Chapter 5: Decision-making
Concepts
Quantitative Decision Making with
Spreadsheet Applications 7th ed.
By Lapin and Whisler
Sec 5.5 : Other Decision Criteria
Sec 5.6: Opportunity Loss and the Expected
Value of Perfect Information
The Maximin Payoff Criterion

The maximin payoff criterion is a
procedure that guarantees that the
decision maker can do no worse than
achieve the best of the poorest outcomes.
Example: Tippi-Toes Payoff Table
Event
(level of
demand)
Light
Act (choice of movement)
Gears and
Levers
Spring Action
Weights and
Pulleys
$25,000
-$10,000
-$125,000
$440,000
$400,000
$740,000
$750,000
Moderate $400,000
Heavy
$650,000
Example


Goal: Ensure a favorable outcome no matter
what happens.
Determine the worst outcome for each act
regardless of the event.
Gears and Light
Levers
demand
$25,000
Spring
Action
Light
demand
-$10,000
Weights
and
Pulleys
Light
demand
-$125,000
Example



Choose an act with the largest lowest
payoff. This guarantees a minimum return
that is the best of the poorest outcomes
possible.
Gears and Levers will guarantee the toy
manufacturer a payoff of at least $25,000.
Gears and Levers is the maximin payoff
act.
Example: Tippi-Toes Payoff Table
Event
(level of
demand)
Light
Act (choice of movement)
Gears and
Levers
Spring Action
Weights and
Pulleys
$25,000
-$10,000
-$125,000
$440,000
$400,000
$740,000
$750,000
-$10,000
-$125,000
Moderate $400,000
Heavy
$650,000
Column $25,000
Minimums
Risk vs. Reward
Event
Act
Event
A1
A2
E1
$0
-$1
E2
1
Column
Minimums
$0
Act
B1
B2
E1
$1
$10,000
10,000
E2
-1
-10,000
-$1
Column
Minimums
-$1
-$10,000
Deficiencies of Maximin Payoff
Criterion


It is an extremely conservative decision
criterion and may lead to some bad
decisions.
It is primarily suited to decision problems
with unknown probabilities that cannot be
reasonably assessed.
The Maximum Likelihood Criterion

The maximum likelihood criterion focuses
on the most likely event to the exclusion
of all others.
Maximum Likelihood Act
Act (Choice of Movement)
Event
(level of
demand)
Probability
Light
Gears &
Levers
Spring Action
Weights & Pulleys
.10
$25,000
-$10,000
-$125,000
Moderate
.70
400,000
440,000
400,000
Heavy
.20
650,000
740,000
750,000
Maximum Likelihood Criterion


Ignores most of other possible outcomes.
Prevalent decision-making behavior.
The Criterion of Insufficient Reason



Used when decision maker has no
information about the event probabilities.
Assumes each event has a probability of
1/(number of events) of occuring.
Some knowledge of the probability of an
event is almost always available.
The Bayes Decision Rule



The Bayes decision rule chooses the act
maximizing expected payoff.
It makes the greatest use of all available
information.
Its major deficiency occurs when
alternatives involve different magnitudes
of risk.
Event Probability
Act C1
Act C2
Payoff
Payoff x
Prob
Payoff
Payoff x
Prob
E1
.5
-$1,000,000
-$500,000
$250,000
$125,000
E2
.5
2,000,000
1,000,000
750,000
375,000
Expected
Payoff
$500,000
$500,000
Opportunity Loss


Opportunity loss is the amount of payoff
that is forgone by not selecting the act
that has the greatest payoff for the event
that actually occurs.
To calculate opportunity losses the
maximum payoff for each row is
determined and it’s then subtracted from
its respective row maximum.
Event
(level of
demand)
Payoff
Gears &
Levers
Spring
Action
Weights &
Pulleys
Light
$25,000
-$10,000
-$125,000
$25,000
Moderate
400,000
440,000
400,000
440,000
Heavy
650,000
740,000
750,000
750,000
Row maximum-Payoff = Opportunity Loss
(in thousands of dollars)
Light
25-25=0
25-(-10)=35
25-(-125)=150
Moderate
440-400=40
440-440=0
440-400=40
Heavy
750-650=100
750-740=10
750-750=0
Row
Maximum
Opportunity Loss Table
Event
(level of
demand)
Act (choice of movement)
Gears & Levers
Spring Action
Weights &
Pulleys
Light
$0
$35,000
150,000
Moderate
40,000
0
40,000
Heavy
100,000
10,000
0
The Bayes Decision Rule and
Opportunity Loss

The Bayes decision rule is to select the act
that has the maximum expected payoff or
the minimum expected opportunity loss.
Event
Probability
(level of
demand)
Act (choice of movement)
Gears & Levers
Spring Action
Weights & Pulleys
Loss
Loss x
Prob
Loss
Loss
Loss x
Prob
Loss x
Prob
Light
.10
$0
$0
$35,000 $3,500
$150,000 $15,000
Moderate
.70
40,000
28,000
0
0
40,000
28,000
Heavy
.20
100,000 20,000
10,000
2,000
0
0
Expected
Opportunity Loss
$48,000
$5,500
$43,000
The Expected Value of Perfect
Information



When the decision maker can acquire perfect
information the decision will be made under
certainty. Then the decision maker can
guarantee the best decision.
We want to investigate the worth of such
information before it is obtained, so we will
determine the expected payoff once perfect
information is obtained.
This quantity is called the expected payoff under
certainty.
Calculating Expected Payoff Under
Certainty
1.
2.
3.
Determine the highest payoff for each
event.
Multiply the maximum payoffs with their
respective event probabilities. Then sum
these amounts.
Determine the worth of perfect
information to the decision maker.
Example: Highest Payoff for each
Event
Event(l Probabi Act
evel of lity
deman
Gears & Spring
d)
Levers
Action
Under Certainty
Weights Maxim
&
um
Pulleys Payoff
Chosen Payoff
Act
x Prob
Light
.10
$25,000 -$10,000
Moderate
.70
400,000 440,000 400,000 440,000 SA
308,000
Heavy
.20
650,000 740,000 750,000 750,000 W&P
150,000
-$125,000
$25,000 G&L
Expected Payoff
under certainty
$2,500
460,500
Expected Value of Perfect
Information (EVPI)




EVPI = Expected payoff under certainty
- Maximum expected payoff.
Our example:
EVPI = $460,500-$455,000 = $5,500.
This is the greatest amount of money the
decision maker would be willing to pay to
obtain perfect information about what
demand will be.