© 2002 prentice-hall, inc.chap 17-1 basic business statistics (8 th edition) chapter 17 decision...
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© 2002 Prentice-Hall, Inc. Chap 17-1
Basic Business Statistics(8th Edition)
Chapter 17Decision Making
© 2002 Prentice-Hall, Inc. Chap 17-2
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. Chap 17-3
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. Chap 17-4
List Possible Actions or Events
Payoff Table Decision Tree
Two Methods of Listing
© 2002 Prentice-Hall, Inc. Chap 17-5
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)
© 2002 Prentice-Hall, Inc. Chap 17-6
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. Chap 17-7
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”
© 2002 Prentice-Hall, Inc. Chap 17-8
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
© 2002 Prentice-Hall, Inc. Chap 17-9
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. Chap 17-10
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
© 2002 Prentice-Hall, Inc. Chap 17-11
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. Chap 17-12
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
© 2002 Prentice-Hall, Inc. Chap 17-13
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
© 2002 Prentice-Hall, Inc. Chap 17-14
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
© 2002 Prentice-Hall, Inc. Chap 17-15
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
© 2002 Prentice-Hall, Inc. Chap 17-16
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
© 2002 Prentice-Hall, Inc. Chap 17-17
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
© 2002 Prentice-Hall, Inc. Chap 17-18
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. Chap 17-19
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
© 2002 Prentice-Hall, Inc. Chap 17-20
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.
© 2002 Prentice-Hall, Inc. Chap 17-21
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
© 2002 Prentice-Hall, Inc. Chap 17-22
Decision Making with Sample Information
Permits revising old probabilities based on new information
NewInformation
RevisedProbability
PriorProbability
© 2002 Prentice-Hall, Inc. Chap 17-23
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
© 2002 Prentice-Hall, Inc. Chap 17-24
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)
© 2002 Prentice-Hall, Inc. Chap 17-25
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
© 2002 Prentice-Hall, Inc. Chap 17-26
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
© 2002 Prentice-Hall, Inc. Chap 17-27
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. Chap 17-28
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. Chap 17-29
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.
© 2002 Prentice-Hall, Inc. Chap 17-30
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
© 2002 Prentice-Hall, Inc. Chap 17-31
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. Chap 17-32
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
© 2002 Prentice-Hall, Inc. Chap 17-33
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