Chapter Topics
•The Payoff Table and Decision Trees
•Opportunity Loss
•Criteria for Decision Making
•Expected Monetary Value
•Return to Risk Ratio
Features of Decision Making
•List Alternative Courses of Action
(Possible Events or Outcomes)
•Determine ‘Payoffs’
(Associate a Payoff with Each Event or Outcome)
•Adopt Decision Criteria
(Evaluate Criteria for Selecting the Best Course of
Action)
List Possible Actions or
Events
Two Methods
of Listing
Payoff Table
Decision Tree
Payoff Table
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 =$50
x12 = $100
Warm Weather (E2)
x21 = 200
x22 = 125
xij = payoff (profit) for event i and action j
Decision Tree:Example
Food Vendor Profit Tree Diagram
x11 = $50
x21 = 200
x12 = 100
x22 =125
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: $50
Alternative Action: Hot Dogs
Profit: $100
Opportunity Loss = $100 - $50 = $50
Note: Opportunity Loss is always positive
Opportunity Loss: Table
Event
Alternative Course of Action
Sell Soft Drinks Sell Hot Dogs
Optimal
Action
Profit of
Optimal
Action
Cool
Weather
Hot
Dogs
100
100 - 50 = 50
Warm
Weather
Soft
Drinks
200
200 - 200 = 0
100 - 100 = 0
200 - 125 = 75
Decision Criteria
•
•
•
•
•
•
•
Expected Monetary Value (EMV)
The expected profit for taking an action Aj
Expected Opportunity Loss (EOL)
The expected loss for not taking action Aj
Expected Value of Perfect Information (EVPI)
The expected opportunity loss from the best
decision
Decision Criteria -- EMV
•
•
Expected Monetary Value (EMV)
Sum (monetary payoffs of events) 
(probabilities of the
events)
EMVj =
 Xij Pi
N
i=1
EMVj = expected monetary value of action j
xi,j = payoff for action j and event i
Pi = probability of event i occurring
Decision Criteria -- EMV Table
Example: Food Vendor
Pi Event
.50
Cool
.50 Warm
Soft
xijPi
Drinks
$50
$50 .5 = $25
$200
$200 .5 = 100
Hot
Dogs
$100
$100.50 = $50
$125
$25.50 = 62.50
EMV Soft Drink = $125
Better alternative
xijPi
EMV Hot Dog = $112.50
Decision Criteria -- EOL
•
Expected Opportunity Loss (EOL)
• Sum (opportunity losses of events)  (probabilities of
events)
EOLj =
 lij Pi
N
i =1
EOLj = expected monetary value of action j
li,j = payoff for action j and event i
Pi = probability of event i occurring
Decision Criteria -- EOL Table
Example: Food Vendor
Pi
Event Op Loss
Soft Drinks
.50
Cool
.50 Warm
lijPi
OP Loss
Hot Dogs
lijPi
$50
$50.50 = $25
$0
$0.50 = $0
0
$0 .50 = $0
$75
EOL Soft Drinks = $25
Better Choice
$75 .50 = $37.50
EOL Hot Dogs = $37.50
Decision Criteria -- EVPI
Expected Value of Perfect Information (EVPI)
• The expected opportunity loss from the best decision
Expected Profit Under Certainty
-
Expected Monetary Value of the Best Alternative
EVPI (should be a positive number)
• Represents the maximum amount you are willing
to pay to obtain perfect information
EVPI Computation
Expected Profit Under Certainty
= .50($100) + .50($200)
= $150
Expected Monetary Value of the Best Alternative
= $125
EPVI = $25 The maximum you would be willing to
spend to obtain perfect information.
Taking Account of Variability:
FoodVendor
s2 for Soft Drink
= (50 -125)2 .5 + (200 -125)2 .5 = 5625
s for Soft Drink = 75
CVfor Soft Drinks = (75/125)  100% = 60%
s2 for Hot Dogs = 156.25 s for Hot dogs = 12.5
CVfor Hot dogs = 11.11%
Return to Risk Ratio
Expresses the relationship between the return
(payoff) and the risk (standard deviation).
RRR = Return to Risk Ratio =
RRRSoft Drinks = 125/75 = 1.67
EMV j
sj
RRRHot Dogs = 9
You might wish 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.
Note: RRR is the inverse of CV