Chapter 6
Inventory Control
Models
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Learning
Objectives
Students will be able to:
• Understand the importance of
inventory control.
• Use the economic order quantity
(EOQ) to determine how much to
order.
• Compute the reorder point (ROP)
in determining when to order
more inventory.
• Perform sensitivity analysis on
basic inventory quantities.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Learning
Objectives continued
Students will be able to:
• Determine the economic order
quantity without the instantaneous
receipt assumption.
• Handle inventory problems that
allow quantity discounts or have
planned shortages.
• Understand the use of safety stock
with known and unknown stockout
costs.
• Perform ABC analysis.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
6.1 Introduction
6.2 Importance of Inventory Control
6.3 Inventory Decision
6.4 Economic Order Quantity(EOQ):
Determining How Much to Order
6.5 Reorder Point: Determining When
to Order
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline continued
6.6 EOQ without the
Instantaneous Receipt
Assumption
6.7 Quantity Discount Models
6.8 Use of Safety Stock
6.9 ABC Analysis
6.10 Sensitivity Analysis
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory as an Important
Asset
• Inventory can be the most expensive
and the most important asset for an
organization
Inventory
40%
Other Assets
60%
Inventory as a
percentage of total assets
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-6
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory Planning
and Control - Fig. 6.1
Planning on
what
Inventory to
Stock and
How to
Acquire It
Forecasting
Parts/Product
Demand
Controlling
Inventory
Levels
Feedback
Measurements to
Revise Plans and
Forecasts
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-7
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Inventory Process
Suppliers
Customers
Inventory Storage
Raw
Materials
Finished
Goods
Work in
Process
Fabrication
and
Assembly
Inventory Processing
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Importance of Inventory
Control
Five Functions of
Inventory
• Decoupling
• Storing resources
• Adapting to irregular supply and
demand
• Enabling the company to take
advantage of quantity discounts
• Avoiding stockouts and shortages
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-9
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory Decisions
• How much to order
• When to order
wish to minimize total inventory
cost
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory Costs
• Cost of the items
• Cost of ordering
• Cost of carrying, or holding
inventory
• Cost of safety stock
• Cost of stockouts
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-11
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Ordering Costs
• Developing and sending purchase orders
• Processing and inspecting incoming
inventory
• Bill paying
• Inventory inquiries
• Utilities, phone bills, etc., - purchasing
department.
• Salaries/wages - purchasing department
employees
• Supplies (e.g., forms and paper) purchasing department
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-12
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Carrying Costs
• Cost of capital
• Taxes
• Insurance
• Spoilage
• Theft
• Obsolescence
• Salaries/wages - warehouse employees
• Utilities/building costs - warehouse
• Supplies (e.g., forms, paper) warehouse
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-13
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory Usage Over
Time - Fig. 6.2
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Costs as Functions of Order
Quantity - Fig. 6.3
Annual
Cost
Total Cost Curve
Minimum
Cost
Carrying
(holding)
Cost Curve
Ordering
(set-up)
Cost Curve
Q*
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
Order Quantity
6-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Costs as Functions of Order
Quantity - Fig. 6.3
$ Cost
Inventory Cost versus Order Quantity
Minimum
Cost
Order Cost
Optimal Quantity
Quantity
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Steps in Finding the
Optimum Inventory
• Develop an expression for the
ordering cost.
• Develop and expression for the
carrying cost.
• Set the ordering cost equal to
the carrying cost.
• Solve this equation for the
optimum desired.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-17
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
EOQ : Basic
Assumptions
• Demand is known and constant
• Lead time is known and constant
• Receipt of inventory is instantaneous
• Quantity discounts are not possible
• The only variable costs are the cost of
setting up or placing an order, and the
cost of holding or storing inventory over
time
• Stockouts can be completely avoided if
orders are placed at the appropriate time
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-18
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Developing the EOQ
• Annual ordering cost:
Annual demand

Number of units per order
D
 Co
Q
• Annual holding or carrying cost:
 Average Inventory * Carrying Cost Per Year
Q
 Ch
2
• Total inventory cost:
D
Q
C t  Co  Ch
Q
2
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-19
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
EOQ
Per Unit Carrying Cost:
Q* 
2DC
0
Ch
Percentage Carrying
Cost:
Q
*
2DC0
IP
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-20
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inputs and Outputs of
the EOQ Model
Input Values
Output Values
Annual Demand
(D)
Economic
Order
Quantity
(EOQ)
Ordering Cost
(Co)
Carrying Cost
(Ch)
EOQ
Models
Reorder
Point
(ROP)
Lead Time
(L)
Demand Per Day
(d)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-21
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Reorder Point (ROP)
Curve - Fig. 6.4
ROP = (Demand per day) x (Lead time for
a new order, in days) = d x L
Inventory Level (Units)
Q*
Slope = Units/Day = d
ROP
(Units)
Lead Time (Days) L
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-22
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory Control and
the Production Process
Inventory Level
Production
Portion of
Cycle
Maximum
Inventory
Level
Demand
Portion
of Cycle
Demand
Portion
of Cycle
Time
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-23
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Production Quantity
EOQ
• Annual Carrying Cost:
Q
d
(1 
)C h
2
p
• Annual Ordering Cost:
D
Cs
Q
• Setup Cost:
• Ordering Costs:
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-24
D
Co
Q
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Production Quantity
EOQ
2DC o
Q 
 d
C h 1  
 p
*
p
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-25
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Quantity Discount
Models - Fig. 6.6
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-26
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Quantity Discount
Steps
• 1. Calculate Q for each discount
• 2. Adjust Q upward if quantity
is too low for discount
• 3. Compute total cost for each
discount
• 4. Select Q with the the lowest
total cost
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-27
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Inventory on
Hand
The Use of Safety
Stock
Fig. 6.7
Inventory on
Hand
Time
Stockout
Stockout
is avoided
Time
Safety Stock
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-28
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Use of Safety
Stock
• Known stockout costs:
• Given probability of demand, find
total cost for each safety stock
alternative
• Unknown stockout costs:
• Set service level; use normal
distribution
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-29
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Service Level versus
Carrying Costs
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-30
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Summary of ABC
Analysis Table 6.6
• Group A Items - Critical
• Group B Items - Important
• Group C Items - Not That
Important
Are Complex
Quantitative
Control
Inventory
Dollar
Inventory
Techniques
Group Usage (%) Items (%)
Used?
A
B
C
70
20
10
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
10
20
70
6-31
Yes
In some
cases
No
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Percent of Annual
Dollar Usage
ABC Inventory
Analysis
100
90 A
80 Items
70
60
50
40
B
30
Items
20
10
0
1 2 3 4
C
Items
5
6 7
8
9 10
Percent of Inventory Items
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-32
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
ABC Inventory Policies
• Greater expenditure on supplier
development for A items than
for B items or C items
• Tighter physical control on A
items than on B items or on C
items
• Greater expenditure on
forecasting A items than on B
items or on C items
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
6-33
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458