1. Chapter 17 Decision Making
Basic Business Statistics 11th Edition
Chapter 17
Decision Making
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.

2. 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
To use Bayes’ theorem to revise probabilities in light of sample information
About the concept of utility
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

3. 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 Choice/Event combination
Adopt Decision Criteria
Evaluate Criteria for Selecting the Best Course of Action
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

4. List Possible Actions or Events
Two Methods of Listing
Payoff Table
Decision Tree
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

5. Investment Choice (Action)
A Payoff Table
A payoff table shows alternatives, states of nature, and payoffs
States of Nature
(Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy
Stable Economy
Weak Economy
200 50
-120 90
120
-30 40 30 20
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

6. Sample Decision Tree Large factory Average factory Small factory
Strong Economy
200
Large factory
Stable Economy 50
Weak Economy
-120
Strong Economy 90
Average factory
Stable Economy
120
Weak Economy
-30
Strong Economy 40
Small factory
Stable Economy 30
Weak Economy 20
Payoffs
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

7. Opportunity Loss
Opportunity loss is the difference between an actual payoff for an action and the highest possible payoff, given a particular event
Payoff Table
State Of Nature
(Events)
Profit in $1,000’s
(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.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

8. States of Nature (Events)
Opportunity Loss
(continued)
Payoff Table
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy
Stable Economy
Weak Economy
200 50
-120 90
120
-30 40 30 20
Opportunity Loss Table
States of Nature (Events)
Opportunity Loss in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy
Stable Economy
Weak Economy 70
140
110 50
160 90
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

9. Decision Criteria Maximax Maximin Expected Monetary Value (EMV(j))
An optimistic decision criteria
Maximin
A pessimistic decision criteria
Expected Monetary Value (EMV(j))
The expected profit for taking action j
Expected Opportunity Loss (EOL(j))
The expected opportunity loss for taking action j
Expected Value of Perfect Information (EVPI)
The expected opportunity loss from the best decision
Return to Risk Ratio
Takes into account the variability in payoffs
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

10. States of Nature (Events)
Maximax Solution
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy
Stable Economy
Weak Economy
200 50
-120 90
120
-30 40 30 20
Maximum payoff for Large Factory is 200
Maximum payoff for Average Factory is 120
Maximum payoff for Small Factory is 40
Maximax Decision: Build the Large Factory because 200 is the maximum
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

11. States of Nature (Events)
Maximin Solution
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy
Stable Economy
Weak Economy
200 50
-120 90
120
-30 40 30 20
Minimum payoff for Large Factory is -120
Minimum payoff for Average Factory is -30
Minimum payoff for Small Factory is 20
Maximin Decision: Build the Small Factory because 20 is the maximum
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

12. Expected Monetary Value Solution
Goal: Maximize expected value
The expected monetary value is the weighted average payoff, given specified probabilities for each event
Where EMV(j) = expected monetary value of action j
xij = payoff for action j when event i occurs
Pi = probability of event i
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

13. Expected Monetary Value Solution
(continued)
The expected value is the weighted average payoff, given specified probabilities for each event
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy (.2)
200 50
-120 90
120
-30 40 30 20
Suppose these probabilities have been assessed for these three events
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

14. Expected Monetary Value Solution
(continued)
Goal: Maximize expected value
Payoff Table:
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy (.2)
200 50
-120 90
120
-30 40 30 20
Expected Value (EMV)
Example:
EMV (Average factory) = (90)(.3) +
(120)(.5) +
(-30)(.2) = 81
Maximize expected value by choosing Average factory
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

15. Decision Trees Are Another Way To Display & Analyze The Same Information
A Decision tree shows a decision problem, beginning with the initial decision and ending will all possible outcomes and payoffs.
Use a square to denote decision nodes
Use a circle to denote uncertain events
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

16. Add Probabilities and Payoffs
(continued)
Strong Economy
(.3)
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy 90
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
Decision
(.3)
Strong Economy 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Uncertain Events
Probabilities
Payoffs
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

17. Fold Back the Tree Large factory Average factory Small factory
Strong Economy
(.3)
EMV=200(.3)+50(.5)+(-120)(.2)=61
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy
EMV=90(.3)+120(.5)+(-30)(.2)=81 90
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
(.3)
Strong Economy
EMV=40(.3)+30(.5)+20(.2)=31 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

18. Make the Decision Large factory Average factory Small factory
Strong Economy
(.3)
EV=61
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy
EV=81 90
Maximum
EMV=81
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
(.3)
Strong Economy
EV=31 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

19. Expected Opportunity Loss Solution
Goal: Minimize expected opportunity loss
The expected opportunity loss is the weighted average loss, given specified probabilities for each event
Where: EOL(j) = expected opportunity loss of action j
Lij = opportunity loss for action j when event i occurs
Pi = probability of event i
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

20. Expected Opportunity Loss Solution
Goal: Minimize expected opportunity loss
Opportunity Loss Table
States of Nature (Events)
Opportunity Loss in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy (.2) 70
140
110 50
160 90
Example:
EOL (Large factory) = 0(.3) +
70(.5) +
(140)(.2) = 63
Expected Op. Loss (EOL)
Minimize expected op. loss by choosing Average factory
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

21. Expected Opportunity Loss vs. Expected Monetary Value
The Expected Monetary Value (EMV) and the Expected Opportunity Loss (EOL) criteria are equivalent.
Note that in this example the expected monetary value solution and the expected opportunity loss solution both led to the choice of the average size factory.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

22. Value of Information Expected Value of Perfect Information, EVPI
EVPI = Expected profit under certainty
– expected monetary value of the best alternative
(EVPI is equal to the expected opportunity loss from the best decision)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

23. Expected Profit Under Certainty
= expected value of the best decision, given perfect information
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy (.2)
200 50
-120 90
120
-30 40 30 20
Value of best decision for each event:
Example: Best decision given “Strong Economy” is “Large factory”
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

24. Expected Profit Under Certainty
(continued)
States of Nature (Events)
Profit in $1,000’s
Investment Choice (Action)
Large Factory
Average Factory
Small Factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy (.2)
200 50
-120 90
120
-30 40 30 20
Now weight these outcomes with their probabilities to find the expected value.
200(.3)+120(.5)+20(.2) = 124
Expected profit under certainty
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

25. Value of Information Solution
Expected Value of Perfect Information (EVPI)
EVPI = Expected profit under certainty
– Expected monetary value of the best decision
Recall: Expected profit under certainty = 124
EMV is maximized by choosing “Average factory”,
where EMV = 81
so: EVPI = 124 – 81
= 43
(EVPI is the maximum you would be willing to spend to obtain perfect information)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

26. Accounting for Variability
Consider the choice of Stock A vs. Stock B
States of Nature (Events)
Percent Return
Stock Choice (Action)
Stock A
Stock B
Strong Economy (.7) 30 14
Weak Economy (.3)
-10 8
Expected Return:
Stock A has a higher EMV, but what about risk?
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

27. Accounting for Variability
(continued)
Calculate the variance and standard deviation for Stock A and Stock B:
States of Nature (Events)
Percent Return
Stock Choice (Action)
Stock A
Stock B
Strong Economy (.7) 30 14
Weak Economy (.3)
-10 8
Example
Expected Return:
Variance:
Standard Deviation
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

28. Accounting for Variability
(continued)
Calculate the coefficient of variation for each stock:
Stock A has much more relative variability
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

29. Return-to-Risk Ratio Return-to-Risk Ratio (RTRR):
Expresses the relationship between the return (expected payoff) and the risk (standard deviation)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

30. Return-to-Risk Ratio
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
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

31. Decision Making with Sample Information
Prior
Permits revising old probabilities based on new information
Probability
New
Information
Revised
Probability
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

32. Revised Probabilities Example
Additional Information: Economic forecast is strong economy
When the economy was strong, the forecaster was correct 90% of the time.
When the economy was weak, the forecaster was correct 70% of the time.
F1 = strong forecast
F2 = weak forecast
E1 = strong economy = 0.70
E2 = weak economy = 0.30
P(F1 | E1) = P(F1 | E2) = 0.30
Prior probabilities from stock choice example
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

33. Revised Probabilities Example
(continued)
Revised Probabilities (Bayes’ Theorem)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

34. EMV with Revised ProbabilitiesPi
Event
Stock A
xijPi
Stock B
.875
strong 30
26.25 14
12.25
.125
weak
-10
-1.25 8
1.00
Σ = Σ = 13.25
Revised probabilities
EMV Stock B = 13.25
EMV Stock A = 25.0
Maximum EMV
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

35. EOL Table with Revised ProbabilitiesPi
Event
Stock A
xijPi
Stock B
.875
strong 16
14.00
.125
weak 18
2.25
Σ = Σ = 14.00
Revised probabilities
EOL Stock B = 14.00
EOL Stock A = 2.25
Minimum EOL
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

36. Accounting for Variability with Revised Probabilities
Calculate the variance and standard deviation for Stock A and Stock B:
States of Nature (Events)
Percent Return
Stock Choice (Action)
Stock A
Stock B
Strong Economy (.875) 30 14
Weak Economy (.125)
-10 8
Example
Expected Return:
Variance:
Standard Deviation:
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

37. Accounting for Variability with Revised Probabilities
(continued)
The coefficient of variation for each stock using the results from the revised probabilities:
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

38. Return-to-Risk Ratio with Revised Probabilities
With the revised probabilities, both stocks have higher expected returns, lower CV’s, and larger return to risk ratios
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

39. Utility
Utility is the pleasure or satisfaction obtained from an action.
The utility of an outcome may not be the same for each individual.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

40. 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.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

41. Three Types of Utility Curves$ $ $
Risk Averter
Risk Seeker
Risk-Neutral
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

42. 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
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

43. Chapter Summary Described the payoff table and decision trees
Opportunity loss
Provided criteria for decision making
Maximax and Maximin
Expected monetary value
Expected opportunity loss
Return to risk ratio
Introduced expected profit under certainty and the value of perfect information
Discussed decision making with sample information
Addressed the concept of utility
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..