Inventory
• Stock of items held to meet future demand
– Tangible goods
– Intangible goods
• Inventory management answers two questions
– How much to order?
– When to order?
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Types of Inventory
•
•
•
•
•
•
•
•
Raw materials
Purchased parts and supplies
Labor
In-process (partially completed) products
Component parts
Working capital
Tools, machinery, and equipment
Finished goods
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Reasons To Hold Inventory
•
•
•
•
•
•
Meet unexpected demand
Smooth seasonal or cyclical demand
Meet variations in customer demand
Take advantage of price discounts
Hedge against price increases
Quantity discounts
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Two Forms Of Demand
• Dependent
– items used to produce final products
• Independent
– items demanded by external customers
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Inventory Costs
• Carrying Cost
– cost of holding an item in inventory
• Ordering Cost
– cost of replenishing inventory
• Shortage Cost
– temporary or permanent loss of sales when demand
cannot be met
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Inventory Control Systems
• Fixed-order-quantity system (Continuous)
– constant amount ordered when inventory declines
to predetermined level
• Fixed-time-period system (Periodic)
– order placed for variable amount after fixed
passage of time
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ABC Classification System
• Demand volume & value of items vary
• Classify inventory into 3 categories
Class
A
B
C
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% of Units
5 - 15
30
50 - 60
% of Dollars
70 - 80
1515
5 - 10
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ABC Classification Example
Cost
60
350
30
80
30
20
10
320
510
20
Usage
90
40
130
60
100
180
170
50
60
120
Part
9
8
2
1
4
3
6
5
10
7
Value
30,600
16,000
14,000
5,400
4,800
3,900
3,600
3,000
2,400
1,700
$
85,400
Class
A
B
C
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Value
35.8
18.7
16.4
6.3
5.6
4.6
4.2
3.5
2.8
2.0
Items
9,8,2
1, 4, 3
6, 5, 10, 7
Quantity
Cumulative
6.0
6.0
5.0
11.0
4.0
15.0
9.0
24.0
6.0
30.0
13.0
43.0
18.0
61.0
10.0
71.0
12.0
83.0
17.0
100.0
% Value
71
16.5
12.5
% Units
15
25
60
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Assumptions Of Basic EOQ Model
• Demand is known with certainty
• Demand is relatively constant over time
• No shortages are allowed
• Lead time for the receipt of orders is constant
• The order quantity is received all at once
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The Inventory Order Cycle
Inventory Level
Order qty, Q
Demand
rate
Reorder point, R
0
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Lead
time
Order
Order
Placed
Received
Lead
time
Order
Placed
Time
Order
Received
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EOQ Cost Model
CO - cost of placing order
D - annual demand
CC - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
Annual carrying cost =
Total cost =
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Co D
Q
+
Co D
Q
Cc Q
2
Cc Q
2
11
EOQ Model
TC 
TC
Q
0
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Co D
Q

Q
Co D
2
Q
Co D
Q
Co D
2

CcQ
2


Cc
2
Cc
2

Q 
2
Qopt 
CcQ
2
2Co D
Cc
2Co D
Cc
12
Total Cost at Q*
Qopt 
TCmin 
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2Co D
Cc
Co D
Qopt

Cc Qopt
2
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EOQ Model Cost Curves
Annual
cost ($)
Slope = 0
Total Cost
Minimum
total cost
Carrying Cost = CcQ/2
Ordering Cost = CoD/Q
Optimal order
Qopt
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Order Quantity, Q
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EOQ Example
CC = $0.75 per yard
CO = $150
D = 10,000 yards
Find EOQ, TC at Q*, # of order/year,
and cycle time
NOTE: store days = 311
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EOQ Example
2Co D
CoD Cc Qopt
Qopt 
TCmin 

Cc
Qopt
2
2(150)(10,000)
(150)(10,000) (0.75)(2,000)



(0.75)
2,000
2
 2,000 yards
 $750  750  $1,500
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Orders per/yr and Cycle Time
D
10,000
Number of orders per year =

5
Q opt
2,000
311
311
Order cycle time =

 62.2 store days
D/Q opt
5
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EOQ With
Noninstantaneous Receipt
Inventory
level
Q(1-d/p)
Q
(1-d/p)
2
0
Order
receipt period
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Maximum
inventory level
Begin
Order
Average
inventory level
receipt
End
Order
Time
receipt
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EOQ With
Noninstantaneous Receipt
p = production rate
d = demand rate
 d 
Q
Max inv level = Q - d  Q1 - 
p
 p 
1   d  Q  d 
Avg inv level = Q1 -  1 - 
2   p  2  p 
Cc Q  d 
Total carrying cost =
1 - 
2  p 
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EOQ With
Noninstantaneous Receipt
Co D CcQ  d 
1- 
TC 

Q
2  p 
Qopt 
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2Co D
 d 
Cc 1- 
 p 
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Production Quantity Example
CC = $0.75 per yard
CO = $150
D = 10,000 yards
d = 10,000/311 = 32.2 yards per day
p = 150 yards per day
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Optimum Q - Q*
Qopt 

2Co D
 d 
Cc 1 - 
 p 
2(150)(10,000)
 32.2 

0.751 150 
= 2,256.8 yards
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Total Cost
Co D Cc Q d 
1- 
TCmin 

Q
2  p 
(150)(10,000) (0.75)2,256.8  32.2 
1


2,256.8
2
 150 
 $1,329
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Production Run and Max Inv. Levels
Production run
= Q/p
= 2,256.8/150
= 15.05 yards
Number of production runs
= D/Q
= 10,000/2,256.8
= 4.43

d 

32.2 


  1,722 yards
Max inv level = Q 1-   2,256.8 1  p
 150 
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Safety Stocks
• Safety stock
– buffer added to on hand inventory during lead time
• Stockout
– an inventory shortage
• Service level
– probability that the inventory available
during lead time will meet demand
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Inputs and Outputs to Aggregate
Production Planning
Capacity
Constraints
Demand
Forecasts
Size of
Workforce
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Strategic
Objectives
Aggregate
Production
Planning
Production
per month
(in units or $)
Inventory
Levels
Company
Policies
Financial
Constraints
Units or dollars
subcontracted,
backordered, or
lost
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Hierarchical Planning Process
Items
Product lines
or families
Production Planning
Capacity Planning
Aggregate
Production Plan
Resource
Requirements Plan
Individual
products
Master Production
Schedule
Rough-Cut
Capacity Plan
Components
Material
Requirements Plan
Capacity
Requirements Plan
Shop Floor
Schedule
Input/Output
Control
Manufacturing
operations
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Resource level
Plants
Critical work
centers
All work
centers
Individual
machines
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