Operation management 6e by russel and taylor ch13

Chapter 13
Inventory Management
Operations
Operations Management
Management -- 66thth Edition
Edition
Roberta Russell & Bernard W. Taylor, III

Copyright 2009 John Wiley & Sons, Inc.

Beni Asllani
University of Tennessee at Chattanooga


Lecture Outline
 Elements of Inventory Management
 Inventory Control Systems
 Economic Order Quantity Models
 Quantity Discounts
 Reorder Point
 Order Quantity for a Periodic Inventory
System
Copyright 2009 John Wiley & Sons, Inc.

13-2


What Is Inventory?
 Stock of items kept to meet future
demand
 Purpose of inventory management




how many units to order
when to order

Copyright 2009 John Wiley & Sons, Inc.

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Inventory and Supply Chain
Management
 Bullwhip effect









demand information is distorted as it moves away
from the end-use customer
higher safety stock inventories to are stored to
compensate

Seasonal or cyclical demand
Inventory provides independence from vendors

Take advantage of price discounts
Inventory provides independence between
stages and avoids work stoppages
Copyright 2009 John Wiley & Sons, Inc.

13-4


Inventory and Quality
Management in the Supply Chain
 Customers usually perceive quality
service as availability of goods they want
when they want them
 Inventory must be sufficient to provide
high-quality customer service in QM

Copyright 2009 John Wiley & Sons, Inc.

13-5


Types of Inventory
 Raw materials
 Purchased parts and supplies
 Work-in-process (partially completed)
products (WIP)
 Items being transported
 Tools and equipment
Copyright 2009 John Wiley & Sons, Inc.

13-6


Two Forms of Demand
 Dependent



Demand for items used to produce
final products
Tires stored at a Goodyear plant are
an example of a dependent demand
item

 Independent



Demand for items used by external
customers
Cars, appliances, computers, and
houses are examples of independent
demand inventory
Copyright 2009 John Wiley & Sons, Inc.

13-7


Inventory Costs
 Carrying cost

 cost of holding an item in inventory

 Ordering cost
 cost of replenishing inventory

 Shortage cost
 temporary or permanent loss of sales
when demand cannot be met
Copyright 2009 John Wiley & Sons, Inc.

13-8


Inventory Control Systems
 Continuous system (fixedorder-quantity)


constant amount ordered
when inventory declines to
predetermined level

 Periodic system (fixed-timeperiod)


order placed for variable
amount after fixed passage of
time

Copyright 2009 John Wiley & Sons, Inc.

13-9


ABC Classification
 Class A



5 – 15 % of units
70 – 80 % of value

 Class B



30 % of units
15 % of value

 Class C



50 – 60 % of units
5 – 10 % of value
Copyright 2009 John Wiley & Sons, Inc.

13-10


ABC Classification: Example

PART
1
2
3
4
5
6
7
8
9
10

UNIT COST

ANNUAL USAGE

$ 60
350
30
80
30
20
10
320
510
20

90
40
130

60
100
180
170
50
60
120

Copyright 2009 John Wiley & Sons, Inc.

13-11


ABC Classification:
Example (cont.)
PART

9
8
2
1
4
3
6
5
10
7

TOTAL
PART

VALUE

$30,600
1
16,000
2
14,000
3
5,400
4
4,800
5
3,900
3,600
6
CLASS
3,000
7
2,400
A
8
1,700
B
9
C
$85,400

10

% OF TOTAL % OF TOTAL

UNIT
ANNUAL
USAGE
VALUECOSTQUANTITY
% CUMMULATIVE

35.9
6.0
$ 60
18.7
5.0
350
16.4
4.0
30
6.3
9.0
5.680
6.0
4.630
10.0
%
OF
TOTAL
4.2
18.0
ITEMS20
VALUE
3.510
13.0

12.0
9, 8,2.8
2
71.0
320
17.0
1, 4,2.0
3
16.5
5107
6, 5, 10,
12.5

20

Copyright 2009 John Wiley & Sons, Inc.

6.0
90
11.0
A40
15.0
130
24.0
30.0
B60
100
40.0
% OF TOTAL
58.0

180QUANTITY
71.0
170
C
83.0
50 15.0
100.0
25.0
60 60.0
120

Example 10.1

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Economic Order Quantity
(EOQ) Models
 EOQ


optimal order quantity that will
minimize total inventory costs

 Basic EOQ model
 Production quantity model

Copyright 2009 John Wiley & Sons, Inc.

13-13

Assumptions of Basic
EOQ Model
 Demand is known with certainty and
is constant over time
 No shortages are allowed
 Lead time for the receipt of orders is
constant
 Order quantity is received all at once

Copyright 2009 John Wiley & Sons, Inc.

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Inventory Order Cycle
Inventory Level

Order quantity, Q

Demand
rate

Average
inventory

Q
2

Reorder point, R

0

Lead
time
Order Order
placed receipt

Lead
time
Order Order
placed receipt

Copyright 2009 John Wiley & Sons, Inc.

Time

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EOQ Cost Model
Co - cost of placing order
Cc - annual per-unit carrying cost

D - annual demand
Q - order quantity

Annual ordering cost =
Annual carrying cost =

Total cost =

CoD
Q

+

Co D
Q
CcQ
2
CcQ
2

Copyright 2009 John Wiley & Sons, Inc.

13-16


EOQ Cost Model
Proving equality of
costs at optimal point

Deriving Qopt
TC =

Co D
Q
CoD

+

CcQ
2

Cc
∂TC
=–
+
2
∂Q
Q
2
0=–
Qopt =

C0 D
Q2

+

Cc

Co D
Q

=

Q =
2

2

2CoD
Cc

Copyright 2009 John Wiley & Sons, Inc.

Qopt =

CcQ
2
2CoD
Cc
2CoD
Cc

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EOQ Cost Model (cont.)
Annual
cost ($)

Total Cost
Slope = 0
Carrying Cost =

Minimum
total cost

Ordering Cost =
Optimal order
Qopt
Copyright 2009 John Wiley & Sons, Inc.

CcQ
2

CoD
Q

Order Quantity, Q

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EOQ Example
Cc = $0.75 per gallon
Qopt =
Qopt =

Co = $150

2CoD
Cc
2(150)(10,000)
(0.75)

Qopt = 2,000 gallons

Orders per year = D/Qopt

TCmin =
TCmin =

D = 10,000 gallons
CoD
Q

+

CcQ
2

(150)(10,000) (0.75)(2,000)
+
2,000
2

TCmin = $750 + $750 = $1,500
Order cycle time = 311 days/(D/Qopt)

= 10,000/2,000
= 5 orders/year
Copyright 2009 John Wiley & Sons, Inc.

= 311/5
= 62.2 store days
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Production Quantity
Model
 An inventory system in which an order is
received gradually, as inventory is
simultaneously being depleted



AKA non-instantaneous receipt model
assumption that Q is received all at once is relaxed

 p - daily rate at which an order is received over
time, a.k.a. production rate
 d - daily rate at which inventory is demanded
Copyright 2009 John Wiley & Sons, Inc.

13-20


Production Quantity Model
(cont.)
Inventory
level

Q(1-d/p)

Maximum
inventory
level

Q
(1-d/p)
2

Average
inventory
level

0
Order
receipt period

Begin
End
order order
receipt receipt

Copyright 2009 John Wiley & Sons, Inc.

Time

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Production Quantity Model
(cont.)
p = production rate
Maximum inventory level = Q -

d = demand rate
Q
d
p

=Q1-

d
p

Q
d
Average inventory level =
1p
2

Qopt =

2CoD
d
Cc 1 - p

CoD CcQ
d
TC =
+
1- p
Q
2
Copyright 2009 John Wiley & Sons, Inc.

13-22


Production Quantity Model:
Example
Cc = $0.75 per gallon

Co = $150

d = 10,000/311 = 32.2 gallons per day
2 Co D
Qopt =

Cc 1 - d
p

p = 150 gallons per day

2(150)(10,000)
=

Co D CcQ
d
TC =
+
1- p
Q
2
Production run =

D = 10,000 gallons

32.2
0.75 1 150

= 2,256.8 gallons

= $1,329

2,256.8
Q
=
= 15.05 days per order
p
150

Copyright 2009 John Wiley & Sons, Inc.

13-23


Production Quantity Model:
Example (cont.)

10,000
D
Number of production runs =
=
= 4.43 runs/year

2,256.8
Q
Maximum inventory level = Q 1 -

d
p

= 2,256.8 1 -

32.2
150

= 1,772 gallons

Copyright 2009 John Wiley & Sons, Inc.

13-24


Solution of EOQ Models with
Excel

Copyright 2009 John Wiley & Sons, Inc.

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