1. Chapter. 8
Independent Demand -Inventory
Prepared by :
Arya Wirabhuana, ST, M.Sc

2. Inventory System
Defined
 Inventory is the stock of any item or resource used
in an organization. These items or resources can
include: raw materials, finished products,
component parts, supplies, and work-in-process.
 An inventory system is the set of policies and
controls that monitor levels of inventory and
determines what levels should be maintained,
when stock should be replenished, and how large
orders should be.

3. A Water Tank Analogy for Inventory
Inventory Level
Supply Rate
Inventory Level
Demand Rate

4. Inventory Cost Structures
 Item cost
 Ordering (or setup) cost
 Carrying (or holding) cost:
– Cost of capital
– Cost of storage
– Cost of obsolescence, deterioration, and loss
 Stock out cost

5. Classifying Inventory Models
 Fixed-Order Quantity Models
– Event triggered
 Fixed-Time Period Models
– Time triggered
7

6. Economic Order Quantity (EOQ)
Assumptions
 Demand rate is constant, recurring, and known.
 Lead time is constant and known.
 No stockouts allowed.
 Material is ordered or produced in a lot or batch and
the lot is received all at once
 Unit cost is constant (no quantity discounts)
 Carrying cost depends linearly on the average level of
inventory
 Ordering (setup) cost per order is fixed
 The item is a single product

7. EOQ Inventory Levels
Order
Interval
Lot size = Q
Average Inventory
Level = Q/2
Time

8. Total Cost of Inventory

9. Basic Fixed-Order Quantity (EOQ) Model Formula
Annual Annual Annual
Total Annual Cost = Purchase + Ordering + Holding
Cost Cost Cost
TC = Total annual cost
D = Demand
C = Cost per unit
D Q Q = Order quantity
TC = DC + S + H S = Cost of placing an order
Q 2
or setup cost
R = Reorder point
L = Lead time
H = Annual holding and storage
cost per unit of inventory

10. Continuous Review System
 Assumption of “constant demand” is relaxed.
 Monitoring of “on hand” stock position in a
continuous system
 Q system (another name for continuous
review system)

11. A Continuous Review (Q) System
R = Reorder Point
Q = Order Quantity
L = Lead time

12. Periodic Review System
 All assumption of EOQ (except that demand
is constant and “no stockout”) remains in
effect.
 Also known as “P System” or “Fixed-order-
Interval System”

13. A Periodic Review (P) System

14. “Time Between Orders (P) and
Target Level (T) Calculation
2S
P
iC D
T  m'  s'
Where:
m’ = average demand over P+L
s’ = safety stock

15. Using P and Q System in Practice
 Use P system when orders must be placed
at specified intervals.
 Use P systems when multiple items are
ordered from the same supplier (joint-
replenishment).
 Use P system for inexpensive items.

16. Special Purpose Model: Price-Break
Model Formula
Based on the same assumptions as the EOQ model,
the price-break model has a similar Qopt formula:
2DS 2(Annual Demand)(Order or Setup Cost)
QOPT = =
iC Annual Holding Cost
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula above will
have to be used with each price-break cost value.

17. Price-Break Example Problem Data
(Part 1)
A company has a chance to reduce their inventory
ordering costs by placing larger quantity orders using the
price-break order quantity schedule below. What should
their optimal order quantity be if this company purchases
this single inventory item with an e-mail ordering cost of
$4, a carrying cost rate of 2% of the inventory cost of the
item, and an annual demand of 10,000 units?
Order Quantity(units) Price/unit($)
0 to 2,499 $1.20
2,500 to 3,999 1.00
4,000 or more .98

18. Price-Break Example Solution (Part 2)
First, plug data into formula for each price-break value of “C”.
Annual Demand (D)= 10,000 units Carrying cost % of total cost (i)= 2%
Cost to place an order (S)= $4 Cost per unit (C) = $1.20, $1.00, $0.98
Next, determine if the computed Qopt values are feasible or not.
Interval from 0 to 2499, the 2DS 2(10,000)(4)
Qopt value is feasible. QOPT = = = 1,826 units
iC 0.02(1.20)
Interval from 2500-3999, the 2DS 2(10,000)(4)
Qopt value is not feasible. QOPT = = = 2,000 units
iC 0.02(1.00)
Interval from 4000 & more, the 2DS 2(10,000)(4)
Qopt value is not feasible. QOPT = = = 2,020 units
iC 0.02(0.98)

19. Price-Break Example Solution (Part 3)
Since the feasible solution occurred in the first price-break,
it means that all the other true Qopt values occur at the
beginnings of each price-break interval. Why?
Because the total annual cost function is a
Total “u” shaped function.
annual
costs So the candidates
for the price-breaks
are 1826, 2500,
and 4000 units.
0 1826 2500 4000 Order Quantity

20. Annual Usage of Items by Dollar Value
Percentage of
Annual Usage in Total Dollar
Item Units Unit Cost Dollar Usage Usage
1 5,000 $ 1.50 $ 7,500 2.9%
2 1,500 8.00 12,000 4.7%
3 10,000 10.50 105,000 41.2%
4 6,000 2.00 12,000 4.7%
5 7,500 0.50 3,750 1.5%
6 6,000 13.60 81,600 32.0%
7 5,000 0.75 3,750 1.5%
8 4,500 1.25 5,625 2.2%
9 7,000 2.50 17,500 6.9%
10 3,000 2.00 6,000 2.4%
Total $ 254,725 100.0%

21. ABC Chart
45.0% 120.0%
40.0% A B C 100.0%
Cumulative % Usage
35.0%
Percent Usage
30.0% 80.0%
25.0%
60.0%
20.0%
15.0% 40.0%
10.0%
20.0%
5.0%
0.0% 0.0%
3 6 9 2 4 1 10 8 5 7
Item No.
Percentage of Total Dollar Usage Cumulative Percentage

22. Dependent Demand-
Inventory

23. MRP versus Order-Point Systems
Attribute
Attribute M RP
MRP Order Point
Order Point
Demand
Demand Dependent
Dependent Independent
Independent
Order philosophy
Order philosophy Requirements
Requirements Replenishment
Replenishment
Forecast
Forecast Based on master schedule
Based on master schedule Based on past demand
Based on past demand
Control concept
Control concept Control all items
Control all items ABC
ABC
Objectives
Objectives Meet manufacturing needs
Meet manufacturing needs Meet customer needs
Meet customer needs
Lot sizing
Lot sizing Discrete
Discrete EOQ
EOQ
Demand pattern
Demand pattern Lumpy but predictable
Lumpy but predictable Random
Random
Types of inventory Work in process and raw
Types of inventory Work in process and raw Finished goods and spare
Finished goods and spare
materials
materials parts
parts

24. Material Requirements Planning
 How much of an item is needed?
 When is an item needed to complete
– a specified number of units...
– in a specified period of time?
 Dependent demand drives MRP
3

25. Introductory
Example - Dependent Demand
Lead Times
A
A 1 day
B 2 days
B(4) C(2) C 1 day
D 3 days
E 4 days
F 1 day
D(2) E(1) D(3) F(2)
Demand
Product Structure Tree for Assembly A
Day 10 50 A
Day 8 20 B (Spares)
Day 6 15 D (Spares)
Create a schedule to satisfy demand.
4

26. Day: 1 2 3 4 5 6 7 8 9 10
A Required 50
Order Placement 50
LT = 1 day
5

27. Day: 1 2 3 4 5 6 7 8 9 10
A R e q u ire d 50
O rd e r P la c e m e n t 50
B R e q u ire d 20 200
O rd e r P la c e m e n t 20 200
LT = 2
Spares
A
B(4) C(2)
D(2) E(1) D(3) F(2)
6

28. Day: 1 2 3 4 5 6 7 8 9 10
A Required 50
LT=1 Order Placement 50
B Required 20 200
LT=2 Order Placement 20 200
C Required 100
LT=1 Order Placement 100
D Required 55 400 300
LT=3 Order Placement 55 400 300
E Required 20 200
LT=4 Order Placement 20 200
F Required 200
LT=1 Order Placement 200
A
Part D: Day 6
B(4) C(2) 40 + 15 spares
D(2) E(1) D(3) F(2)
7

29. Time Fences
 Frozen
– No schedule changes allowed within this window
 Moderately Firm
– Specific changes allowed within product groups
as long as parts are available
 Flexible
– Significant variation allowed as long as overall
capacity requirements remain at the same levels
9

30. Time Fences
Moderately
Frozen Firm Flexible
Capacity
Forecast and available
capacity
Firm Customer Orders
8 15 26
Weeks
10

31. Aggregate Forecasts
Firm orders
product of demand
from known
plan from random
customers
customers
Master
Engineering
production Inventory
design
schedule transactions
changes
(MPS)
Bill of Material Inventory
material planning record
file (MRP) file
Reports
12

32. Another MRP Example
Item On-Hand Lead Time (Weeks)
X X 50 2
A 75 3
B 25 1
A(2) B(1) C 10 2
D 20 2
C(3) C(2) D(5)
Requirements include 95 units (80 firm orders and 15 forecast) of X in week 10
plus the following spares:
Spares 1 2 3 4 5 6 7 8 9 10
A 12
B 7
C 10
D 15
18

33. Adding some more terminology
 Gross Requirements
 On-hand
 Net requirements
 Planned order receipt
 Planned order release
19

34. C Gross Requirements 45 36 64
LT=2 On-Hand=10 10
Net Requirements 35 36 64
Planned Order Receipt 35 36 64
Planner Order Release 35 36 64
D Gross Requirements 15 135
LT=2 On-Hand=20 15 5
Net Requirements 130
Planned Order Receipt 130
Planner Order Release 130
X
A(2) B(1)
C(3) C(2) D(5)
20

35. Day: 1 2 3 4 5 6 7 8 9 10
X Gross Requirements 95
LT=2 On-Hand=50 50
Net Requirements 45
Planned Order Receipt 45
Planner Order Release 45
A Gross Requirements 90 12
LT=3 On-Hand=75 75
Net Requirements 15 12
Planned Order Receipt 15 12
Planner Order Release 15 12
B Gross Requirements 7 45
LT=1 On-Hand=25 7 18
Net Requirements 27
Planned Order Receipt 27
Planner Order Release 27
C Gross Requirements 45 36 54 10
LT=2 On-Hand=10 10
Net Requirements 35 36 54 10
Planned Order Receipt 35 36 54 10
Planner Order Release 35 36 54 10
D Gross Requirements 15 135
LT=2 On-Hand=20 15 5
Net Requirements 130
Planned Order Receipt 130
Planner Order Release 130
21

36. Manufacturing Resource Planning (MRP II)
 Goal: Plan and monitor all resources of a
manufacturing firm (closed loop):
– manufacturing
– marketing
– finance
– engineering
 Simulate the manufacturing system
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37. Next : Supply Chain Management