© 2002 prentice-hall, inc.chap 17-1 basic business statistics (8 th edition) chapter 17 decision...

© 2002 Prentice-Hall, Inc. Chap 17-1

Basic Business Statistics(8th Edition)

Chapter 17Decision Making


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


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)


List Possible Actions or Events

Payoff Table Decision Tree

Two Methods of Listing


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)

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

Event (Ei)

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

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

Sell Hot Dogs (A2)


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.”


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

(continued)

Event (Ei)Level of Demand

Course of Action (Aj)Production ProcessA B C D

LowModerateHigh

70 80 100 100

120 120 125 120

200 180 160 150

Action C “dominates” Action D Action D is “inadmissible”


Decision Tree:Example

Soft Drinks

Food Vendor Profit Tree Diagram

Hot Dogs

Cool Weather

Cool Weather

Warm Weather

Warm Weather

x11 = $50

x21 = $200

x22 =$125

x12 = $100


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


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

Opportunity Loss: Table

Alternative Course of Action


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


Expected Monetary Value (EMV) = Sum (monetary payoffs of events) (probabilities of the

events)

Decision Criteria -- EMV

Xij PiVj N

EMVj = expected monetary value of action j

Xi,j = payoff for action j and event i

Pi = probability of event i occurring

i = 1

Number of events


Decision Criteria -- EMV Table Example: Food Vendor

Pi Event MV xijPi MV xijPi

Soft HotDrinks 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

Highest EMV = Better alternative

EMV Hot Dog = $112.50


Decision Criteria -- EOL

Expected Opportunity Loss (EOL)Sum (opportunity losses of events) (probabilities of

events)

Lj

lijPi

EOLj = expected opportunity loss of action j

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

Pi = probability of event i occurring

i =1

N


Decision Criteria -- EOL Table Example: Food Vendor

Pi Event 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


Expected Profit Under Certainty

- Expected Monetary Value of the Best Alternative

EVPI (should be a positive number)

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


EVPI ComputationExpected 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


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%


Return to Risk Ratio

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

RRR = Return to Risk Ratio = j

j

EMV


Return to Risk RatioExample: Food Vendor

Soft Drinks Soft DrinksRRR = 1/CV = 1.67

Hot Dogs Hot DogsRRR = 1/CV = 9

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.


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

Microsoft Excel Worksheet


Decision Making with Sample Information

Permits revising old probabilities based on new information

NewInformation

RevisedProbability

PriorProbability


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.

Prior Probability

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


Revising Probabilities Example:Food Vendor

1 1 1 2

1 2

1 1 11 1

1

2 1 22 1

1

| 0.80 | 0.30

0.50 0.50

| .50 .80| .73

.50 .80 .50 .30

|| .27

P F E P F E

P E P E

P E P F EP E F

P F

P E P F EP E F

P F

Revised Probability (Bayes’s Theorem)


Revised EMV Table Example: Food Vendor

Pi Event 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

Highest EMV = Better alternativeRevised probabilities


Revised EOL Table Example: Food Vendor

Pi Event 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


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


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%


Revised Return to Risk Ratio

Soft Drinks Soft DrinksRRR = 1/CV = 90.50/66.59

Hot Dogs Hot DogsRRR = 1/CV = 9.62

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


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

Microsoft Excel Worksheet


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.


Three Types of Utility Curves

Ut i

lity

$ $ $

Uti

lity

Ut i

lity

Risk Averter: Utility rises slower than payoff

Risk Seeker:Utility rises faster than payoff

Risk-Neutral: Maximizes Expected payoff and ignores risk


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.chap 17-1 basic business statistics (8 th edition) chapter 17 decision...

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