Transcript 25000

Quantitative
Module A
Decision-Making
Tools
Announcements

Skip p. 725 – 727, A More Complex
Decision Tree

Assignment 1
Problem or
Opportunity
Qualitative
Analysis
Decision
Quantitative
Analysis
Decision-making
process
Evaluation by
Manager
Decision Analysis
A structured approach to decision-making
under uncertainty.
Examples:
 Decide whether or not to bid on a piece
of property.
 Decide how much to produce of a
seasonal product.
Example: Graft Land Development
Corp.
Graft Land owns 5000 acres that are zoned to be
developed as recreational home sites. Three
development alternatives are being considered:
D1: Develop a small amount of acreage (500 acres)
D2: Develop a med. amount of acreage (2500 acres)
D3: Develop a large amount of acreage (5000 acres)
Example: Graft Land Development
Corp.
Three possible states of nature that Graft
anticipates as possibilities:
S1: Low customer demand
S2: Medium customer demand
S3: High customer demand
Payoff Table

Projected profit depends on the decision
alternative and the state of nature that
occurs.
Table 1 Payoff Table for Graft Land
(Entries in $1000’s)
D1
S1
3500
S2
3000
S3
2700
D2
1000
12500
12400
D3
-500
-250
25000
Which decision alternative would you choose?
Decision theory models
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Decision alternatives – this is a course of
action that may be chosen by the decision
maker.

States of nature – an occurrence that
affects the outcome of the decision; decision
maker has no control over the states of
nature

Payoff – benefit that occurs when a specific
decision is made and a specific state of
nature occurs.
Tools of Decision Theory
Payoff Table
Decision Alternatives
D1
D2
D3
D4
States of Nature
S1
S2
Payoffs
Tools of Decision Theory
Payoffs

S1
Decision Tree
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Decision nodes - •
State-of-nature nodes
-
S2
S1
D1
S2
D2
D3
S1
S2
D4
S1
S2
States of Nature
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Affect the outcome of a decision

Decision-maker has little or no control
over which state will occur.

Must not overlap
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Cover the entire range of possibilities that
may occur
Decision –Making without probabilities
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Implied assumption – states of nature
are equally likely to occur.

3 approaches in text

Optimistic approach: Maximax
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Conservative approach: Maximin

Equally likely
Optimistic approach
Determines the best possible outcome for Graft.
Graft Payoff Table

D1
S1
3500
S2
3000
S3
2700
D2
1000 12500 12400
D3
-500
-250 25000
Max of maximums
Max of row
3500
12500
25000
25000
Find the maximum payoff for each decision alternative (row).
Select the decision alternative with the maximum maximum –
MAXIMAX.
Conservative approach
Determines the best of the worst possible outcome for Graft.
Graft Payoff Table

D1
S1
3500
S2
3000
S3
2700
D2
1000
12500
12400
D3
-500
-250
25000
Max of minimums
Min of row
2700
1000
-500
2700
Find the minimum payoff for each decision alternative (row).
Select the decision alternative with the maximum minimum MAXIMIN
Equally likely approach
Graft Payoff Table
D1
S1
3500
S2
3000
S3
2700
D2
1000
12500
12400
D3
-500
-250
25000
Go to Excel
Find the average payoff for each decision alternative (row).
Select the decision alternative with the maximum average.
Equally likely approach
Deteremines the highest average outcome.
Graft Payoff Table

D1
S1
3500
S2
3000
S3
2700
D2
1000
12500
12400
D3
-500
-250
25000
Max of average
Average
3066.7
8633.3
8083.3
8633.3
Find the average payoff for each decision alternative (row).
Select the decision alternative with the maximum average.
Which is the best decision?
Approach
Decision
Optimistic
Conservative
Equally likely
D3
D1
D2
•Must be decided in the context of the
problem – manager’s decision
Which is the best decision?
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Sometimes the biggest benefit for the manager
in modeling the decision problem is the
PROCESS
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Structure the problem
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What will be decided?
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What are the decision alternatives?
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What states of nature will affect the outcome?
Calculate the payoff table
Decision-making with probabilities
What if Graft estimates the likelihood of
each state of nature occurring.
S1: Low customer demand P(S1) = 0.2
S2: Med. customer demand P(S2) = 0.5
S3: High customer demand P(S3) = 0.3
Would this change your decision?
Would that change your decision?
Graft Payoff Table
D1
0.2
S1
3500
0.5
S2
3000
0.3
S3
2700
D2
1000
12500
12400
D3
-500
-250
25000
Review Probability & Statistics
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P(S1) – the probability of state of nature 1
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Expected value – a measure of the central
location of a probability distribution.
Expected-value Approach
Graft Payoff Table
D1
D2
D3
0.2
S1
3500
0.5
S2
3000
0.3
S3
2700
1000
12500
12400
-500
-250
25000
Expected value
Go to Excel
Find the expected value of each decision alternative (row).
Select the decision alternative with the maximum expected
value.
Expected-value Approach
Represents the average best (with probabilities) outcome for
Graft.
Graft Payoff Table

D1
0.2
S1
3500
0.5
S2
3000
0.3
S3
2700
D2
1000
12500
12400
10170
D3
-500
-250
25000
7275
Max of expected values – Max EV
Expected value
3010
10170
Find the expected value of each decision alternative (row).
Select the decision alternative with the maximum expected
value.
EVwPI – Expected value under certainty
What if we had a crystal ball and we
knew with certainty which state of
nature would occur?
EVwPI – expected value WITH perfect
information
EVwPI
Graft Payoff Table
0.2
0.5
0.3
S1
S2
S3
D1
3500
3000
2700
D2
1000
12500
12400
D3
-500
-250
25000
If S1  D1
If S2 D2
EVwPI = 0.2(3500) + 0.5(12500) + 0.3(25000)
If S3 D3
EVwPI
Graft Payoff Table
0.2
0.5
0.3
S1
S2
S3
D1
3500
3000
2700
D2
1000
12500
12400
D3
-500
-250
25000
If S1  D1
EVwPI = 14450
If S2 D2
If S3 D3
EVPI

EVPI – expected value OF perfect
information
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How much would Graft be willing to
pay for a crystal ball?
EVPI
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EVPI
= EVwPI – Max EV
= 14450 - 10170
= 4280
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If Graft could survey people in order to
better assess the demand, they should
pay no more than $4280 for the
information (survey).
Decision Trees
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Graphical tool for a decision
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Decision nodes - •
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State-of-nature nodes - 
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A map to all possible outcomes
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Particularly useful when there is a sequence of
decisions to be made.
Decision Tree for Graft Land
Payoffs
0.2*3500 + 0.5 *3000 + 0.3* 2700
3010
Low Demand
(0.20)
Medium Demand
(0.50)
High Demand
(0.30)
3500
3000
2700
Develop Small
10170
Develop
Medium
10170
Low Demand
(0.20)
1000
Medium Demand
(0.50)
12500
High Demand
(0.30)
12400
Develop large
7275
Low Demand
(0.20)
-500
Medium Demand
(0.50)
-250
High Demand
(0.30)
25000
Hale’s TV Productions

Hale’s TV Productions (HTP) is considering producing a
pilot for a comedy series. HTP hopes to convince a
major television network to purchase the series. While
the network may reject the pilot and the series, it may
also purchase the program for 1 or 2 years. HTP may
decide to produce the pilot or transfer the rights for the
series to a competitor for $100,000.

What are the decision alternatives?
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What are the states of nature?
HTP Payoff Table
States of Nature
Alternatives
S1: Reject S2: 1 yr S3: 2 yr
D1: Produce Pilot
-100
50
150
D2: Sell
100
100
100
HTP without probabilities
States of Nature
Alternatives
S1 S2 S3 Optimistic Conservative Equally
Approach Approach Likely
D1
-100 50 150
D2
100 100 100
Max
Decision
HTP without probabilities
States of Nature
Alternatives
S1 S2 S3 Optimistic Conservative Equally
Approach Approach Likely
150
-100
33.3
D1
-100 50 150
100
100 100.0
D2
100 100 100
150
100
100
Max
D1
D2
D2
Decision
HTP with Probabilities
Assuming the probability estimates for the
states of nature are:
P(reject) = .2
P(1 yr) = .3
P(2 yr) = .5
What should the company do?
HTP with probabilities
•
Draw the decision tree.
•
Determine all expected values and Max EV.
•
Determine EVwPI.
•
Determine EVPI.
•
What’s the maximum that HTP should be willing
to spend on a survey?
HTP Decision Tree, Expected Values and
Max EV
Payoffs
Reject series
(0.20)
Run series 1 yr
(0.30)
Produce Pilot
Run series 2 yrs
(0.50)
-100
50
150
Sell rights
100
HTP Payoff Table and Expected
Values
0.2 0.3 0.5
States of Nature
Alternatives
S1 S2 S3
D1
-100 50 150
D2
100 100 100
Max EV
EV
70
100
100
HTP EVwPI and EVoPI
0.2 0.3 0.5
States of Nature
Alternatives S1 S2
S3
D1
-100 50 150
D2
100 100 100 EVwPI
Best if Si
occurs
100 100 150
125
EVPI = EVwPI – Max EV
= 125 – 100
= 25
Excel OM Spreadsheet