Chapter 12 – Independent
Demand Inventory Management
Operations Management
by
R. Dan Reid & Nada R. Sanders
4th Edition © Wiley 2010
PowerPoint Presentation by R.B. Clough – UNH
M. E. Henrie - UAA
© Wiley 2010
Wall Street Speaks
(compiled by Teradata, a division of NCR)
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“Shares of Intel Corp. fell to an 11-month
low on Wednesday, leading a decline in
semiconductor-industry stocks a day after
the world’s largest chipmaker warned that
its inventories had risen sharply”, this
despite 96% growth in quarterly profit. –
Reuters, July 14, 2004
“Cisco Systems Inc. on Tuesday reported
that quarterly profit surges 41%, but its
shares fell sharply in after-hours trade on a
rise in inventories.” - Reuters, August 10,
2004
© Wiley 2010
Wall Street Speaks
(compiled by Teradata, a division of NCR)
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“The day Nike announced the breakdown in its
chain, the company’s stock dropped 20%, an
amount so staggering that it makes the $100
million loss (in sales) seem like pocket change.” –
Computer World, November 10, 2003
“General Motors was down 3.1%, or $1.37, at
$42.75, after analysts with Goldman Sachs and
Lehman Brothers downgraded their ratings of the
stock, amid worries of inventory buildup.” –AP,
July 30, 2004
“Blind execution [of a production plan] in the face
of variation can tie up hundreds of millions in
working capital and prevent you from supporting
customer demand.” -Teradata
© Wiley 2010
Types of Inventory
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Inventory comes in many shapes and sizes
such as
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Raw materials – purchased items or extracted
materials transformed into components or
products
Components – parts or subassemblies used in final
product
Work-in-process – items in process throughout the
plant
Finished goods – products sold to customers
Distribution inventory – finished goods in the
distribution system
© Wiley 2010
Types of Inventory
© Wiley 2010
Uses of Inventory
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Anticipation or seasonal inventory
Fluctuation Inventory or Safety stock: buffer
demand fluctuations
Lot-size or cycle stock: take advantage of
quantity discounts or purchasing efficiencies
Transportation or Pipeline inventory
Speculative or hedge inventory protects against
some future event, e.g. labor strike
Maintenance, repair, and operating (MRO)
inventories
© Wiley 2010
Principal Quantitative Models in Ch. 12
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Inventory Turnover & Days or
Weeks of Supply
P-Models: Periodic Review Models
Q-Models: Continuous Review
Models
ABC Classification
© Wiley 2010
Inventory Investment Measures Example 1: The Coach Motor
Home Company has annual cost of goods sold of $10,000,000. The
average inventory value at any point in time is $384,615. Calculate
inventory turnover and weeks/days of supply. Assume 52 weeks.

Inventory Turnover:
Turnover 

annual cost of goods sold $10,000,000

 26 inventory turns
average inventory value
$384,615
Weeks/Days of Supply:
Weeks of Supply 
average inventory on hand in dollars
$384,615

 2weeks
average weekly usage in dollars
$10,000,000/52
If there are 5 work days per week, that is 10 days of supply.
© Wiley 2010
Inventory Investment Measures Example 2: At Genuine
Reproductions, the annual cost of goods sold was $3,000,000 last
year. The average inventory value was $250,000. Calculate
inventory turnover, the weeks of supply, and days of supply for last
year. (Ch. 12, #3)

Inventory Turnover:
Turnover 

annual cost of goods sold $3,000,000

 12 inventory turns
average inventory value
$250,000
Weeks/Days of Supply:
Weeks of Supply 
average inventory on hand in dollars
$250,000

 4.33 weeks
average weekly usage in dollars
$3,000,000/52
That means (5)(4.33) = 21.67 days of supply.
© Wiley 2010
Inventory Control Models
Feature
Q-Model:
P-Model:
Continuous
Review
Periodic Review
Order Quantity
Q - constant
q – variable
When to order
When inventory hits
reorder level R
At review period,
every T time units
Recordkeeping
At each + or -
Only at review time
T
Qq all else equal
Inventory Size
Maintenance
higher
lower
Types of items
High value
ordinary
Source: Chase, Jacobs, & Aquilano (McGraw-Hill)
© Wiley 2010
Most Important Inventory Costs
Holding
Costs
Ordering
Cost
Denoted H; includes the variable
expenses incurred by the plant related
to the volume of inventory held
e.g. 15-25%
Denoted S; fixed, constant dollar
amount incurred for each order placed
© Wiley 2010
Periodic (P) Review Systems
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Orders are placed at specified, fixed-time intervals
(e.g. every Friday), for a order size (q) to bring onhand inventory (OH) up to the target inventory (TI),
similar to the min-max system.
Advantages are:
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No need for a system to continuously monitor item
Items ordered from the same supplier can be reviewed on
the same day saving purchase order costs
Disadvantages:
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Replenishment quantities (q) vary
Order quantities may not quality for quantity discounts
On the average, inventory levels will be higher than Q
systems-more stockroom space needed
© Wiley 2010
Managing Periodic (P) Review Systems
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Prior to implementation,
management must decide
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Replenishment period, i.e., time
between orders
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Can use convenience or EOQ approximation
calculation to determine RP
Cycle service level, i.e., the
probability of satisfying customer
demand
© Wiley 2010
Periodic Review System Calculations
Safety Stock
SS = zσRP+L
where z denotes the z-score needed for the desired
service level, and
 RP L   t RP  L
is the standard deviation of demand during the
combined Review Period and Lead Time. Here
we need to be given σt the standard deviation of
demand per unit time (day or week).
P-Models always include Safety Stock!
© Wiley 2010
Periodic Review System Calculations
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Target Inventory level:
TI = d(RP + L) + SS
d = average period demand
RP = review period (days, wks)
L = lead time (days, wks)
SS = Safety Stock (as above)
Replenishment Quantity (q)=TI-OH

OH is on-hand inventory
© Wiley 2010
Periodic Review System Calculations
Total Annual Cost
 Annual Ordering Cost  Average Annual Holding Cost
 no. days in work year   TI - dL 
S  
 
H
 review period in days   2 
(Weeks can be used as time units instead of days.)
Note: This formula is not clearly stated in the text!
© Wiley 2010
Periodic Review (P) Model, Example 1: Your firm’s demand is
normally distributed with mean 48/week and standard deviation
8. Lead time is 2 weeks, and the desired cycle service level is
94%. Initially, your review period is 1 week (every Friday you
take inventory). Find the safety stock and the Target Inventory
Level. [Ch. 12 #27.]
Safety Stock SS = z94σRP+L
z94 =1.55
 RP L   t RP  L
 (8)  1  2
 (8)  (1.732)
 13.86
Area = .44
Stockout!
Tail Area = .06
Area left
of y-axis =
.50
Safety Stock SS =
(1.55)(13.86) = 21.48 -> 22
0
© Wiley 2010
Z94 = 1.55
z
Periodic Review (P) Model, Example 1, continued: [Ch. 12 #27.]
We found Safety Stock SS = (1.55)(13.86)
= 21.48 -> 22
Next find the Target Inventory level (TI):
TI = d(RP + L) + SS
= (48)(1+2) + 22
= 166 units
Follow-up: if you have 100 units on hand (OH =100),
Order quantity q =
TI – OH = 66
© Wiley 2010
Periodic Review (P) Model, Example 1, extended: [Ch. 12 #27.]
Suppose that the unit order cost is S = $25 and the unit holding cost is
H=$2. Assuming 50 working weeks in the year, what is the total annual
cost of inventory?
Total Annual Cost
 Annual Ordering Cost  Average Annual Holding Cost
 no. weeks in work year   TI - dL 
S  
 
H
 review period in weeks   2 
 50   166  (48)  (2) 
  
2
2
 1  

= $50 + $70 = $120
© Wiley 2010
Periodic Review (P) Model, Example 2: Average daily demand for
a product is 20 units. The review period is 30 days, and lead
time is 10 days. Management has set a policy of satisfying 96
percent of demand from items in stock. At the beginning of the
review period there are 200 units in inventory on hand. The daily
standard deviation of demand is 4 units. (Chase, Jacobs, & Aquilano.)
Safety Stock SS = z96σRP+L
z96 =1.75
 RP L   t RP  L
 (4)  30  10
 (4)  (6.325)
 25.298
Area = .46
Stockout!
Tail Area = .04
Area left
of y-axis =
.50
Safety Stock SS =
(1.75)(25.298) = 44.27 -> 45
0
© Wiley 2010
Z96 = 1.75
z
Periodic Review (P) Model, Example 2, continued.
We found Safety Stock SS = (1.75)(25.298)
= 44.27 -> 45
Next find the Target Inventory level (TI):
TI = d(RP + L) + SS
= (20)(30+10) + 45
= 845 units
Follow-up: if you have 200 units on hand (OH =200),
Order quantity q =
TI – OH = 845 – 200 = 645
© Wiley 2010
Periodic Review (P) Model, Example 2, extended: Suppose that
the unit order cost is S = $120 and the unit holding cost is H=$4.
Assuming 260 working days in the year, what is the total annual cost of
inventory?
Total Annual Cost
 Annual Ordering Cost  Average Annual Ordering Cost
 no. days in work year 
 TI - dL 
 S  
 
H
 2 
 review period in days 
 260 
 845  (20)  (10) 

 120  
4
2
 30 


= $1040 + $1290 = $2330
© Wiley 2010
Economic Order Quantity
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EOQ Assumptions:
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Demand is known & constant no safety stock is required
Lead time is known & constant
No quantity discounts are
available
Ordering (or setup) costs are
constant
All demand is satisfied (no
shortages)
The order quantity arrives in a
single shipment
© Wiley 2010
Total Annual Inventory Cost
with EOQ Model
Let D= annual demand
Total annual cost
= annual ordering cost + annual holding costs
 D
Annual Ordering Cost  (no. orders per year )  (unit ordering cost )    S
Q
Q
Annual Holding Costs  (average inventory level )  (unit holding cost )    H
2
© Wiley 2010
Total Annual Inventory Cost
with EOQ Model
 D
Q
Total Annual Cost    S    H
2
Q
Total Annual Cost is minimized
at the Economic Order Quantity
Q EOQ 
2DS
H
© Wiley 2010
Reorder Point for Q-Model
Reorder when the stock level
drops to the amount that will
be used during the lead time;
thus
R = dL
where d is the daily demand
and L is the lead time in days.
L
[Note that time units of
weeks can also be used. Just
make sure units match.]
© Wiley 2010
Continuous Review (Q) Model, Example 1: A computer assembler
has annual demand of 10,000. They want to manage inventory for circuit
boards which have an annual holding cost (H) of $6 per unit, and an
ordering cost (S) of $75. Calculate the EOQ, the reorder point (R), and TC
if the purchasing lead time is 5 days; assume 250 working days per year.
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EOQ (Q)
Q

2DS

H
2 * 10,000 * $75
 500 units
$6
Reorder Point (R)
10,000
R  dL 
* 5 days  200 units
250 days

Total Inventory Cost (TC)
 10,000 
 500 
TC  
$75  
$6  $1500  $1500  $3000
 500 
 2 
© Wiley 2010
Safety Stock for probabilistic Q-Model
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If demand or lead time is
uncertain, safety stock can be
added to improve order-cycle
service levels
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Revised Reorder Point
R = dL +SS
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Here safety stock SS =zσdL,
where z is the number of
standard deviations for the
desired service level, and σdL
is standard deviation of the
demand during lead time
© Wiley 2010
Computing Safety Stock
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Order-cycle service level is
the probability that demand
during lead time will not exceed
on-hand inventory
A 95% service level means
the stockout risk is 5%, and
has a z-score Z95=1.645
Area left
of y-axis =
.50
© Wiley 2010
Area = .45
Stockout!
Tail Area = .05
0
Z95 = 1.645
z
Safety Stock Continuous Review (Q) Model, Example 1: Back to
the computer assembler with an annual demand of 10,000. Now suppose
that they determine that demand is probabilistic and in particular normally
distributed. Calculate the Reorder Point with safety stock for a 95%
service level if σdL =10 units.
Revised Reorder Point
R = dL +SS
 10,000 
  5 days  z95   dL
 
 250 days 
 40   5 days  1.645 10
 216.45 units
© Wiley 2010
Q-model versions
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Economic Order Quantity (EOQ)
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Economic Production Quantity (EPQ)
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An optimizing method used for determining order
quantity and reorder points; can include safety stock
A model that allows for incremental product delivery
Quantity Discount Model
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Modifies the EOQ process to consider cases where
quantity discounts are available
© Wiley 2010
ABC Inventory Classification
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ABC classification is a method for determining
level of control and frequency of review of inventory
items
A Pareto analysis can be done to segment items into
value categories depending on annual dollar volume
A Items – typically 20% of the items accounting for
80% of the inventory value-use Q system
B Items – typically an additional 30% of the items
accounting for 15% of the inventory value-use Q or P
C Items – Typically the remaining 50% of the items
accounting for only 5% of the inventory value-use P
© Wiley 2010
The AAU Corp. is considering doing an ABC analysis on
its entire inventory but has decided to test the
technique on a small sample of 15 of its SKU’s. The
annual usage and unit cost of each item is shown below
© Wiley 2010
(A) First calculate the annual dollar
volume for each item
© Wiley 2010
B) List the items in descending order based on annual dollar
volume. (C) Calculate the cumulative annual dollar volume as a
percentage of total dollars. (D) Classify the items into groups
© Wiley 2010
Graphical solution For Example 12.15 showing
the ABC classification of materials
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The A items (106 and 110) account for 60.5% of the value and 13.3% of the items
The B items (115,105,111,and 104) account for 25% of the value and 26.7% of the
items
The C items make up the last 14.5% of the value and 60% of the items
How might you control each item classification? Different ordering rules for each?
© Wiley 2010
Determining Order Quantities
Lot-for-lot
Order exactly what is needed
Fixed-order Specifies the number of units to order
quantity
whenever an order is placed
Min-max
system
Order n
periods
Places a replenishment order when
the on-hand inventory falls below the
predetermined minimum level.
Order quantity is determined by total
demand for the item for the next n
© Wiley 2010
periods
Examples of Ordering Approaches
Lot for Lot Example
4
60
0
60
5
55
0
55
6
85
0
85
7
75
0
75
8
85
Fixed Order Quantity Example with Order Quantity of 200
1
2
3
4
Requirements
70
70
65
60
Projected-on-Hand (30)
160
90
25
165
Order Placement
200
200
5
55
110
6
85
25
7
75
150
200
8
85
65
Min-Max Example with min.= 50 and max.= 250 units
1
2
3
Requirements
70
70
65
Projected-on-Hand (30)
180
110
185
Order Placement
220
140
4
60
125
5
55
70
6
85
165
180
7
75
90
8
85
165
160
4
60
140
200 2010
© Wiley
5
55
85
6
85
0
7
75
85
160
8
85
0
Requirements
Projected-on-Hand (30)
Order Placement
1
70
0
40
Order n Periods with n = 3 periods
1
Requirements
70
Projected-on-Hand (30)
135
Order Placement
175
2
70
0
70
2
70
65
3
65
0
65
3
65
0
85
Justifying Smaller Order Quantities
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JIT or “Lean Systems” would recommend reducing
order quantities to the lowest practical levels
Benefits from reducing Q’s:
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Improved customer responsiveness (inventory = Lead time)
Reduced Cycle Inventory
Reduced raw materials and purchased components
Justifying smaller EOQ’s:
Q

2DS
H
Reduce Q’s by reducing setup time (S). Consider S
as a variable. “Setup reduction” is a well
documented, structured approach to reducing S.
© Wiley 2010
Inventory Record Accuracy
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Inaccurate inventory records can cause:
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Lost sales
Disrupted operations
Poor customer service
Lower productivity
Planning errors and expediting
© Wiley 2010
Inventory Record Accuracy
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Two methods are available for checking record
accuracy
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Periodic counting - physical inventory is taken periodically,
usually annually
Cycle counting-daily counting of prespecified items provides
the following advantages:
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Timely detection and correction of inaccurate records
Elimination of lost production time due to unexpected stock
outs
Structured approach using employees trained in cycle counting
© Wiley 2010
Ultimate Objective of
Inventory Management
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Provide desired customer service level
Customer service is the ability to satisfy
customer requirements
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Percentage of orders shipped on schedule
Percentage of line items shipped on schedule
Percentage of dollar volume shipped on
schedule
Idle time due to material and component
shortages
© Wiley 2010
Customer Service Level Examples
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Percentage of Orders Shipped on Schedule
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Percentage of Line Items Shipped on Schedule
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Good measure if orders have similar value. Does not capture value.
If one company represents 50% of your business but only 5% of
your orders, 95% on schedule could represent only 50% of value
Recognizes that not all orders are equal, but does not capture
$ value of orders. More expensive to measure. Ok for finished goods.
A 90% service level might mean shipping 225 items out of the total
250 line items totaled from 20 orders scheduled
Percentage Of Dollar Volume Shipped on Schedule

Recognizes the differences in orders in terms of both line items and
$ value
© Wiley 2010
Inventory Management Across
the Organization
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Inventory management policies affect
functional areas throughout
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Accounting is concerned of the cost
implications of inventory
Marketing is concerned as stocking
decision affect the level of customer
service
Information Systems is involved to tack
and control inventory records
© Wiley 2010
Chapter 12 Highlights

Raw materials, purchased components, workin-process, finished goods, distribution
inventory and maintenance, repair and
operating supplies are all types of inventory.
Inventories have several uses: anticipation
inventory is built before it is needed;
fluctuation stock provides a cushion; cycle
stock is a result of the company’s ordering
quantity; transportation inventory includes
items in transit; speculative inventory is a
buildup to protect against some future event
and MRO inventory supports daily operations
© Wiley 2010
Chapter 12 Highlights


The objectives of inventory management are to
provide the desired level of customer service, to
allow cost-efficient operations, and to minimize
inventory investment. Customer service can be
measured in several ways, including as a percentage
of orders shipped on schedule, a percentage of line
items shipped on schedule, a percentage of dollar
volume shipped on schedule, or idle time due to
material and component shortages. Cost-efficient
operations are achieved by using inventory as buffer
stocks allowing a stable year-round workforce, and
spreading the setup cost over a larger number of
Inventory performance is measured by turns/supply.
Inventory costs include item cost, holding cost,
ordering cost, and shortage cost.
© Wiley 2010
Chapter 12 Highlights


(continued)
Inventory investment is measured in inventory
turnover and/or level of supply. Inventory
performance is calculated as inventory turnover or
weeks, days, or hours of supply.
Relevant inventory costs include items costs, holding
costs, and shortage costs. Holding costs include
capital costs, storage costs, and risk costs. Ordering
costs are fixed costs for placing an order or
performing a setup. Shortage costs included costs
related to additional paperwork, additional shipping
expense, and the intangible cost of lost customer
goodwill.
© Wiley 2010
Chapter 12 Highlights


(continued)
Lot-for-lot, fixed-order quantity, min-max
systems, order n periods, periodic review
systems, EOQ models, quantity discount
models, and single-period models can be
used to determine order quantities.
Ordering decisions can be improved by
analyzing total costs of an inventory policy.
Total costs include ordering cost, holding
cost, and material cost
© Wiley 2010
Chapter 12 Highlights



(continued)
Practical considerations can cause a company
to not use the optimal order quantity, that is,
minimum order requirements
Smaller lot sizes give a company flexibility
and shorter response times. The key to
reducing order quantities is to reduce
ordering or setup costs.
Calculating the appropriate safety stock policy
enables companies to satisfy their customer
service objective at minimum costs. The
desired customer service level determines the
appropriate z value.
© Wiley 2010
Chapter 12 Highlights



(continued)
Inventory decisions about perishable products
can be made using the single-period
inventory model. The expected payoff is
calculated to assist the quantity decision
The ABC classification system allows a
company to assign the appropriate level of
control and frequency of review of an item
based on its annual dollar volume
Cycle counting is a method for maintaining
accurate inventory records. Determining what
and when to count are the major decisions
© Wiley 2010
Chapter 12 Highlights







(continued)
Order Q’s can be determined by using L4L, fixed order Q’s, minmax, order n periods, quantity discounts, and single period
systems.
Ordering decisions can be improved by analyzing TC
Smaller lot sizes increase flexibility and reduce response time.
Safety stock can be added to reorder point calculations to meet
desired service level z value.
Inventory decisions about perishable products can be made by
using the single-period inventory model.
ABC analysis can be used to assign the appropriate level of
control and review frequency based on the annual dollar volume
of each item.
Cycle counting of pre-specified items is an accepted method for
maintaining inventory records
© Wiley 2010