Operations
Management
Inventory Management
Chapter 12
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Outline
 GLOBAL COMPANY PROFILE: AMAZON.COM
 FUNCTIONS OF INVENTORY

Types of Inventory
 INVENTORY MANAGEMENT
ABC Analysis
 Record Accuracy
 Cycle Counting
 Control of Service Inventories

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Outline - Continued
 INVENTORY MODELS
Independent versus Dependent Demand
 Holding, Ordering, and Setup Costs

 INVENTORY MODELS FOR INDEPENDENT
DEMAND
Basic Economic Order Quantity (EOQ) Model
 Minimizing Costs
 Reorder Points
 Production Order Quantity Model
 Quantity Discount Models

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Outline - Continued
 PROBABILISTIC MODELS WITH CONSTANT
LEAD TIME
 FIXED PERIOD (P) SYSTEMS
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Learning Objectives
When you complete this chapter, you should be
able to :
Identify or Define:
ABC analysis
 Record accuracy
 Cycle counting
 Independent and dependent demand
 Holding, Ordering, and Setup Costs

Describe or Explain:

The functions of inventory and basic inventory
models
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AMAZON.com
 Jeff Bezos, in 1995, started AMAZON.com as a
“virtual” retailer – no inventory, no warehouses, no
overhead; just a bunch of computers.
 Growth forced AMAZON.com to excel in inventory
management!
 AMAZON is now a worldwide leader in warehouse
management and automation.
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Order Fulfillment at AMAZON
1. You order items;, computer assigns your order to
distribution center [closest facility that has the
product(s)]
2. Lights indicate products ordered to workers who
retrieve product and reset light.
3. Items placed in crate with items from other
orders, and crate is placed on conveyor. Bar
code on item is scanned 15 times – virtually
eliminating error.
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Order Fulfillment at AMAZONContinued
4. Crates arrive at central point where items are
boxed and labeled with new bar code.
5. Gift wrapping done by hand (30 packages per
hour)
6. Box is packed, taped, weighed and labeled
before leaving warehouse in a truck.
7. Order appears on your doorstep within a week
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What is Inventory?
 Stock of materials
 Stored capacity
 Examples
© 1995
Corel Corp.
© 1984-1994 T/Maker Co.
© 1984-1994 T/Maker Co.
© 1995 Corel Corp.
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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
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Types of Inventory
 Raw material
 Work-in-progress
 Maintenance/repair/operating supply
 Finished goods
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The Material Flow Cycle
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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
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Inventory Classifications
Inventory
Process
stage
Raw Material
WIP
Finished Goods
© 1984-1994
T/Maker Co.
Number
& Value
Demand
Type
A Items
B Items
C Items
Independent
Dependent
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Other
Maintenance
Operating
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The Material Flow Cycle
Input
Other
Wait
Time
Move
Time
Queue
Time
Setup
Time
Run
Time
Output
Cycle Time
1 Run time: Job is at machine and being worked on
2 Setup time: Job is at the work station, and the work station is being
"setup."
3 Queue time: Job is where it should be, but is not being processed
because other work precedes it.
4 Move time: The time a job spends in transit
5 Wait time: When one process is finished, but the job is waiting to be
moved to the next work area.
6 Other: "Just-in-case" inventory.
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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

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Classifying Items as ABC
Class
A
B
C
% Annual $ Usage
100
80
60
% $ Vol
80
15
5
% Items
15
30
55
A
40
B
20
C
0
0
50
100
% of Inventory Items
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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)
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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
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Techniques for Controlling
Service Inventory Include:
 Good personnel selection, training, and discipline
 Tight control of incoming shipments
 Effective control of all goods leaving the facility
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Independent versus
Dependent Demand
 Independent demand - demand for item is
independent of demand for any other item
 Dependent demand - demand for item is
dependent upon the demand for some other item
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Inventory Costs
 Holding costs - associated with holding or
“carrying” inventory over time
 Ordering costs - associated with costs of placing
order and receiving goods
 Setup costs - cost to prepare a machine or
process for manufacturing an order
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Holding (Carrying) Costs
 Obsolescence
 Insurance
 Extra staffing
 Interest
 Pilferage
 Damage
 Warehousing
 Etc.
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Inventory Holding Costs
(Approximate Ranges)
Category
Cost as a
% of Inventory Value
Housing costs (building rent, depreciation,
operating cost, taxes, insurance)
6%
(3 - 10%)
Material handling costs (equipment, lease
or depreciation, power, operating cost)
3%
(1 - 3.5%)
Labor cost from extra handling
3%
(3 - 5%)
Investment costs (borrowing costs, taxes,
and insurance on inventory)
11%
(6 - 24%)
3%
(2 - 5%)
26%
Pilferage, scrap, and obsolescence
Overall carrying cost
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Ordering Costs
 Supplies
 Forms
 Order processing
 Clerical support
 Etc.
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Setup Costs
 Clean-up costs
 Re-tooling costs
 Adjustment costs
 Etc.
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Inventory Models
 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.
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EOQ Assumptions
 Known and constant demand
 Known and constant lead time
 Instantaneous receipt of material
 No quantity discounts
 Only order (setup) cost and holding cost
 No stockouts
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Inventory Usage Over Time
Usage Rate
Inventory Level
Order quantity = Q
(maximum
inventory level)
Minimum
inventory 0
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Average
Inventory
(Q*/2)
Time
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EOQ Model
How Much to Order?
Annual Cost
Minimum
total cost
Order (Setup) Cost Curve
Optimal
Order Quantity (Q*)
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Order quantity
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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
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Order quantity
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Why Order 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.
Description
Purchase
Description Qty.
Qty.
Description
Microwave Qty. 11
Description
Microwave
Microwave
Microwave
11
Order quantity
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Deriving an EOQ
1. Develop an expression for setup or ordering
costs
2. Develop an expression for holding cost
3. Set setup cost equal to holding cost
4. Solve the resulting equation for the best order
quantity
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EOQ Model
When To Order
Inventory Level
Average
Inventory
(Q*/2)
Optimal
Order
Quantity
(Q*)
Reorder
Point
(ROP)
Time
Lead Time
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EOQ Model Equations
Optimal Order Quantity
2 ×D ×S
H
D
=N =
Q*
= Q* =
Expected Number of Orders
Expected Time Between Orders
d =
D
Working Days
/ Year
ROP = d × L
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=T =
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
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The Reorder Point (ROP) Curve
Q*
Inventory level (units)
Slope = units/day = d
ROP
(Units)
Time (days)
Lead time = L
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Production Order Quantity Model
 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
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EOQ POQ Model
When To Order
Usage only takes
place
Inventory Level
Maximum
inventory
level
Both production
and usage take
place
Time
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EOQ POQ Model
When To Order
Inventory Level
Average
Inventory
Optimal
Order
Quantity
(Q*)
Reorder
Point
(ROP)
Time
Lead Time
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Reasons for Variability in Production
Most variability is caused by waste or by poor
management. Specific causes include:
employees, machines, and suppliers produce units that do
not conform to standards, are late or are not the proper
quantity
 inaccurate engineering drawings or specifications
 production personnel try to produce before
drawings or
specifications are complete
 customer demands are unknown

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POQ Model Inventory Levels
Inventory Level
Production portion of cycle
Demand portion of cycle with no
supply
Supply
Begins
Time
Supply
Ends
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POQ Model Equations
Maximum inventory level
Setup Cost
Holding Cost
=
D
Q
2*D*S
d
H* 1 p
= Q* =
p
Optimal Order Quantity
= Q*
(
1 -
( )
d
p
)
* S
= 0.5 * H * Q
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( )
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d
p
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per day
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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
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Quantity Discount Schedule
Discount
Number
1
Discount
Quantity
0 to 999
Discount
(%)
No discount
Discount
Price (P)
$5.00
2
1,000 to 1,999
4
$4.80
3
2,000 and over
5
$4.75
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Quantity Discount – How Much to
Order
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Probabilistic Models
 Answer how much & when to order
 Allow demand to vary
Follows normal distribution
 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
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Probabilistic Models
When to Order?
Inventory Level
Frequency
Service
Level
P(Stockout)
Optimal
Order
Quantity
SS
X
ROP
Reorder
Point
(ROP)
Safety Stock (SS)
Place
order
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Lead Time
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Receive
order
Time
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Fixed Period Model
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: P&G representative calls every 2 weeks
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Inventory Level 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
On-Hand Inventory
Target maximum
Q1
Q4
Q2
Q3
p
p
p
Time
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Fixed Period Model
When to Order?
Inventory Level
Period
Target maximum
Period
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Period
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Time
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