Decision Making for business leader in company

Decision Making
Statistics for Managers Using Microsoft
Excel, 5e © 2008 Prentice-Hall, Inc. Chap 17-1

Learning Objectives
In this chapter, you learn:
• To use payoff tables and decision
trees to evaluate alternative courses
of action
• To use several criteria to select an
alternative course of action
• About the concept of utility
Excel, 5e © 2008 Prentice-Hall, Inc.
Chap 17-2

Steps in Decision Making
• List Alternative Courses of Action
– Choices or actions
• List Uncertain Events
– Possible events or outcomes
• Determine ‘Payoffs’
– Associate a Payoff with Each Event/Outcome
combination
• Adopt Decision Criteria
– Evaluate Criteria for Selecting the Best Course
of Action

Payoff Table
A payoff table shows alternatives, states of
nature, and payoffs
Chap 17-4
Profit in $1,000’s
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small
Factory
Strong Economy
Stable Economy
Weak Economy
200
50
-120
90
120
-30
40
30
20

Decision Tree
Chap 17-5
Large factory
Small factory
Average factory
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Payoffs
200
50
-120
40
30
20
90
120
-30

Opportunity Loss
Chap 17-6
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small
Factory
Strong Economy
Stable Economy
Weak Economy
200
50
-120
90
120
-30
40
30
20
The action “Average factory” has payoff 90 for “Strong Economy”. Given “Strong
Economy”, the choice of “Large factory” would have given a payoff of 200, or
110 higher. Opportunity loss = 110 for this cell.
Opportunity loss is the difference between an actual payoff
for an action and the optimal payoff, given a particular event
Payoff
Table

Opportunity Loss
(Events)
Investment Choice (Action)
Large
Factory
Average
Factory
Small
Factory
Strong Economy
Stable Economy
Weak Economy
200
50
-120
90
120
-30
40
30
20
Chap 17-7
Opportunity Loss in
$1,000’s
(Events)
Large
Factory
Average
Factory
Small
Factory
Strong Economy
Stable Economy
Weak Economy
0
70
140
110
0
50
160
90
0
Payoff
Table
Opportunity
Loss Table

Decision Criteria
• Expected Monetary Value (EMV)
– The expected profit for taking action Aj
• Expected Opportunity Loss (EOL)
– The expected opportunity loss for taking action Aj
• Expected Value of Perfect Information (EVPI)
– The expected opportunity loss from the best
decision
Chap 17-8

Expected Monetary Value
• The expected monetary value is the weighted average payoff,
given specified probabilities for each event
Chap 17-9



N
i
i
ij P
X
j
EMV
1
)
(
Where EMV(j) = expected monetary value of action j
Xij = payoff for action j when event i occurs
Pi = probability of event i
Goal: Maximize expected value

• The expected value is the weighted average
payoff, given specified probabilities for each
event
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small Factory
Strong Economy (0.3)
Stable Economy (0.5)
Weak Economy (0.2)
200
50
-120
90
120
-30
40
30
20
Chap 17-10
Suppose these
probabilities
have been
assessed for
these three
events

• Example: EMV (Average factory) = 90(.3) +
120(.5) + (-30)(.2) = 81
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small
Factory
Weak Economy (0.2)
200
50
-120
90
120
-30
40
30
20
EMV (Expected Values) 61 81 31
Chap 17-11
Payoff Table:

Expected Opportunity Loss
• The expected opportunity loss is the weighted average loss,
given specified probabilities for each event



N
1
i
i
ijP
L
EOL(j)
Where EOL(j) = expected opportunity loss of action j
Lij = opportunity loss for action j when event i occurs
Pi = probability of event i
Goal: Minimize expected opportunity loss

Expected Opportunity Loss
• Example: EOL (Large factory) = 0(.3) + 70(.5)
+ (140)(.2) = 63
Opportunity Loss in
$1,000’s
(Events)
Large
Factory
Average
Factory
Small
Factory
Weak Economy (0.2)
0
70
140
110
0
50
160
90
0
Expected Opportunity
Loss (EOL)
63 43 93
Chap 17-13
Opportunity Loss Table

Expected Profit Under Certainty
• Expected
profit under
certainty
= expected
value of the
best
decision,
given perfect
information
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small Factory
Weak Economy (0.2)
200
50
-120
90
120
-30
40
30
20
Chap 17-14
Example: Best decision given “Strong
Economy” is “Large factory”
200 120 20
Value of best decision
for each event:

Expected Profit Under Certainty
• Now weight
these
outcomes
with their
probabilities
to find the
expected
profit under
certainty:
(Events)
Investment Choice
(Action)
Large
Factory
Average
Factory
Small Factory
Weak Economy (0.2)
200
50
-120
90
120
-30
40
30
20
Chap 17-15
200 120 20
200(.3)+120(.5)+20(.2)
= 124

Value of Information Solution
• Expected Value of Perfect Information (EVPI)
EVPI = Expected profit under certainty
– Expected monetary value of the best decision
Chap 17-16
so: EVPI = 124 – 81
= 43
Recall: Expected profit under certainty = 124
EMV is maximized by choosing “Average factory,”
where EMV = 81
(EVPI is the maximum you would be willing to spend to obtain perfect information)

Accounting for Variability
Chap 17-17
Percent Return
(Events)
Stock Choice
(Action)
Stock A Stock B
Strong Economy
(.7)
30 14
Weak Economy
(.3)
-10 8
Expected Return
(EMV)
18.0 12.2
Consider the choice of Stock A vs. Stock B
Stock A has a higher
EMV, but what about
risk?

Percent Return
(Events)
Stock Choice
(Action)
Stock A Stock B
Strong Economy (.7) 30 14
Weak Economy (.3) -10 8
Expected Return (EMV) 18.0 12.2
Variance 336.0 7.56
Standard Deviation 18.33 2.75
Chap 17-18
Calculate the variance and standard deviation
0
.
336
)
3
(.
)
18
10
(
)
7
(.
)
18
30
(
)
X
(
P
μ)
X
(
σ 2
2
N
1
i
i
2
i
2
A 






 

Example:

Chap 17-19
Calculate the coefficient of variation for each stock:
%
83
.
101
100%
0
.
18
33
.
18
100%
EMV
σ
CV
A
A
A 




%
54
.
22
100%
2
.
12
75
.
2
100%
EMV
σ
CV
B
B
B 




Stock A has
much more
relative
variability

Return-to-Risk Ratio
Chap 17-20
j
σ
EMV(j)
RTRR(j) 
You might want to consider Stock B if you don’t like risk.
Although Stock A has a higher Expected Return, Stock B has a
much larger return to risk ratio and a much smaller CV.
982
.
0
33
.
18
0
.
18
σ
EMV(A)
RTRR(A)
A



436
.
4
75
.
2
2
.
12
σ
EMV(B)
RTRR(B)
B




Utility
• Utility is the pleasure or satisfaction
obtained from an action.
• The utility of an outcome may not be the
same for each individual.

Utility Example
Each incremental $1 of profit does not have the
same value to every individual:
•A risk averse person, once reaching a goal,
assigns less utility to each incremental $1.
•A risk seeker assigns more utility to each
incremental $1.
•A risk neutral person assigns the same utility to
each extra $1.
Chap 17-22

Maximizing Expected Utility
• Making decisions in terms of utility, not $
–Translate $ outcomes into utility outcomes
–Calculate expected utilities for each action
–Choose the action to maximize expected
utility
Chap 17-4

Decision Making for business leader in company

Decision Making for business leader in company

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