Quantity 1
Discount Quantity 2

76. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
TC for Discount 3
Order Quantity
Discount Quantity 1 Q*
Discount Quantity 2

77. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
TC for Discount 3
Outside discount range
Order Quantity
Disc Qty 1 Q*
Discount Quantity 2

78. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
TC for Discount 3 X
Order Quantity
Discount Quantity 1
Q* adjusted
Disc Qty 2

79. Quantity Discount Model: How Much to Order?
Total Cost
TC for Discount 1
Price 1
Price 2
Price 3
TC for Discount 2
TC for Discount 3
Quantity Ordered
Order Quantity
Lowest cost not in discount range
Discount Quantity 1
Discount Quantity 2

80. Quantity Discount Model Steps
Compute EOQ for each quantity discount price
Is computed EOQ in discount range?
If not, use the lowest cost quantity in discount range
Compute total cost for EOQ or lowest cost quantity in discount range
Select quantity with lowest total cost