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## PowerPoint Slideshow about 'Basic Business Statistics (8 th Edition)' - niesha

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Chapter Topics

- The payoff table and decision trees
- Opportunity loss
- Criteria for decision making
- Expected monetary value
- Expected opportunity loss
- Return to risk ratio
- Expected profit under certainty
- Decision making with sample information
- Utility

© 2002 Prentice-Hall, Inc.

Features of Decision Making

- List alternative courses of action
- List possible events or outcomes or states of nature
- Determine “payoffs”
- (Associate a payoff with each course of action and each event pair)
- Adopt decision criteria
- (Evaluate criteria for selecting the best course of action)

© 2002 Prentice-Hall, Inc.

List Possible Actions or Events

Two Methods of Listing

Payoff Table

Decision Tree

© 2002 Prentice-Hall, Inc.

Payoff Table (Step 1)

Consider a food vendor determining whether to sell soft drinks or hot dogs.

Course of Action (Aj)

Sell Soft Drinks (A1)

Sell Hot Dogs (A2)

Event (Ei)

Cool Weather (E1) x11 =$50x12 = $100

Warm Weather (E2) x21 = $200 x22 = $125

xij = payoff (profit) for event i and action j

© 2002 Prentice-Hall, Inc.

Payoff Table (Step 2):Do Some Actions Dominate?

- Action A “dominates” action B if the payoff of action A is at least as high as that of action B under any event and is higher under at least one event.
- Action A is “inadmissible” if it is dominated by any other action(s).
- Inadmissible actions do not need to be considered.
- Non-dominated actions are called “admissible.”

© 2002 Prentice-Hall, Inc.

Action C “dominates” Action D

Action D is “inadmissible”

Payoff Table (Step 2):Do Some Actions Dominate?(continued)

Course of Action (Aj)Production Process

Event (Ei)

Level of Demand

A B C D

70 80 100 100

120 120 125 120

200 180 160 150

Low

Moderate

High

© 2002 Prentice-Hall, Inc.

Decision Tree:Example

Food Vendor Profit Tree Diagram

x11 = $50

Cool Weather

Warm Weather

Soft Drinks

x21 = $200

Hot Dogs

x12 = $100

Cool Weather

Warm Weather

x22 =$125

© 2002 Prentice-Hall, Inc.

Opportunity Loss: Example

Highest possible profit for an event Ei - Actual profit obtained for an action Aj

Opportunity Loss (lij)

Event: Cool Weather

Action: Soft Drinks Profit x11 : $50

Alternative Action: Hot Dogs Profit x12 : $100

Opportunity Loss l11 = $100 - $50 = $50

Opportunity Loss l12 = $100 - $100 = $0

© 2002 Prentice-Hall, Inc.

Opportunity Loss: Table

Alternative Course of Action

Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action

Cool Hot 100 100 - 50 = 50 100 - 100 = 0 Weather Dogs

Warm Soft 200 200 - 200 = 0 200 - 125 = 75 Weather Drinks

© 2002 Prentice-Hall, Inc.

Decision Criteria

- Expected monetary value (EMV)
- The expected profit for taking an action Aj
- Expected opportunity loss (EOL)
- The expected loss for taking action Aj
- Expected value of perfect information (EVPI)
- The expected opportunity loss from the best decision

© 2002 Prentice-Hall, Inc.

Decision Criteria -- EMV

Expected Monetary Value (EMV) =

Sum(monetary payoffs of events) (probabilities of the events)

Number of events

N

Vj

Xij

Pi

i = 1

EMVj = expected monetary value of action j

Xi,j = payoff for action j and event i

Pi = probability of event i occurring

© 2002 Prentice-Hall, Inc.

Decision Criteria -- EMV Table Example: Food Vendor

PiEvent MV xijPi MV xijPi

Soft Hot

Drinks Dogs

.50 Cool $50 $50 .5 = $25 $100 $100.50 = $50

.50 Warm $200 $200 .5 = 100 $125 $125.50 = 62.50

EMV Soft Drink = $125

EMV Hot Dog = $112.50

Highest EMV = Better alternative

© 2002 Prentice-Hall, Inc.

Decision Criteria -- EOL

Expected Opportunity Loss (EOL)

Sum (opportunity losses of events) (probabilities of events)

N

Lj

lij

Pi

i =1

EOLj= expected opportunity loss of action j

li,j = opportunity loss for action j and event i

Pi = probability of event i occurring

© 2002 Prentice-Hall, Inc.

Decision Criteria -- EOL Table Example: Food Vendor

PiEvent Op Loss lijPi Op Loss lijPi

Soft Drinks Hot Dogs

.50 Cool $50 $50.50 = $25 $0 $0.50 = $0

.50 Warm 0 $0 .50 = $0 $75 $75 .50 = $37.50

EOL Soft Drinks = $25

EOL Hot Dogs = $37.50

Lowest EOL = Better Choice

© 2002 Prentice-Hall, Inc.

EVPI

- Expected value of perfect information (EVPI)
- The expected opportunity loss from the best decision
- Represents the maximum amount you are willing to pay to obtain perfect information

Expected Profit Under Certainty - Expected Monetary Value of the Best Alternative

EVPI (should be a positive number)

© 2002 Prentice-Hall, Inc.

EVPI Computation

Expected Profit Under Certainty

= .50($100) + .50($200)

= $150

Expected Monetary Value of the Best Alternative

= $125

EVPI = $150 - $125 = $25

= Lowest EOL

= The maximum you would be willing to spend to obtain perfect information

© 2002 Prentice-Hall, Inc.

Taking Account of VariabilityExample: Food Vendor

2 for Soft Drink

= (50 -125)2 .5 + (200 -125)2 .5 = 5625

for Soft Drink = 75

CVfor Soft Drinks = (75/125) 100% = 60%

2 for Hot Dogs = 156.25 for Hot dogs = 12.5

CVfor Hot dogs = (12.5/112.5) 100% = 11.11%

© 2002 Prentice-Hall, Inc.

Return to Risk Ratio

Expresses the relationship between the return (expected payoff) and the risk (standard deviation)

© 2002 Prentice-Hall, Inc.

Return to Risk RatioExample: Food Vendor

You might want to choose hot dogs. Although soft drinks have the higher Expected Monetary Value, hot dogs have a much larger return to risk ratio and a much smaller CV.

© 2002 Prentice-Hall, Inc.

Decision Making in PHStat

- PHStat | decision-making | expected monetary value
- Check the “expected opportunity loss” and “measures of valuation” boxes
- Excel spreadsheet for the food vendor example

© 2002 Prentice-Hall, Inc.

Permits revising old probabilities based on new informationDecision Making with Sample Information

Prior

Probability

New

Information

Revised

Probability

© 2002 Prentice-Hall, Inc.

Revised Probabilities Example: Food Vendor

Additional Information: Weather forecast is COOL.

When the weather is cool, the forecaster was correct 80% of the time.

When it has been warm, the forecaster was correct 70% of the time.

F1 = Cool forecast

F2 = Warm forecast

E1 = Cool Weather = 0.50

E2 = Warm Weather = 0.50

P(F1 | E1) = 0.80 P(F1 | E2) = 0.30

Prior Probability

© 2002 Prentice-Hall, Inc.

Revising Probabilities Example:Food Vendor

- Revised Probability (Bayes’s Theorem)

© 2002 Prentice-Hall, Inc.

Revised EMV Table Example: Food Vendor

PiEvent Soft xijPi Hot xijPi

Drinks Dogs

.73 Cool $50 $36.50 $100 $73

.27 Warm $200 54 125 33.73

EMV Soft Drink = $90.50

EMV Hot Dog = $106.75

Revised probabilities

Highest EMV = Better alternative

© 2002 Prentice-Hall, Inc.

Revised EOL Table Example: Food Vendor

PiEvent Op Loss lijPi OP Loss lijPi

Soft Drink Hot Dogs

.73 Cool $50 $36.50 $0 0

.27 Warm 0 $0 75 20.25

EOL Soft Drinks = 36.50

EOL Hot Dogs = $20.25

Lowest EOL = Better Choice

© 2002 Prentice-Hall, Inc.

Revised EVPI Computation

Expected Profit Under Certainty

= .73($100) + .27($200)

= $127

Expected Monetary Value of the Best Alternative

= $106.75

EPVI = $127 - $106.75 = $20.25

= The maximum you would be willing to spend to obtain perfect information

© 2002 Prentice-Hall, Inc.

Taking Account of Variability: Revised Computation

2 for Soft Drinks

= (50 -90.5)2 .73 + (200 -90.5)2 .27 = 4434.75

for Soft Drinks = 66.59

CVfor Soft Drinks = (66.59/90.5) 100% = 73.6%

2 for Hot Dogs = 123.1875 for Hot dogs = 11.10

CVfor Hot dogs = (11.10/106.75) 100% = 10.4%

© 2002 Prentice-Hall, Inc.

Revised Return to Risk Ratio

You might want to choose Hot Dogs. Hot Dogs have a much larger return to risk ratio.

© 2002 Prentice-Hall, Inc.

Revised Decision Makingin PHStat

- PHStat | decision-making | expected monetary value
- Check the “expected opportunity loss” and “measures of valuation” boxes
- Use the revised probabilities
- Excel spreadsheet for the food vendor example

© 2002 Prentice-Hall, Inc.

Utility

- Utility is the idea that each incremental $1 of profit does not have the same value to every individual
- A risk averse person, once reaching a goal, assigns less value to each incremental $1.
- A risk seeker assigns more value to each incremental $1.
- A risk neutral person assigns the same value to each incremental $1.

© 2002 Prentice-Hall, Inc.

Three Types of Utility Curves

Utility

Utility

Utility

$

$

$

Risk Averter: Utility rises slower than payoff

Risk Seeker:Utility rises faster than payoff

Risk-Neutral: Maximizes Expected payoff and ignores risk

© 2002 Prentice-Hall, Inc.

Chapter Summary

- Described the payoff table and decision trees
- Opportunity loss
- Provided criteria for decision making
- Expected monetary value
- Expected opportunity loss
- Return to risk ratio
- Introduced expected profit under certainty
- Discussed decision making with sample information
- Addressed the concept of utility

© 2002 Prentice-Hall, Inc.

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