Transcript Chapter 5: Decision

Homework due next Tuesday,
September 22
p. 156 # 5-7, 5-8, 5-9
Please use complete sentences to
answer any questions and make.
Include any tables you are asked
to make.
Chapter 5: Decision-making
Concepts
Quantitative Decision Making with
Spreadsheet Applications 7th ed.
By Lapin and Whisler
Section 5-7: Decision Tree Analysis
Some slides are from Business Statistics:
A Decision-Making Approach
6th Edition found at www.clt.astate.edu/asyamil/groebner6ed/ppt/ch18ppln.ppt
The Bayes Decision Rule

Takes into account all the information about the chances
for various payoffs.
Act (Choice of Movement)
Probability
Event
(level of
demand
)
Gears & Levers
Payoff
Payoff x Payoff
Prob
Payoff x Payoff
Prob
Light
.10
$25,000
$2500
$10,000
-$1000
Moderat .70
e
400,00
0
280,000
440,00
0
308,000 400,000 280,00
Heavy
650,00
0
130,000
740,00
0
148,000 750,000 150,00
.20
Expected
Payoff:
$412,500
Spring Action
Weights & Pulleys
Payoff x
Prob
$125,000 $12,500
0
0
$455,000
$417,500
Other Decision Criteria



Maximin Payoff Criterion – choose the best
of the worst outcomes.
Maximum Likelihood Criterion – focus on
the most likely event to the exclusion of all
others.
The Criterion of Insufficient Reason –
every event has the same probability.
Table vs. Tree




Payoff table: simple decisions
Decisions made at different points in time
with uncertain events occurring between
decisions.
Tree gives more flexibility.
Tree shows every possible course of
action and all possible outcomes.
Decision Tree
A decision tree is a picture of all the
possible courses of action and the
consequent possible outcomes.




A box is used to indicate the point at which a
decision must be made,
The branches going out from the box indicate
the alternatives under consideration
A circle represents an event (usually has a
probability)
The branches going out from the circle
represent outcomes of the event.
Sample Decision Tree
Strong Economy
Large factory
Stable Economy
Weak Economy
Strong Economy
Average factory
Stable Economy
Weak Economy
Strong Economy
Small factory
Stable Economy
Weak Economy
Add Probabilities and Payoffs
(continued)
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
Average factory
90
Stable Economy (.5)
120
Strong Economy
Small factory
(.2)
(.3)
Stable Economy (.5)
Weak Economy
Uncertain Events
(States of Nature)
-120
Strong Economy (.3)
Weak Economy
Decision
(.2)
(.2)
-30
40
30
20
Probabilities Payoffs
Decision Tree Analysis

Each node is evaluated in terms of its
expected payoff.



The decision tree is folded back by
maximizing expected payoff.



Event forks: expected payoffs are computed.
Act forks: the greatest value is brought back.
Inferior acts are pruned from the tree.
The pruned tree indicates the best course of
action, the one maximizing expected payoff.
The process works backward in time.
Fold Back the Tree
EV=200(.3)+50(.5)+(-120)(.2)=61
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
EV=90(.3)+120(.5)+(-30)(.2)=81
Average factory
Small factory
-120
Strong Economy (.3)
90
Stable Economy (.5)
120
Weak Economy
EV=40(.3)+30(.5)+20(.2)=31
(.2)
(.2)
-30
Strong Economy (.3)
40
Stable Economy (.5)
30
Weak Economy
(.2)
20
Make the Decision
EV=61
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
EV=81
Average factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy
EV=31
Small factory
(.2)
(.2)
-120
90
Maximum
120
-30
Strong Economy (.3)
40
Stable Economy (.5)
30
Weak Economy
(.2)
20
EV=81