# 003-chap2Supp2number2 by fanzhongqing

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```									    Chapter 2 Supplement 2: Decision Analysis

Second session

operations management
Quantitative decision-making techniques
for situations where uncertainty exists

1
Decision Making Criteria Under Uncertainty

» Our decision making may differ from others

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and also under different circumstances,
depending upon levels of risk, reward, and
conditions.

Example:
» Win \$1 or one chance in 10 of winning \$10

» Win \$1M or one chance in 10 of winning \$10M

2
Decision Making Criteria Under Uncertainty

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Maximax criterion            → “high-stakes gambler”
Choose decision with the maximum of the maximum payoffs

Maximin criterion             → “risk-averse”
Choose decision with the maximum of the minimum payoffs

Minimax regret criterion           → “minimum regret”
Choose decision with the minimum of the maximum regrets
for each alternative

3
Situation

» There are two lines, each with a “prize”.

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Which line will you chose?

» Line 1: Fast food
coupon worth \$10

» Line 2: Restaurant coupon
worth \$100
OR
\$1 free soft drink coupon

4
Payoff Table

Choice?                        Outcome 1               Outcome 2

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Line 1                 \$10 fast food coupon     \$10 fast food coupon
Line 2                 \$100 restaurant coupon   \$1 soft drink coupon

Maximax criterion
Choose decision with the maximum of the maximum
payoffs

Line 1 max payoff =
Line 2 max payoff =
Maximax →

5
Payoff Table

Choice?                        Outcome 1               Outcome 2

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Line 1                 \$10 fast food coupon     \$10 fast food coupon
Line 2                 \$100 restaurant coupon   \$1 soft drink coupon

Maximin criterion
Choose decision with the maximum of the minimum
payoffs

Line 1 min payoff =
Line 2 max payoff =
Maximin →

6
Payoff Table

Choice?                        Outcome 1               Outcome 2

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Line 1                 \$10 fast food coupon     \$5 fast food coupon
Line 2                 \$100 restaurant coupon   \$1 soft drink coupon

Minimax regret criterion
Choose decision with the minimum of the maximum
regrets for each alternative

Line 1 max regret =
Line 2 max regret =
Minimax regret →

7
Decision Making with Probabilities

 Risk involves assigning probabilities to states of

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nature

 Expected value is a weighted average of
decision outcomes in which each future state of
nature is assigned a probability of occurrence

8
Expected Value

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n
EV (x) =    p(xi)xi
i =1

where
xi = outcome i
p(xi) = probability of outcome i

9
Decision Analysis

We’ve dealt with states of nature, and

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probabilities of outcomes…

What about situations that are far
more complex? Where there are
more steps in a situation analysis?

10
Sequential Decision Trees

 A graphical method for analyzing decision

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situations that require a sequence of decisions
over time
 Decision tree consists of
 Square nodes - indicating decision points

 Circles nodes - indicating states of nature

 Arcs - connecting nodes

11
Simple Decision Tree

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OUTCOME

DECISION POINT    ARCS CONNECTING NODES

OUTCOME

12
Simple Decision Tree

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STATE or OUTCOME “A”
probability of
outcome A

DECISION POINT

probability of
outcome B
STATE or OUTCOME “B”

13
Expected Value Class Experiment

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EV = 1* \$.01
= \$0.01
guaranteed
P=1.00

3 in a row
P=⅛

3H/T EV = ⅛* \$.08
= \$0.01
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Expected Value Class Experiment

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EV = 1* \$.10
= \$0.10
guaranteed
P=1.00

3 in a row
P=⅛

3H/T EV = ⅛* \$.80
= \$0.10
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Expected Value Class Experiment

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EV = \$1.00

guaranteed
P=1.00

3 in a row
P=⅛

3H
EV = \$1.00

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Sequential Decision Tree

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C

A

DECISION POINT
D

B

17
Sequential Decision Tree: Education Decisions

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yes MBA

yes     MBA?

Stay in school?
no BS/BA

no    HS diploma

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Decision Analysis: Replace Tire?

There are two “states of nature: “flat” and “no flat”
With probabilities of 0.1 and 0.9 respectively

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new Cost = \$50
YES

replace
tire?
flat   Cost = \$50 (tire) + \$100 (tow)

NO           Probability = 0.1

Probability = 0.9

no
Cost = \$0
flat

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Decision Analysis: Investment

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Up
0.2

Purchase          0.6
Mod
mutual fund
0.2
Down          Stock split
Invest?                             0.2

0.2
Up
0.8
Purchase         0.6
Individual             Mod           No split
stock           0.2
Down

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Decision Analysis: Investment

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Probabilities on any “branch”
0.2
must sum to 1.0
Purchase          0.6
mutual fund
0.2

Stock split
Invest?                          0.2

0.2
0.8
Purchase         0.6
Individual                          No split
stock           0.2

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Decision Analysis: Investment

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120%   Investment “growths”
0.2            at each “leaf” are
“states of nature”
Purchase           0.6
\$100          110%
mutual fund
0.2
90%       +110% Stock split
Invest?                              0.2

140%
0.2
0.8
Purchase          0.6
Individual \$100         115%         100% No split
stock            0.2
75%

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Decision Analysis: Investment

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EV = probability x growth x \$100
120%   EV = (0.2)(1.2)(\$100)
0.2
EV = \$24
Purchase           0.6
\$100          110%
mutual fund
0.2
90%             +110% Stock split
Invest?                                    0.2

140%
0.2
0.8
Purchase          0.6
Individual \$100         115%               100% No split
stock            0.2
75%

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Decision Analysis: Investment

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120%   EV = probabilityGrowth x growth x
0.2
probabilitySplit x growthSplit
Purchase           0.6          EV = (0.2)(1.4)(0.2)(1.1)(\$100)
\$100          110%
mutual fund                      EV = \$6.16
0.2
90%        +110% Stock split
Invest?                                0.2

140%
0.2
0.8
Purchase          0.6
Individual \$100         115%           100% No split
stock            0.2
75%

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Decision Analysis: Investment

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120% \$24
0.2

Purchase           0.6
\$100          110% \$66
mutual fund
0.2
90% \$18      +110%\$6.16
Invest?                                  0.2
Stock split
140%
0.2
0.8
Purchase          0.6
Individual \$100         115% \$69         100% \$22.40
stock            0.2              No split
75% \$15

25
Decision Analysis: Investment

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120% \$24
0.2

Purchase           0.6
\$100          110% \$66    \$108
mutual fund
0.2
90% \$18      +110%\$6.16
Invest?                                  0.2
Stock split
140%
0.2
Purchase                            0.8                \$112.56
0.6
Individual \$100         115% \$69         100% \$22.40
stock            0.2              No split
75% \$15

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Situation analysis: Need a car

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» Have up to \$7,000 to spend
» Expect to keep it 5 years
» New or old? What make? Warranty?
» Whether to / how to finance?
Caveats
» This example based on 2005 data
» Does not factor
– costs assigned to unreliability
– benefits assigned to “newness” factor
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States of nature (financial)?

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» Expense
– New cars higher than used cars
» Depreciation rate
– New car depreciation higher, varies among makes
» Repair cost
– Higher for older vehicles, varies among makes
» Cost-of-money
– If auto loan is needed

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Automobile Depreciation

1.2
Porsche 911
Honda Civic
1

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Chevy Cavalier
Buick Regal
0.8
n          years to 50%
value

0.6

3      4                  7                 9
0.4

0.2

0
2004
0      2003
1    2002
2     2001
3     2000
4     1999
5     1998
6     1997
7         1996
8      1995
9     1994
10    1993
11
29 Ref:   http://www.kbb.com/                   years past purchase

User choices narrowed to:

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1. 2005 Honda Civic Coupe EX              \$18,150
– 2 door, automatic, 4 cylinder, 1.7 liter VTEC
– bucket seats, CD, cruise, AC, AB, custom wheels, keyless entry
2. 1995 Honda Civic Coupe EX                \$6,695
– 84,000 miles
3. 2005 Chevy Cavalier LS Sport \$17,975
– 2 door, automatic, 4 cylinder, 2.2 liter
– bucket seats, CD, cruise, AC, AB, custom wheels, keyless entry
4. 1998 Chevy Cavalier LS Sport             \$6,695
– 72,000 miles

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First two decisions

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new
new or
Honda Civic EX
used

used
which
make?

new
new or
Chevy Cavalier           used

used

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new
Honda Civic EX   new or
used
used
which

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make?
new
Additional Decision Path for Used Cars
new or
Chevy
used
used

Y   warranty cost
warranty?

used

P1      repair cost 1

N

P2      repair cost 2
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Complete Decision Tree

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new
new or                                        Y   warranty cost
Honda Civic EX
used                       warranty?
used
which
make?

new
new or                        Y               N
repair costs
Chevy Cavalier    used
warranty?     warranty cost
used

N           repair costs

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Auto Depreciation: Honda Civic & Chevy Cavalier

20000
Honda Civic
18000
Chevy Cavalier

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16000
purchase price (dollars)

14000

12000

10000

8000

6000

4000

2000

0
2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993
0    1    2    3    4    5    6    7     8    9   10   11
Ref:                       http://www.kbb.com/
year of manufacture
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new
Honda Civic EX   new or
used
used

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which
make?
new
Assumed Repair Costs for Used Cars
new or
Chevy
used
used

Y \$1695
warranty?

used

P=0.20        \$5000

N            repair cost

P=0.80        \$1000
35

C = \$18,150

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new    D = \$7,130                                    C = \$6,695
new or                                             Y    \$1695 D = \$1,100
Honda Civic EX
used            I = \$7,500       warranty?                  RC = \$1,800
used                                                 I = \$5,000
which                            95
make?
C = \$17,975                            P=0.20        \$5000
new    D = \$10,345
new or                              Y   \$1695      N            repair cost
Chevy Cavalier     used
I = \$7,500
warranty?
used                                          P=0.80        \$1000
98
P=0.20         \$5000
C = \$6,695
C = cost of purchase                                 N            repair cost
D = \$2,935
D = depreciation                                                                RC = \$1,800
I = insurance                                            P=0.80         \$1000    I = \$5,000
RC = repair (non-warranty option)
36
Sequential Decision Tree

AC = Expected Accumulated Cost per 5 years (non-financed) after sale of car

operations management
new    AC = 14,630
new or                                          Y   AC = \$7,795
Honda Civic EX
used                             warranty?
used
which
make?

new    AC = \$17,845
N
Chevy Cavalier
new or                              Y                  AC = \$7,900
used
warranty?
AC = \$9,735
used

N         AC = \$9,630

37
Sequential Decision Tree
NC = Expected Net Cost per 5 years 5 year loan available at 6% APR after sale

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new    NC = \$16,230
new or                                         NC = \$7,795
Honda Civic EX
used                             warranty?
used
which
make?

new    NC = \$19,445
NC =         N
Chevy Cavalier
new or                                                 NC = \$7,900
used
warranty?   \$10,145
used

N         NC = \$10,250

38

Cost* of Vehicle for Five Years

operations management
New                 Used         Used
car              no warranty    warranty
Honda                 \$16,230                  \$7,900     \$7,795
Civic EX
Chevy                 \$19,445                  \$10,250   \$10,145
Cavalier LS
Sport

* depreciation, insurance, financing, repair

39
Decision Analysis: Life Insurance

» Decision:

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• Higher cost
• Provides accumulated cash value
• Covers until old age
• Lower cost
• No cash value
• Limited term
» States of nature
– ROI from whole life insurance
– ROI from “investing the difference” between whole & term
– ROI from investing the difference in 401K

40
Decision Analysis: Home Purchase

» Decision:
– Rental housing

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•   Lower initial cost
•   Limited term
•   More flexibility
•   No tax savings
•   Higher initial cost, lower long term cost
•   Provides accumulated equity
•   Provides unlimited term living
•   Potential large tax savings
» States of nature
– Home appreciation rates
– Rental rate increases
– Mortgage rates

41

States of nature

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» Family income of \$60,000/year
» Tax bracket: 50%
» Condo rental: \$2000/month
» Home purchase: \$3000/month, of which \$1500 is
interest payment and deductable at 50% rate
» Home appreciation
–   5% chance of no appreciation
–   25% chance of \$10,000 appreciation per year
–   50% chance of \$20,000 appreciation per year
–   20% chance of \$40,000 appreciation per year
“Long term cost” of home purchase: ~\$1400 per month
42

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