1. Operations Management
Chapter 4 –
Inventory Management
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 7e
Operations Management, 9e

2. 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
If this course is the first exposure of students to manufacturing, it might be useful to discuss the decoupling function.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

3. Types of Inventory Raw material Work-in-progress
Maintenance/repair/operating supply
Finished goods
It might be useful here to explicitly discuss the purpose of each type of inventory.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

4. 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
Of the items listed on this slide, the least obvious to most students is the manner in which inventory can be used to hide production problems.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

5. 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
It might be helpful here to discuss some of the differences in the ways we would manage items in the three different levels. What actions would we actually take in managing A versus in managing C?
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

6. Classifying Items as ABC20 40 60 80
100 50
% Annual $ Usage A B C
Class
% $ Vol
% Items 15 30 5 55
Are we back to Pareto analysis?
% of Inventory Items
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

7. 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
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

8. Holding (Carrying) Costs
Obsolescence
Insurance
Extra staffing
Interest
Pilferage
Damage
Warehousing
Etc.
You might ask students if they can identify an industry for which the cost of obsolescence is particularly important. Is the number of such industries likely to grow or decline?
The same question could be asked regarding pilferage.
The question could be asked in a more general manner: Are there industries for which one or another of the areas listed is of particular or unusual importance?
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

9. Inventory Holding Costs (Approximate Ranges)
Cost as a
% of Inventory Value 6%
(3 - 10%) 3%
( %)
(3 - 5%)
11%
(6 - 24%)
(2 - 5%)
26%
Category
Housing costs (building rent, depreciation, operating cost, taxes, insurance)
Material handling costs (equipment, lease or depreciation, power, operating cost)
Labor cost from extra handling
Investment costs (borrowing costs, taxes, and insurance on inventory)
Pilferage, scrap, and obsolescence
Overall carrying cost
Note that this slide suggest holding costs are, on average, about 26% of the inventory value
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

10. Ordering Costs Supplies Forms Order processing Clerical support Etc.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

11. Setup Costs Clean-up costs Re-tooling costs Adjustment costs Etc.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

12. Inventory Models Fixed order-quantity models Probabilistic models
Economic order quantity
Production order quantity
Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
This slide simply introduces some of the available models. Additional details are provided in subsequent slides.
© T/Maker Co.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

13. 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
Students should be asked to consider the degree to which each of these assumptions is accurate.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

14. Inventory Usage Over Time
Inventory Level
Average Inventory (Q*/2)
Minimum inventory
Order quantity = Q (maximum inventory level)
Usage Rate
One should link this model to the assumptions. You should also explore, at least briefly, how this picture would change if the assumptions were not met.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

15. EOQ Model How Much to Order?
Order quantity
Annual Cost
Holding Cost Curve
Total Cost Curve
Order (Setup) Cost Curve
Optimal Order Quantity (Q*)
Minimum total cost
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

16. Why Holding Costs Increase
More units must be stored if more are ordered
Purchase Order
Description
Qty.
Microwave
1000
Order quantity
Purchase Order
Description
Qty.
Microwave 1
Order quantity
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

17. Why Order Costs Decrease
Cost is spread over more units
Example: You need 1000 microwave ovens
Purchase Order
Description
Qty.
Microwave 1
1 Order (Postage $ 0.33)
1000 Orders (Postage $330)
Order quantity
1000
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

18. Deriving an EOQ Develop an expression for setup or ordering costs
Develop an expression for holding cost
Set setup cost equal to holding cost
Solve the resulting equation for the best order quantity
Students may find it helpful if you actually go through each of these steps - at least through writing the equation, and setting setup cost equal to holding cost.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

19. EOQ Model When To Order Inventory Level Time Average Inventory (Q*/2)
Reorder Point (ROP)
Time
Inventory Level
Average Inventory (Q*/2)
Lead Time
Optimal Order Quantity (Q*)
One should link this model to the assumptions. You should also explore, at least briefly, how this picture would change if the assumptions were not met.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

20. EOQ Model Equations = × Q* D S H N T d ROP L 2 Optimal Order Quantity
Expected Number of Orders
Expected Time Between Orders
Working Days /
Year = × Q* D S H N T d
ROP L 2
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
For some students, it is most important at this point to explain in detail the meaning and significance of each equation. It might be helpful to actually work through a numerical example.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

21. The Reorder Point (ROP) CurveQ*
ROP (Units)
Slope = units/day = d
Lead time = L
Time (days)
Inventory level (units)
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

22. 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
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

23. Quantity Discount Schedule
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
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

24. Quantity Discount – How Much to Order
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

25. 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
One point to stress here is that this is simply an extension of the original EOQ model where we are now allowing the demand to vary. Students should become accustomed to seeking such extensions as the need arises.
The next slide presents a graphical view of this model.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

26. Probabilistic Models When to Order?
Reorder Point (ROP)
Optimal
Order Quantity X
Safety Stock (SS)
Time
Inventory Level
Lead Time SS
ROP
Service Level
P(Stockout)
Place order
Receive order
Frequency
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J 32

27. 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
This represents a model in which orders are based upon time, not the quantity needed. The following slide provides a graphical representation.
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

28. 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 p Q1 Q2 Q3 Q4
Target maximum
Time
On-Hand Inventory
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

29. Fixed Period Model When to Order?
Time
Inventory Level
Target maximum
Period
Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J