Transcript BA 555 Practical Business Analysis Decision Analysis PrecisionTree 

BA 555 Practical Business Analysis
Agenda
 Decision Analysis
 PrecisionTree
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Decision-making under Certainty
 Decision-making under certainty entails the
selection of a course of action when we know the
results that each alternative action will yield.
 This type of decision problems can be solved by
linear/integer programming technique.
 Example: A company produces two different auto
parts A and B. Part A (B) requires 2 (2) hours of
grinding and 2 (4) hours of finishing. The company
has two grinders and three finishers, each of which
works 40 hours per week. Each Part A (B) brings a
profit of $3 ($4). How many items of each part
should be manufactured per week?
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Decision-making under Uncertainty
 Decision-making under uncertainty entails the selection of a course
of action when we do not know with certainty the results that each
alternative action will yield.
 This type of decision problems can be solved by statistical techniques
along with good judgment and experience.
 Example 1 (p.105). McCovery Development Co. has purchased land
in Texas, on the shore of the Gulf of Mexico, and is attempting to
determine the size of the condominium complex it should build. Three
sizes are being considered: small, medium, and large. Management
also contemplates three possible levels of demand: low, medium, and
high, each equally probable. (1). If the demand is high, McCovey will
make $900K if they build the large complex, $600K if they build the
medium complex, and $400K if they build the small complex. (2). If the
demand is medium, McCovey will make $300K if they build the large
complex, $600K if they build the medium complex, and $400K if they
build the small complex. (3). If the demand is low, McCovery will lose
$300K if they build the large complex, will make $100K if they build the
medium complex, and will make $400K if they build the small complex.
What is the optimal strategy of the company?
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Elements of a Decision Analysis
(p.106)
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Alternative/Action: An alternative (or action) is a course of action intended to
solve a problem.
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State of Nature and Probabilities: The uncontrollable future events that affect
the payoff associated with a decision alternative.
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Low demand (1/3)
Medium demand (1/3)
High demand (1/3)
Payoff: The outcome measure, such as profit or cost. Each combination of a
decision alternative and a state of nature has an associated payoff.
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Build a small size of condominium complex
Build a medium size of condominium complex
Build a large size of condominium complex
If the demand is high, McCovey will make $900K if they build the large complex.
If the demand is low, McCovery will lose $300K if they build the large complex.
Payoff Matrix: A tabular representation of the payoffs for a decision problem.
The rows of the matrix correspond to the decision alternatives, and the columns
of the matrix correspond to the possible states of nature.
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Decision Rules for Single-Stage
Decision Problems
 The Maximax Decision Rule
 The Maximin Decision Rule
 The Minimax Regret Decision Rule
 The Expected Monetary Value Decision Rule
 The Expected Regret Decision Rule
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The Maximax Decision Rule
Decision maker optimistically believes that nature will always be “on her/his side”
regardless of what decision s/he makes. The decision is made on the alternative that
leads to the largest possible payoff.
Step 1. determine the maximum payoff for each alternative.
Step 2. choose the alternative associated with the largest maximum payoff.
Decision
Small
Medium
Large
Low
$400
$100
($300)
Medium
$400
$600
$300
High
$400
$600
$900
MAX
$400
$600
$900
** optimal decision
Counterexample:
Decision
A
B
1
30
29
State of Nature
2
-10000
29
MAX
30
29
** optimal decision
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The Maximin Decision Rule
Decision maker pessimistically assumes that nature will always be “against her/him”
regardless of what decision s/he makes. This decision rule can be used to hedge against
the worst possible outcome of a decision.
Step 1. determine the minimum payoff for each alternative.
Step 2. choose the alternative associated with the largest minimum payoff.
Decision
Small
Medium
Large
Low
$400
$100
($300)
Medium
$400
$600
$300
High
$400
$600
$900
min
$400
$100
($300)
** optimal decision
Counterexample:
Decision
A
B
1
1000
29
State of Nature
2
28
29
MAX
28
29
** optimal decision
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The Minimax Regret Decision
Rule
 Regret Matrix: a table summarizes the possible opportunity losses
that could result from each decision alternative under each state of
nature. Each entry in the regret matrix shows the difference between
the maximum payoff that can occur under a given state of nature and
the payoff that would be realized from each alternative under the same
state of nature.
Small Complex
Medium Complex
Large Complex
Low Demand
$0
$300
$700
States of Nature
Medium Demand
$200
$0
$300
High Demand
$500
$300
$0
Probability
0.333
0.333
0.333
Regret Matrix
Alternatives
(Actions)
Step 1. create a regret matrix
Step 2. determine the maximum regret for each alternative.
Step 3. choose the alternative associated with the smallest maximum regret.
Decision
Small
Medium
Large
Low
$0
$300
$700
Medium
$200
$0
$300
High
$500
$300
$0
MAX
$500
$300
$700
** optimal decision
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The EMV Decision Rule
 Expected Monetary Value (EMV): the weighted
average of the payoffs, with weights given by the
probabilities of the different states of nature. This
rule selects the decision alternative with the largest
expected monetary value.
Step 1. calculate the EMV for each alternative
Step 2. choose the alternative associated with the largest EMV.
Decision
Small
Medium
Large
Low
$400
$100
($300)
Medium
$400
$600
$300
High
$400
$600
$900
Probability
0.333
0.333
0.333
EMV
$400
$433
$300
** optimal decision
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The Expected Opportunity Loss
Decision Rule
Step 1. calculate the EOL from the regret matrix for each alternative.
Step 2. choose the alternative associated with the smallest EOL.
Decision
Small
Medium
Large
Low
$0
$300
$700
Medium
$200
$0
$300
High
$500
$300
$0
Probability
0.333
0.333
0.333
EOL
$233
$200
$333
** optimal decision
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Decision Tree Using the EMV Rule
a decision Read
node (box),
the choose
tree the branch with the best EMV. Decision Tree is a graphical
a chance node (circle), compute the EMV.
representation of the decision problem
from left to right
LowD
33.3%
400
Small
FALSE
0
400
400
33.3%
400
HighD
33.3%
0
400
0
400
400
33.3%
33%
100
100
33.3%
33%
Size
433.3333333
LowD
Medium
TRUE
0
433.3333333
600
600
HighD
33.3%
33%
600
600
LowD
33.3%
-300
FALSE
0
In a decision tree,
•decisions are denoted by boxes.
•random (uncertain) outcomes are
denoted by circles.
Demand
MediumD
Large
that shows the sequential nature of the
decision-making process.
Demand
MediumD
Apt Complex
0
0
-300
Demand
300
MediumD
33.3%
300
HighD
33.3%
900
0
300
0
900
Solve the tree
from right to left
• At a box, choose the branch
with the best EMV.
• At a chance node (circle),
computer the EMV.
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Solving Multi-Stage Decision
Problems – Decision Tree
 Oilco must determine whether or not to drill for oil in the South
China Sea. It costs $1M and if oil is found the value is
estimated to be $6M. At present, Oilco believes there is a 45%
chance that the field contains oil. Before drilling, Oilco can hire
(for $100K) a geology firm to obtain more information about the
likelihood that the field will contain oil. Oilco believes there is a
50% chance that the geologist will issue a favorable report, and
a 50% chance of an unfavorable report. Given a favorable
report, there is a 80% chance that the field contains oil. Given
an unfavorable report, there is a 10% chance that the field
contains oil. Construct a decision tree to identify Oilco’s
possible actions. Clearly label each node and provide sufficient
information (e.g., payoff, probability) on each node and branch.
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Example 2
A developer is considering building a new mall in one of four cities in Texas. The
developer believes that the payoff for each decision will depend on the extent of
economic growth in the state of Texas. Below is given the future payoff table as
identified by the developer.
Austin
Dallas
El Paso
Houston
Galveston
Payoff Matrix (in $1,000,000’s)
Economic Growth
Low
Medium
High
0.80
2.00
2.50
0.90
1.80
2.20
1.10
1.90
2.40
1.50
1.70
2.00
0.90
1.80
2.10
Probability
0.20
0.40
EMV
0.40
The developer is interested in maximizing expected gain in dollars. In what city should
the mall be located?
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Expected Value of Perfect Information
Expected Value of Sample Information
 EVPI = EMV free perfect information – EMV
with no information
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How much would you pay for perfect
information?
 EVSI = EMV with free sample information –
EMV with no information
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Suppose a market research shows that the
probabilities of having a low, med., high
demand are 0.25, 0.50, 0.25.
How much would you pay for sample
information (e.g., market research)?
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