Operations
Management
Inventory Management
Chapter 12
12-1
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
What is Inventory?
Stock of materials
Stored capacity
© 1995
Corel Corp.
© 1984-1994 T/Maker Co.
© 1984-1994 T/Maker Co.
© 1995 Corel Corp.
12-2
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Types of Inventory
 Raw material
 Work-in-progress
 Maintenance / repair / operating supplies
 Finished goods
12-3
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
The Material Flow Cycle
12-4
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
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
12-5
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Disadvantages of Inventory
 Higher costs
Interest or opportunity costs
 Holding (or carrying) costs – storage, handling, taxes,
insurance, shrinkage
 Ordering (or setup) costs

 Risk of deterioration or obsolescence
 Hides production problems


Yield / scrap variations
Unscheduled downtime
Total cost = 20% - 40% of inventory value / year
12-6
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Pressures on inventory
Pressure for lower inventory
•Inventory investment
•Inventory holding cost
Pressure for higher inventory
•Customer service
•Other costs related to inventory
12-7
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Different Views of Inventory
Types of Inventory
Demand Type
Cycle
Pipeline
Safety Stock
Anticipation
Independent
Dependent
Process stage
Raw Material
Work in Process
Finished Goods
Annual $ Volume
A
B
C
Other
Maintenance / Repair
Operating Supplies
12-8
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
How Is Inventory Created?
 Cycle Inventory – result of lot size
Q+0
Average cycle inventory =
2
 Pipeline Inventory – in transit
Pipeline inventory = DL = dL
 Safety Stock
 Anticipation Inventory
Types of Inventory
Cycle
Pipeline
Safety Stock
Anticipation
12-9
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Calculations
We use 70 hypodermic needles a week.
We buy them in lots of 280. It takes three
weeks for order handling and shipment.
Cycle inventory
= Q/2
= 280/2
= 140 needles
Pipeline inventory = DL = dL
= (70 needles/week)(3 weeks)
= 210 drills
12-10
Inventory Worksheets
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Reduction Tactics
 Cycle inventory
Reduce lot size
 Pipeline inventory
Reduce lead time
 Safety Stock
Reduce uncertainties
 Anticipation inventory
Various
12-11
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
ABC Analysis
 Divides on-hand inventory into three classes on
the basis of annual dollar volume – A, B, and C

$ volume = Annual demand x Unit cost
 Policies based on ABC analysis



Develop class A suppliers more
Maintain tighter physical control of A items
Forecast A items more carefully
Annual $ Volume
A
B
C
12-12
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
ABC Analysis
% Annual $ Usage
100
80
60
Class
A
B
C
% $ Vol
80
15
5
% Items
20
30
50
A
40
B
20
C
0
0
50
100
% of Inventory Items
12-13
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Models for
Independent Demand
 Fixed order-quantity models
Help answer the
inventory planning
questions!
Economic order quantity
 Production order quantity
 Quantity discount

 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
12-14
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
EOQ – Economic Order Quantity
 Objective:
minimize (ordering cost + holding cost)
 Assumptions:






Known and constant demand
Known and constant lead time
Instantaneous receipt of material
No quantity discounts
Only ordering / setup cost and holding cost
No stockouts
12-15
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Usage Over Time
Usage Rate
Inventory Level
Q
Average
Cycle
Inventory
Q
2
0
Time
12-16
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
EOQ Model
How Much to Order?
Annual Cost
Minimum
total cost
Ordering (Setup) Cost
Optimal
Order Quantity (Q*)
12-17
Order quantity (Q)
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Why Holding Costs Increase
More units must be stored if more are ordered
Purchase Order
Description
Qty.
Microwave
1
Purchase Order
Description
Qty.
Microwave
1000
Order quantity
12-18
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Why Ordering Costs Decrease
Cost is spread over more units
Example: You need 1000 microwave ovens
1 Order (Postage $ 0.33)
1000 Orders (Postage $330)
Purchase Order
Description
Qty.
Microwave
1000
PurchaseOrder
Order
Purchase
PurchaseOrder
OrderQty.
Purchase
Description
Description Qty.
Qty.
Description
Microwave Qty. 11
Description
Microwave
Microwave
Microwave
11
Order quantity
12-19
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
EOQ Model – When to Order
Inventory Level
Q*
Average
Cycle
Inventory
Reorder
Point
(ROP)
Time
Lead Time
12-20
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
EOQ Model Equations
Optimal Order Quantity
Expected Number of Orders
2 ×D ×S
H
=N = D
Q*
= Q* =
=T =
Expected Time Between Orders
d =
D
Working Days
Working Days
/ Year
N
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
/ Year
ROP = d × L
12-21
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Models for
Independent Demand
 Fixed order-quantity models
Help answer the
inventory planning
questions!
Economic order quantity
 Production order quantity
 Quantity discount

 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
12-22
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
POQ – Production Order Quantity
 Answers how much to order and 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
12-23
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
EOQ POQ Model
Usage only takes
place
Inventory Level
Maximum
inventory
level
Both production
and usage take
place
Time
12-24
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Models for
Independent Demand
 Fixed order-quantity models
Help answer the
inventory planning
questions!
Economic order quantity
 Production order quantity
 Quantity discount

 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
12-25
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Quantity Discount Model
 Answers how much to order & when to order
 Allows quantity discounts

Other EOQ assumptions apply
 Trade-off is between lower price & increased holding cost
Discount
Number
Discount
Quantity
Discount
(%)
Discount
Price (P)
1
0 to 999
No discount
$ 5.00
2
1,000 to 1,999
4
$ 4.80
3
2,000 and over
5
$ 4.75
12-26
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Quantity Discount – How Much to Order
12-27
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Models for
Independent Demand
 Fixed order-quantity models
Help answer the
inventory planning
questions!
Economic order quantity
 Production order quantity
 Quantity discount

 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
12-28
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Frequency
Probabilistic Models
 Answer how much &
when to order
 Allow demand to vary

Service
Level
P(Stockout)
X
Other EOQ assumptions apply
 Consider service level & safety stock
Service level = 1 – Probability of stockout
 Higher service level means more safety stock
 More safety stock means higher ROP

12-29
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Level
Frequency
Probabilistic Models - When to Order?
Service
Level
P(Stockout)
SS
X
ROP
Reorder
Point
(ROP)
Safety Stock (SS)
Time
Lead Time
Place
order
Receive
order
12-30
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Models for
Independent Demand
 Fixed order-quantity models
Help answer the
inventory planning
questions!
Economic order quantity
 Production order quantity
 Quantity discount

 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
12-31
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Fixed Period (P) Systems
 Answers how much to order
 Orders placed at fixed intervals


Inventory brought up to target amount
Amount ordered varies
 No continuous inventory count

Possibility of stockout between intervals
 Useful when vendors visit routinely

Example: Office Max representative calls every week
12-32
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory in a Fixed Period System
Various amounts (Qi) are ordered at regular time
intervals (p) based on the quantity necessary to
bring inventory up to target maximum
Target maximum
On-Hand Inventory
Q1
Q4
Q2
Q3
p
p
p
Time
12-33
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Comparison of Q and P Systems
 Continuous Review System (Q)
A system designed to track the remaining inventory
of an item each time a withdrawal is made, to
determine whether it is time to replenish
 Periodic Review System (P)
A system in which an item’s inventory position is
reviewed periodically rather than continuously
12-34
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Comparison of Q and P Systems
 Continuous Review System (Q)
Individual review frequencies
 Possible quantity discounts
 Lower, less-expensive safety stocks

 Periodic Review System (P)
Convenient to administer
 Orders may be combined
 Inventory position only required at review

12-35
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Inventory Measures
Average inventory = $2 million
Cost of goods sold = $10 million
52 business weeks per year
Average inventory value
Weekly sales (at cost)
$2 million
=
= 10.4 weeks
($10 million)/(52 weeks)
Weeks of supply =
Inventory turns =
=
Annual sales (at cost)
Average inventory value
$10 million
= 5 turns/year
$2 million
12-36
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Summary
 Functions of inventory –
Inventory enables value creation for many processes




Costs of inventory
Different views of inventory
Inventory reduction tactics
ABC and EOQ are traditional tools used to manage
inventory – still used in many circumstances
 Continuous review system (Q) for high-value parts;
Periodic review system (P) for some low value parts
 Weeks of Supply and inventory turns are widely-used
measures of inventory
12-37
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458