3-2
Learning Objectives
1. Listthe steps of the decision-making
process.
2. Describe the types of decision-making
environments.
3. Make decisions under uncertainty.
4. Use probability values to make decisions
under risk.
After completing this chapter, students will be able to:
After completing this chapter, students will be able to:
3.
3-3
Learning Objectives
5. Developaccurate and useful decision
trees.
After completing this chapter, students will be able to:
After completing this chapter, students will be able to:
4.
3-4
Introduction
What isinvolved in making a good
decision?
Decision theory is an analytic and
systematic approach to the study of
decision making.
A good decision is one that is based
on logic, considers all available data
and possible alternatives, and the
quantitative approach described here.
5.
3-5
The Six Stepsin Decision Making
1. Clearly define the problem at hand.
2. List the possible alternatives.
3. Identify the possible outcomes or states
of nature.
4. List the payoff (typically profit) of each
combination of alternatives and
outcomes.
5. Select one of the mathematical decision
theory models.
6. Apply the model and make your decision.
6.
3-6
Thompson Lumber Company
Step1 –
Step 1 – Define the problem.
The company is considering
expanding by manufacturing and
marketing a new product – backyard
storage sheds.
Step 2 –
Step 2 – List alternatives.
Construct a large new plant.
Construct a small new plant.
Do not develop the new product line
at all.
Step 3 –
Step 3 – Identify possible outcomes.
The market could be favorable or
unfavorable.
7.
3-7
Thompson Lumber Company
Step4 –
Step 4 – List the payoffs.
Identify conditional values
conditional values for the
profits for large plant, small plant, and
no development for the two possible
market conditions.
Step 5 –
Step 5 – Select the decision model.
This depends on the environment and
amount of risk and uncertainty.
Step 6 –
Step 6 – Apply the model to the data.
Solution and analysis are then used to
aid in decision-making.
8.
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Thompson Lumber Company
STATEOF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant 200,000 –180,000
Construct a small plant 100,000 –20,000
Do nothing 0 0
Table 3.1
Decision Table with Conditional Values for
Thompson Lumber
9.
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Types of Decision-Making
Environments
Type1:
Type 1: Decision making under certainty
The decision maker knows with
knows with
certainty
certainty the consequences of every
alternative or decision choice.
Type 2:
Type 2: Decision making under uncertainty
The decision maker does not know
does not know the
probabilities of the various outcomes.
Type 3:
Type 3: Decision making under risk
The decision maker knows the
knows the
probabilities
probabilities of the various outcomes.
10.
3-10
Decision Making Under
Uncertainty
1.Maximax (optimistic)
2. Maximin (pessimistic)
3. Criterion of realism (Hurwicz)
4. Equally likely (Laplace)
5. Minimax regret
There are several criteria for making decisions
under uncertainty:
11.
3-11
Maximax
Used to findthe alternative that maximizes the
maximum payoff.
Locate the maximum payoff for each alternative.
Select the alternative with the maximum
number.
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MAXIMUM IN
A ROW ($)
Construct a large
plant
200,000 –180,000 200,000
Construct a small
plant
100,000 –20,000 100,000
Do nothing 0 0 0
Table 3.2
Maximax
Maximax
12.
3-12
Maximin
Used to findthe alternative that maximizes
the minimum payoff.
Locate the minimum payoff for each alternative.
Select the alternative with the maximum
number.
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MINIMUM IN
A ROW ($)
Construct a large
plant
200,000 –180,000 –180,000
Construct a small
plant
100,000 –20,000 –20,000
Do nothing 0 0 0
Table 3.3 Maximin
Maximin
13.
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Criterion of Realism(Hurwicz)
This is a weighted
eighted average
average compromise
between optimism and pessimism.
Select a coefficient of realism , with 0≤α≤1.
A value of 1 is perfectly optimistic, while a
value of 0 is perfectly pessimistic.
Compute the weighted averages for each
alternative.
Select the alternative with the highest value.
Weighted average = (maximum in row)
+ (1 – )(minimum in row)
14.
3-14
Criterion of Realism(Hurwicz)
For the large plant alternative using = 0.8:
(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000
For the small plant alternative using = 0.8:
(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
CRITERION
OF REALISM
( = 0.8) $
Construct a large
plant
200,000 –180,000 124,000
Construct a small
plant
100,000 –20,000 76,000
Do nothing 0 0 0
Table 3.4
Realism
Realism
15.
3-15
Equally Likely (Laplace)
Considersall the payoffs for each alternative
Find the average payoff for each alternative.
Select the alternative with the highest average.
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
ROW
AVERAGE ($)
Construct a large
plant
200,000 –180,000 10,000
Construct a small
plant
100,000 –20,000 40,000
Do nothing 0 0 0
Table 3.5
Equally likely
Equally likely
16.
3-16
Minimax Regret
Based onopportunity loss
opportunity loss or regret
regret, this is
the difference between the optimal profit and
actual payoff for a decision.
Create an opportunity loss table by determining
the opportunity loss from not choosing the best
alternative.
Opportunity loss is calculated by subtracting
each payoff in the column from the best payoff
in the column.
Find the maximum opportunity loss for each
alternative and pick the alternative with the
minimum number.
3-18
Minimax Regret
Table 3.7
STATEOF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant 0 180,000
Construct a small plant 100,000 20,000
Do nothing 200,000 0
Opportunity Loss Table for Thompson Lumber
19.
3-19
Minimax Regret
Table 3.8
STATEOF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MAXIMUM IN
A ROW ($)
Construct a large
plant
0 180,000 180,000
Construct a small
plant
100,000 20,000 100,000
Do nothing 200,000 0 200,000
Minimax
Minimax
Thompson’s Minimax Decision Using Opportunity Loss
20.
3-20
Decision Making UnderRisk
This is decision making when there are several
possible states of nature, and the probabilities
associated with each possible state are known.
The most popular method is to choose the
alternative with the highest expected monetary
expected monetary
value (
value (EMV
EMV).
).
This is very similar to the expected value calculated in
the last chapter.
native i) = (payoff of first state of nature)
x (probability of first state of nature)
+ (payoff of second state of nature)
x (probability of second state of nature)
+ … + (payoff of last state of nature)
x (probability of last state of nature)
21.
3-21
EMV for ThompsonLumber
Suppose each market outcome has a probability of
occurrence of 0.50.
Which alternative would give the highest EMV?
The calculations are:
rge plant) = ($200,000)(0.5) + (–$180,000)(0.5)
= $10,000
mall plant) = ($100,000)(0.5) + (–$20,000)(0.5)
= $40,000
o nothing) = ($0)(0.5) + ($0)(0.5)
= $0
22.
3-22
EMV for ThompsonLumber
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($) EMV ($)
Construct a large
plant
200,000 –180,000 10,000
Construct a small
plant
100,000 –20,000 40,000
Do nothing 0 0 0
Probabilities 0.50 0.50
Table 3.9 Largest
Largest EMV
EMV
23.
3-23
Expected Value ofPerfect
Information (EVPI)
EVPI places an upper bound on what you should
pay for additional information.
EVPI = EVwPI – Maximum EMV
EVwPI is the long run average return if we have
perfect information before a decision is made.
EVwPI = (best payoff for first state of nature)
x (probability of first state of nature)
+ (best payoff for second state of nature)
x (probability of second state of nature)
+ … + (best payoff for last state of nature)
x (probability of last state of nature)
24.
3-24
Expected Value ofPerfect
Information (EVPI)
Suppose Scientific Marketing, Inc. offers
analysis that will provide certainty about
market conditions (favorable).
Additional information will cost $65,000.
Should Thompson Lumber purchase the
information?
25.
3-25
Expected Value ofPerfect
Information (EVPI)
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($) EMV ($)
Construct a large
plant
200,000 -180,000 10,000
Construct a small
plant
100,000 -20,000 40,000
Do nothing 0 0 0
With perfect
information
200,000 0 100,000
Probabilities 0.5 0.5
Table 3.10
EVwPI
EVwPI
Decision Table with Perfect Information
26.
3-26
Expected Value ofPerfect
Information (EVPI)
The maximum EMV without additional information is
$40,000.
EVPI = EVwPI – Maximum EMV
= $100,000 - $40,000
= $60,000
So the maximum Thompson
should pay for the additional
information is $60,000.
27.
3-27
Expected Value ofPerfect
Information (EVPI)
The maximum EMV without additional information is
$40,000.
EVPI = EVwPI – Maximum EMV
= $100,000 - $40,000
= $60,000
So the maximum Thompson
should pay for the additional
information is $60,000.
Therefore, Thompson should not
pay $65,000 for this information.
28.
3-28
Expected Opportunity Loss
Expected opportunity loss
Expected opportunity loss (EOL) is the
cost of not picking the best solution.
First construct an opportunity loss table.
For each alternative, multiply the
opportunity loss by the probability of that
loss for each possible outcome and add
these together.
Minimum EOL will always result in the
same decision as maximum EMV.
Minimum EOL will always equal EVPI.
29.
3-29
Expected Opportunity Loss
argeplant) = (0.50)($0) + (0.50)($180,000)
= $90,000
mall plant) = (0.50)($100,000) + (0.50)($20,000)
= $60,000
o nothing) = (0.50)($200,000) + (0.50)($0)
= $100,000
Table 3.11
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($) EOL
Construct a large plant 0 180,000 90,000
Construct a small
plant
100,000 20,000 60,000
Do nothing 200,000 0 100,000
Probabilities 0.50 0.50
Minimum
Minimum EOL
EOL
30.
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Sensitivity Analysis
Sensitivityanalysis examines how the decision
might change with different input data.
For the Thompson Lumber example:
P = probability of a favorable market
(1 – P) = probability of an unfavorable market
3-35
Decision Trees
Anyproblem that can be presented in a
decision table can also be graphically
represented in a decision tree.
decision tree.
Decision trees are most beneficial when a
sequence of decisions must be made.
All decision trees contain decision points
decision points
or nodes,
nodes, from which one of several alternatives
may be chosen.
All decision trees contain state-of-nature
state-of-nature
points
points or nodes,
nodes, out of which one state of
nature will occur.
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Five Steps of
DecisionTree Analysis
1. Define the problem.
2. Structure or draw the decision tree.
3. Assign probabilities to the states of
nature.
4. Estimate payoffs for each possible
combination of alternatives and states of
nature.
5. Solve the problem by computing
expected monetary values (EMVs) for
each state of nature node.
37.
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Structure of DecisionTrees
Trees start from left to right.
Trees represent decisions and outcomes
in sequential order.
Squares represent decision nodes.
Circles represent states of nature nodes.
Lines or branches connect the decisions
nodes and the states of nature.
38.
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Thompson’s Decision Tree
FavorableMarket
Unfavorable Market
Favorable Market
Unfavorable Market
Do
Nothing
Construct
Large
Plant
1
Construct
Small Plant
2
Figure 3.2
A Decision Node
A State-of-Nature Node
39.
3-39
Thompson’s Decision Tree
FavorableMarket
Unfavorable Market
Favorable Market
Unfavorable Market
Do
Nothing
Construct
Large
Plant
1
Construct
Small Plant
2
Alternative with best
EMV is selected
Figure 3.3
EMV for Node
1 = $10,000
= (0.5)($200,000) + (0.5)(–$180,000)
EMV for Node
2 = $40,000
= (0.5)($100,000)
+ (0.5)(–$20,000)
Payoffs
$200,000
–$180,000
$100,000
–$20,000
$0
(0.5)
(0.5)
(0.5)
(0.5)
