Discussion Q

Suppose you have been given the task of reducing inventory in your company, without negatively impacting customer service. What actions might you be able to take to accomplish the task? (125-150 words) Use Taco Bell as example 

Use the attached Source only 

No Ai

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Chapter 7

Managing Inventories

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2

Learning Objectives

7-1 Define the different types and roles of inventory in the supply
chain.

7-2 Explain the financial impact of inventory on firm performance.

7-3 Explain and compute asset productivity and customer
service–related measures of inventory performance.

7-4 Calculate inventory policy parameters to minimize total
acquisition cost in continuous review, periodic review, and
single period models.

7-5 Determine the cost of a company’s service level policy.

7-6 Explain the advantages and disadvantages of different
inventory location strategies.

7-7 Describe practical techniques for inventory planning and
management.

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Learning Objective 7-1

Inventory at PolyCor

p

Inventory:

• When do I order?

• How much do I order?

• Where do I deploy the inventory?

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Learning Objective 7-

1

Types of Inventory

• Raw materials and component parts: items that are
bought from suppliers to use in the production of a produc

t

• Work in process inventory: inventory that is in the
production process

• Finished goods inventory: items that are ready for sale to
customers

• MRO inventory: maintenance, repair, and operating
supplies

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Learning Objective 7-1

Roles of Inventory

• Balancing supply and demand: decouples differences in
supply and demand requirements

• Buffers against uncertainties: variation in supply and
demand are managed with buffer (safety) stock

• Enabling economies of buying: price discounts or reduced
shipping costs

• Enabling geographic specialization: supply and demand
locations vary

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Types of Stock

• Cycle Stocks: inventory repeatedly produced/ordered and
used to fill deman

d

• Seasonal Stocks: additional inventories produced in
advance of seasonal peak demands or held after seasonal
peak supplies

• Buffer (or Safety) Stock: extra inventory held to guard
against uncertainty in demand or supply

• Speculative Stock: stock purchased or produced to hedge
against future price increases or shortages

Learning Objective 7-1

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Learning Objective 7-1

Student Activity (1 of 6)

Each of the uses of inventory described has a
particular cause. For example, safety stock is needed
because managers are uncertain about demand or
supply. For each inventory type, list the cause(s) and
how each cause could be reduced or eliminated,
thereby reducing the need for inventory.

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Learning Objective 7-2

Financial Impact of Inventory

Carrying (Holding) Costs
Ordering and Setup

Costs
Stockout Costs

• Opportunity cost (including
cost of capital)

• Storage and warehouse
management

• Taxes and insuranc

e

• Obsolescence, spoilage, and

shrinkage
• Materials handling, tracking,

and management

• Purchased items:
placing and receiving
orders

• Made items: change-
over between items

• Lost sales or
customer loyalty

• Expediting
• Schedule disruption

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Learning Objective 7-2

Student Activity (2 of 6)

Using your library’s electronic databases or a Web
browser, find three articles that describe specific
companies and their efforts to reduce inventory.
Summarize the different reasons given for the desire
to reduce inventory.

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0

Measures of Inventory Performance:
Inventory Turnover (1 of 2)

Inventory Turnover: ratio between average
inventory on hand and level of sales

= Cost of goods sold/Average inventory at cost

= Net sales/Average inventory at selling price

= Unit sales/Average inventory in units

Learning Objective 7-3

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Learning Objective 7-3

Measures of Inventory Performance:
Inventory Turnover (2 of 2)

Advantages of high turnover:

• “Fresh” inventory from high sales

• Reduced risk of obsolescence or need to mark down

• Reduced total carrying costs

• Lower asset investment and higher productivity

Dangers of high turnover:

• Stockouts may mean lower sales

• Increased costs from missing quantity requirements

• Increased purchasing, ordering, and receiving time,
effort, and cost

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Learning Objective 7-3

Measures of Inventory Performance:
Inventory Turnover—Example 7-2

Suppose a firm has an annual cost of goods sold of $500
million and its average inventory level during the year is
$80 million at cost. What is the firm’s inventory turnover?

Inventory turnover

=

= Cost of goods sold/Average inventory level

= $500/$80

= 6.25 turns

Or, in terms of days

= 365 days/6.25 times

= 58.4 days

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Learning Objective 7-3

Measures of Inventory Performance: Days of
Supply, Service Level, Stockouts

• Days of Supply: length of time operations can be
supported with inventory on hand

• Service Level: ability to meet customer demand
without a stockout

• Stockout: no inventory is available

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Measures of Inventory Performance: Days of
Supply—Example 7-3

Suppose there are currently 2,000,000 finished
automobiles sitting in dealer or manufacturing
facility lots. If expected sales of automobiles are
25,000 units per day, how many days of supply are
there?

= Current inventory/Expected daily sales

= 2,000,000/2

5,000

= 80 days

Learning Objective 7-3

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Student Activity (3 of 6)

Choose three companies that are competitors in an
industry of interest to you. Find their most recent
annual reports and compute and compare their
inventory turnover ratios. Explain the financial and
marketing implications of the differences in
inventory turnover rates for each of the three
companies.

Learning Objective 7-3

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Learning Objective 7-4

Inventory Management Systems (1 of 2)

• Independent Demand: demand for an item is
beyond control of the organizatio

n

• Dependent Demand: demand for an item is
driven by demand for another item

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Learning Objective 7-4

Inventory Management Systems (2 of 2)

• Continuous Review Model: inventory is
constantly monitored to decide when a
replenishment order needs to be placed

• Periodic Review Model: management system
built around checking and ordering inventory at
some regular interval

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Total Acquisition Costs (1 of 2)

• Total Acquisition Cost: sum of all relevant annual
inventory costs

– Holding Costs: associated with storing and assuming
risk of having inventory

– Ordering Costs: associated with placing orders and
receiving supply

Learning Objective 7-4

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Total Acquisition Costs (2 of 2)

TAC = annual ordering cost + annual carrying cost

TAC = Co (D/Q) + UCi * Q/2

N = D/

Q

I = Q/2

Where:

N = orders per year I = average inventory level

D = annual demand Co= order cost

Q = order quantity U = unit cost

Ci = % carrying cost per year

Learning Objective 7-4

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Total Acquisition Costs—Example 7.4

If we need 3,000 units per year at a unit price of $20 and
we order 500 each time, at a cost of $500 per order, with
a carrying cost of 20 percent, what is the TAC?

N = D/Q = 3000/500 = 6 orders per year

I = Q/2 = 500/2 = 250 average inventory

TAC = ordering cost + carrying cost

= Co (D/Q) + (UCi )(Q/2)

= $50 (3000/500) + ($20 × 20%) × (500/2)

= $1,300

Where:

N = D/Q Q = 500 I = Q/2

U = $20 D = 3,000 Co = $50 Ci = 20%

Learning Objective 7-4

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Total Acquisition Costs—Example 7.5

If we need 3,000 units per year at a unit price of $20 and
we order 200 each time, at a cost of $500 per order, with
a carrying cost of 20 percent, what is the TAC?

N = D/Q = 3000/200 = 15 orders per year

I = Q/2 = 200/2 = 100 average inventory

TAC = ordering cost + carrying cost

= Co(D/Q) + (UCi)(Q/2)

= $50(3000/200) + ($20 × 20%) × (200/2)

= $1,150

Where:

N = D/Q Q = 200 I = Q/2

U = $20 D = 3,000 Co = $50 Ci = 20%

Learning Objective 7-4

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Total Acquisition Costs Comparison

Figure 7-1 Trexoid Inventory Saw-Tooth Diagram: Order
Quantity 500

Figure 7-2 Trexoid Inventory Saw-Tooth Diagram: Order
Quantity 200

Learning Objective 7-4

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Learning Objective 7-4

Economic Order Quantity (EOQ) (1 of 4)

• Economic Order Quantity (EOQ): minimizes
total acquisition costs; points at which ordering
costs and carrying costs are equal

EOQ

=
2DC

0

UC

i

D = Annual Demand

C
0

= Ordering cost

U =Unit cost

C
i
=Holding cost

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Learning Objective 7-4

Economic Order Quantity (EOQ) (2 of 4)

Example 7-6

If we need 3,000 units per year at a unit price of $20, at a
cost of $50 per order with a carrying cost of 20 percent,
what is lowest TAC order quantity?

EOQ =
2DC

0

UC
i

=
2´3000´50

20´20%

=273.86 =

274

D = 3,000

C
0

= $50

U = $20

C
i
= 20%

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Learning Objective 7-4

Economic Order Quantity (EOQ) (3 of 4)

Example 7-6

If we need 3,000 units per year at a unit price of $20, at a
cost of $50 per order with a carrying cost of 20 percent,
what is lowest TAC order quantity?

3000/274 = 10.948, rounded to 11.
Average inventory will be 137 units.

TAC = Order cost + Inventory carrying cost = 11($50)
+ 137($20)(.2) = $550 + $548 = $1,098

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Learning Objective 7-4

Economic Order Quantity (EOQ) (4 of 4)

Figure 7-3 EOQ Cost Trade-Offs

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Learning Objective 7-4

Reorder Point (1 of 2)

• Reorder Point: minimum level of inventory that
triggers a replenishment

• When to order:

ROP = d( ) t
d = average demand per time period

t = average supplier lead time

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Reorder Point (2 of 2)

Example 7-7
If you use 10 units per day, and the lead time for
resupply is 9 days, how low can your inventory get
before placing a new order?

ROP = d( ) t
= 9´10

= 90

d =10

t = 9

Learning Objective 7-4

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EOQ Extensions

Assumptions underlying EOQ:

• No quantity discounts

• No lot size restrictions

• No partial deliveries

• No variability

• No product interactions

Learning Objective 7-4

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Quantity Discounts

Determining best price break quantity:

• Identify price breaks/lot size restrictions

• Calculate EOQ for each price/lot size

• Evaluate viability of each option

• Calculate TAC for each option

• Select best TAC option

Learning Objective 7-4

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Learning Objective 7-4

Total Acquisition Costs

TAC+C
0

D

Q

æ

è
ç

ö

ø
÷+UC

i

Q

2

æ

è
ç

ö

ø
÷+UD

C
0

= Ordering cost

D = Annual demand

Q = Order quantity

U =Unit cost

C
i
=Holding cost

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Total Acquisition Costs—Without Price
Discount

Example 7-8

If we need 3,000 units per year at a unit price of $20, at a cost
of $50 per order with a carrying cost of 20 percent, what is TAC
with a Q=1,000?

Where:

C
0

= $50 D = 3,000 Q =

1,000

U = $20 C
i
= 20%

TAC =

C
o

D

Q

æ

è
ç

ö

ø
÷+UC

i

Q

2

æ

è
ç

ö

ø
÷+UD

= $50
3,000

274

æ

è
ç

ö

ø
÷+$20´ 20%

274

2

æ

è
ç

ö

ø
÷+$20´3,000

= $61,095.45

Learning Objective 7-4

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Learning Objective 7-4

Total Acquisition Costs—With Price
Discount

Example 7-8

If we need 3,000 units per year at a unit price of $19, at a cost
of $50 per order with a carrying cost of 20 percent, what is TAC
with a Q=1,000?

Where: C
0

= $50 D = 3,000 Q =1,000

U = $19 C
i
= 20%

TAC =C
o

D

Q

æ

è
ç

ö

ø
÷+UC

i

Q

2

æ

è
ç

ö

ø
÷+UD

= $50
3,000

1,000

æ

è
ç

ö

ø
÷+$19´ 20%

1,000

2

æ

è
ç

ö

ø
÷+$19´3,000

= $59,050

TAC at unit cost $20= $61,095.45, new price saves

$2,045.45

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Student Activity (4 of 6)

Think about several instances where you have
bought a larger quantity of an item than you would
normally buy. What factors influenced you to do so?
Explain how those factors relate to the discussion of
EOQ and TAC.

Learning Objective 7-4

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Learning Objective 7-4

Production Order Quantity (1 of 2)

Production Order Quantity: most economical order
quantity when units become available at rate produced









−

=

p

d
UC

DC
Q

i

p

1

2 0

D = Annual demand

C
o

= Ordering cost

C
i
=Holding cost

U =Unit cost

d = daily rate of demand

p = daily rate of production

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Learning Objective 7-4

Production Order Quantity (2 of 2)

Example 7-9

Q
p

= EOQ

D = 500,000

C
0

= $2,000

C
i
= 25%

U = $10

d = 2,000

p = 5,000

Economic Production Size:

Q
p

=
2DC

0

C
i
U 1-

d

p

æ

è
ç

ö

ø
÷

=
2´500,000´$2,000

25%´$10 1-
2,000

5,000

æ

è
ç

ö

ø
÷

= 36,514.84

= 36,515

Length of Production Days:

=Q p

= 36,515 5,000 =7.3 days

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Production Order Quantity—Example 7-9

Consider the manufacturer of the Trexoid video games you have been
ordering for your store. The manufacturer expects annual demand from
all retailers to be 500,000 units of Trexoid games. It receives orders from
retailers for, on average, 2,000 units per day (250 days per year). To
change from production of another game to production of Trexoid requires
a setup cost of $2,000. Once production of Trexoid units begins, it can
produce 5,000 units per day. The cost to produce a unit of Trexoid is $10.
Finally, the manufacturer has determined that its inventory carrying cost
is 25 percent annually. The fundamental question to answer is how many
units of Trexoid should be ordered in each production run? It is also useful
to know the length of the production run in days.

Qp= production order quantity (the same concept as EOQ)

D = annual demand = 500,000

Co= setup cost (the same concept as ordering cost in EOQ) = $2,000

Ci = annual inventory carrying cost percentage = 25%

U = unit cost = $10

d = daily rate of customer demand = 2,000

p = daily rate of production = 5,000

Learning Objective 7-4

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Student Activity (5 of 6)

Verify the difference between the Qp quantity and
the EOQ. You can do that by using the standard EOQ
formula and assuming that all items produced arrive
simultaneously.

Learning Objective 7-4

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Standard Deviation of Demand During Lead
Time (1 of 2)

Variation can occur in both demand rates and lead
times

s
ddlt

= ts
2

d
+ d 2s

2

1

s
ddlt

= standard deviation of demand during lead time

t = average lead time

s
d

= standard deviation of demand

d = average demand

s
t
= standard deviation of lead time

Learning Objective 7-4

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Standard Deviation of Demand During Lead
Time (2 of 2)

Example 7-10
Average demand is 10 units per day with standard
deviation of 1.5, and lead time of 10 days with
standard deviation of 2.5 days.

days 2.5

dayper 10

units 1.5

days 10

=

=

=

=

t

d

d

t





( )

( )

units 25.4=

+=

+=

222

2

5.2105.19

1

22
 d

d
tddlt

Learning Objective 7-4

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Determining Service Levels (1 of 2)

Service Level Policy: determining the acceptable
stockout risk level

SS =s
ddlt

SS = safety stock

z = standard deviations needed for service level

s
ddlt

= standard deviation of demand during lead time

Learning Objective 7-5

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Learning Objective 7-5

Determining Service Levels (2 of 2)

Example 7-11
Standard deviation of demand during lead time is
25.4 units, and acceptable stockout level is 5
percent (95 percent service level). From the z table
= 1.65

SS = zs
ddlt

=1.65´ 25.4

= 42 units

Safety stock carrying cost:

$19´42 units´20%=$159.60 year

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Learning Objective 7-5

Standard Deviations and Probabilities

Table 7-2 Standard Deviations and Probabilities

Number of Deviations
Required

Probability of Being in
Stock

Probability of
Stockout

1 84.13% 15.77%

1.04 85 15

1.28 90 10

1.65 95 5

1.96 97.5 2.5

2.0 97.72 2.28

2.33 99 1

3.0 99.86 0.14

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Learning Objective 7-5

Cost Related to Service Levels

Table 7-3 Cost Related to Trexoid Service Levels

Std. Deviations
of Safety Stock

Probability of
in Stock

Probability of
Stockout

Safety Stock
Required

Safety Stock
Inventory
Carrying

Cost

1 84.13% 15.77% 25 $ 95.0

1.04 85 15 26 98.8

1.28 90 10 33 125.4

1.65 95 5 42 159.6

1.96 97.5 2.5 50 190.0

2.0 97.72 2.28 51 193.8

2.33 99 1 59 224.2

3.0 99.86 0.14 76 288.8

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Learning Objective 7-5

Relationship between Inventory
Investment and Product Availability

Figure 7-4 Relationship between Inventory Investment and Product Availability

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Learning Objective 7-5

Revisiting ROP and Average Inventory

Example 7-12
Considering uncertainty

ROP = reorder point

d = average lead time

t = average demand

SS = safety stock

Q = order quantity

ROP = d ´ t( ) +

SS

average inventory =
Q

2
+ SS

ROP = 10´9( ) +42 =132 units

average inventory =

1000

2

æ

è
ç

ö

ø
÷+42=542

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Periodic Review Model (1 of 3)

Order Interval: fixed time between inventory review; on-hand
level is unknown during this uncertainty period

UP =Uncertainty period

OI = Order interval

t = lead time

d = average daily demand

z = standard deviations of safety stock desired

s
ddup

= standard deviation of demand during

the uncertainty period

A= inventory on hand

UP =OI + t

Q = d UP( ) + zs
ddup

– A

Learning Objective 7-5

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Learning Objective 7-5

Periodic Review Model (2 of 3)

Example 7-13
Orders are placed every 30 days and average lead
time is 9 days. Standard deviation of demand is 1.5
units.

UP =Uncertainty period

OI =30 days

t = 9 days

s
d

=1.5 units

UP =OI + t

= 30+9 =39 days

s
ddup

= UP( )s d

2

= 39( ) 1.52( ) = 9.37

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Learning Objective 7-5

Periodic Review Model (3 of 3)

Example 7-14
There are currently 105 units in stock.

UP =39 days

OI =30 days

t = 9 days

d =10 units

z = 95%=1.65

s
ddup

= 9.37

A =105

( )

( ) ( )

units 301=

−+=

−+=

−+=

10516390

10537.965.13910

AzUPdQ ddup

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Learning Objective 7-5

Single Period Inventory Model (1 of 2)

Single Period Inventory Model: items are ordered once,
and have little leftover value (newsvendor problem)

Target Service Level: probability of meeting all demand
for an item

C
stockout

=Unit selling price -Unit cost

C
overstock

=Unit cost +Disposal cost -Salvage value

1- TSL( ) Cstockout( ) = TSL C
overstock( )

TSL =
C
stockout

C
stockout

+C
overstock

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Learning Objective 7-5

Single Period Inventory Model (2 of 2)

Example 7-15

Units cost $10 and sell for $30, unsold units have no
value, and there is no disposal or salvage value.

C
stockout

=Unit selling price -Unit cost

C
overstock

=Unit cost +Disposal cost -Salvage value

TSL =
C
stockout

C
stockout

+C
overstock

C
so

= $30-$10 = $20

C
os

= $10+0-0 = $10

TSL =
$20

$20+$10
= .667

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Impact of Location on Inventory Requirements
(1 of 2)

Square Root Rule: estimate of impact of changing
the number of locations on quantity of inventory
held

SS
n

=

N

n

N
e

´ SS
e

SS
n

= system safety stock for the new number of locations

N
n

= total number of new locations

N
e
=number of existing locations

SS
e
= system safety stock for the number of existing locations

Learning Objective 7-6

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Impact of Location on Inventory Requirements
(2 of 2)

Example 7-16
A single warehouse currently has 1,000 units of safety stock.
How much is needed if a second warehouse is added?

410,1

1000
1

2

1000

1

2

=

=

=

=

=

=

=

e

e

n

n

e

e

n

n

SS
N

N
SS

SS

N

N

SS

locations ofnumber

new the ofstock safety

Learning Objective 7-6

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prior written consent of McGraw-Hill Education.7-54

Inventory Related to Number of Locations

Figure 7-5 Inventory Related to Number of Locations

Learning Objective 7-6

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Learning Objective 7-6

Managing Inventory

• Managing Cycle Stock: reducing lot sizes

• Managing Safety Stock: using ABC analysis and
reducing lead time

• Managing Locations: balance inventory, lead time,
and service levels

• Implementing Inventory Models: matching
management system to specific items

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Managing Inventory: ABC Analysis

• ABC Analysis: ranking inventory by importance

• Pareto’s Law: small percentage of items have a large impact
on sales, profit, or importance to a company

Figure 7-6
ABC
Classification
of Inventory

Learning Objective 7-6

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Learning Objective 7-7

Inventory Information Systems and
Accuracy

• Inventory Record Accuracy

– Cycle Counting: inventory is physically counted on

a routine schedule

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Managing Inventory Across the Supply
Chain (1 of 2)

Bullwhip Effect: variation increases upstream in the
supply chain (from consumer to manufacturers)

Figure 7-7 The Bullwhip Effect: An Example

Learning Objective 7-7

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Managing Inventory Across the Supply
Chain (2 of 2)

• Supplier-Managed Inventory (SMI): the
vendor is responsible for managing inventory for
the customer

– Vendor monitors and replenishes inventory balances

– Customer saves holding costs

– Vendor has higher visibility of inventory usage

• Collaborative Planning, Forecasting, and
Replenishment (CPFR): supply chain partners
sharing information

Learning Objective 7-7

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Blockchain

• Blockchain: a decentralized, distributed, and
public digital ledger used to record transactions
across many computers

– Provides visibility and prevents distortion of data

Learning Objective 7-7

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Student Activity (6 of 6)

Find a YouTube video (there are many) that
describes blockchain and gives an example of its
use.

Learning Objective 7-7

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Managing Inventories Summary

1. There are multiple types of inventory.

2. Inventory fulfills multiple roles.

3. Inventory is an asset, and has multiple costs.

4. An inventory policy determines how much and when to order.

5. Continuous systems monitor on-hand inventory levels.

6. Safety stock levels are linked with service levels.

7. Periodic review systems count inventory at specific intervals.

8. Number of storage locations impacts inventory levels.

9. Managers should work to reduce inventory requirements.

10. Each item must have a unique identification and accuracy.

11. Bullwhip effect occurs when a small change in demand results in a
large change up the supply chain.

12. Vendor-managed inventory may reduce bullwhip effect and overall
inventory levels.