Transcript Lecture Notes

Chapter 5: Decision-making
Concepts
Quantitative Decision Making with
Spreadsheet Applications 7th ed.
By Lapin and Whisler
Decision Theory
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Making a choice from a set of alternatives.
Analyze which alternative optimizes
outcome.
Uses probability and statistics.
Want a system for making the best choice.
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Payoff table
Decision tree
Certainty
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Decision making under certainty involves
making a choice where all outcomes are
determined solely by the choice you make.
Example: Choosing what to wear.
Uncertainty
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Decision making under uncertainty
involves making a choice where the
outcomes are only partially determined by
choice. This is more complex.
Example: Whether to carry an umbrella
(or rain jacket).
Acts, Outcomes, and Events
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Acts are the decision maker’s choices.
Outcomes are the success of the decision
(level of enjoyment, amount of profit, etc)
Events are the uncertainty that can occur
in some situations.
Example
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Choose what to wear.
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Acts – available outfits.
Outcomes – how good you look.
Should you carry an umbrella?
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Act – carry an umbrella or don’t.
Event – It rains or it doesn’t
Outcomes – depend on both the act and the
event.
Decision Table
Event
(p.124)
Act
Carry Umbrella Don’t Carry
Umbrella
Rain
No rain
Stay Dry
Get Wet
Carry
Be dry and free
something extra
you don’t need
Decision Tree
Stay Dry
Rain
No Rain
Carry Umbrella
Don’t Carry Umbrella
Carry something
extra you don’t
need
Get Wet
Rain
No Rain
Be dry and free
Some Terms to Know
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Two measures:
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Uncertainty
Comparative worth/Payoff
Example (p.127)
Choosing a Movement for TippiToes
A toy manufacturer must choose among four
prototype designs for Tippi-Toes, a dancing
ballerina doll. Each prototype represents a
different technology. One is a complete
arrangement of gears and levers. The second is
similar, but it uses springs. Another works on
the principle of weights and pulleys. The fourth
design is controlled pneumatically through a
series of valves.
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Choice of movement designs is based
solely on comparison of the contributions
to profits made by the four prototypes.
Only the following three events will be
considered: Light demand(25,000 units),
Moderate demand (100,000 units) or
Heavy demand (150,000 units).
Example
Event
(level of
demand)
Light
Act (choice of movement)
Gears and Spring
Levers
Action
Weights
and
Pulleys
$25,000
-$10,000
-$125,000 -$300,000
$440,000
$400,000
$300,000
$740,000
$750,000
$700,000
Moderate $400,000
Heavy
$650,000
Pneumatic
Reducing the number of
alternatives
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An act that is dominated by another is an
inadmissable act. If every entry in a
single column of the payoff table is less
than or equal to the corresponding entry
in a column of another act then it is an
inadmissable act. The remaining acts are
admissable acts.
Example
Event
(level of
demand)
Light
Act (choice of movement)
Gears and
Levers
Spring Action
Weights and
Pulleys
$25,000
-$10,000
-$125,000
$440,000
$400,000
$740,000
$750,000
Moderate $400,000
Heavy
$650,000
Maximizing Expected Payoff:
The Bayes Decision Rule
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Suppose the following probabilities are
associated to the demand for Tippi-Toes:
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Light demand
Moderate demand
Heavy demand
.10
.70
.20
totals to 1.00
Act (Choice of Movement)
Event
Probability
Gears & Levers
(level of
demand)
Payoff
Payoff x
Prob
Spring Action
Weights & Pulleys
Payoff
Payoff x
Prob
Payoff
-$1000
-$125,000 -$12,500
Payoff x
Prob
Light
.10
$25,000
$2500
-$10,000
Moderat
e
.70
400,000
280,000
440,000 308,000
400,000
280,000
Heavy
.20
650,000
130,000
740,000 148,000
750,000
150,000
Expected
Payoff:
$412,500
$455,000
$417,500