Chapter 3
Decision Analysis
Decision Theory
• Decision theory is the analytic and
systematic approach for making the
best decision.
Features of Decision Making
• Decision making is for __________.
a. past
b. future
c. both past and future
• A decision is about a (an) _________.
a. status
b. action
c. condition
• The process of making decision is a process
of __________.
a. producing b. manufacturing c. creating
d. cooking
e. selecting
f. fabricating
Components in Decision
Making (1 of 2)
• Alternatives of a decision
– A list of choices, one of which will be selected
as the decision by the decision maker.
• States of Nature
– Possible conditions that may actually occur
in the future, which will affect the outcome
of your decision but are beyond your
control.
Components in Decision
Making (2 of 2)
• Payoffs
– a payoff is the outcome of a decision
alternative under a state of nature. The
larger the payoff the better.
• The decision alternatives, states of nature
and payoffs are organized in a decision
table.
Decision Table for the Thompson
Lumber Example
States of Nature
Decision Alternatives
Favorable
Market
Unfavorable
Market
Build a large plant
$200,000
-$180,000
Build a small plant
$100,000
-$20,000
Doing nothing
$0
$0
Types of Decision Making
• Decision making under certainty
– The outcome of a decision alternative is
known (i.e., there is only one state of nature.)
• Decision making under risk
– The outcome of a decision alternative is not
known, but its probability is known.
• Decision making under uncertainty
– The outcome of a decision alternative is not
known, and even its probability is not
known.
Decision Making under
Uncertainty
• The outcome of a decision alternative is
not known, and even its probability is not
known.
• A few criteria (approaches) are available
for the decision makers to select
according to their preferences and
personalities.
Criterion 1: Maximax (Optimistic)
• Step 1. Pick maximum payoff of each
alternative.
• Step 2. Pick maximum of those
maximums in Step 1; its corresponding
alternative is the decision.
• “Best of bests”.
Maximax Decision
for Thompson Lumber
States of Nature
Row
Decision
Favorable Unfavorable Maximum
Alternatives
market
market
Large plant
200,000
–180,000
200,000
Small plant
100,000
–20,000
100,000
Do nothing
0
0
0
Max(Row max’s) = Max(200,000, 100,000, 0) = 200,000.
So, the decision is ‘Large plant’.
For Whom?
• MaxiMax is an approach for:
– Risk taker who tends not to give up
attractive opportunities regardless of
possible failures, or
– Optimistic decision maker in whose eyes
future is bright.
Criterion 2: Maximin (Pessimistic)
• Step 1. Pick minimum payoff of each
alternative
• Step 2. Pick the maximum of those
minimums in Step 1, its corresponding
alternative is the decision
• “Best of worsts”
Maximin Decision
for Thompson Lumber
States of Nature
Row
Decision
Favorable Unfavorable Minimum
Alternatives
market
market
payoffs
Large plant
200,000
–180,000
–180,000
Small plant
100,000
–20,000
–20,000
Do nothing
0
0
0
Max(Row Min’s) = Max(–180,000, –20,000, 0) = 0.
So, the decision is ‘do nothing’.
For Whom?
• MaxiMin is an approach for:
– Risk averter who tends to avoid bad
outcomes despite of some possible
attractive outcomes; or
– Pessimistic decision maker in whose eyes
future is obscure.
Criterion 3: Hurwicz (Realism)
• Step 1. Calculate Hurwicz value for
each alternative
• Step 2. Pick the alternative of largest
Hurwicz value as the decision.
Hurwicz Value
• Hurwicz value of an alternative
= (row max)() + (row min)(1-)
where  (01) is called coefficient of
realism.
Decision by Hurwicz Value
=0.8
Decision
Alternatives
Large plant
Small plant
Do nothing
for Thompson Lumber
States of Nature
Favorable Unfavorable
market
market
200,000 –180,000
100,000
–20,000
0
0
Hurwicz
values
124,000
76,000
0
Max(Hurwicz values) = Max(124,000,76,000,0) = 124,000.
So, the decision is ‘large plant’.
For Whom?
• Hurwicz method can be used by
decision makers with different
preferences on risks.
– For a person who tends to take risk, a larger 
is used;
– For a person who tends to be conservative, a
smaller  is used.
• What if  = 1?
• What if  = 0?
Criterion 4: Equally Likely
• Step 1. Calculate the average payoff for
each alternative.
• Step 2. The alternative with highest
average if the decision.
Decision by Equally Likely
for Thompson Lumber
Decision
Alternatives
Large plant
Small plant
Do nothing
States of Nature
Favorable Unfavorable
market
market
200,000 –180,000
100,000
–20,000
0
0
Row
Average
10,000
40,000
0
Max(Row avg’s) = Max(10,000, 40,000, 0) = 40,000.
So, the decision is ‘small plant’.
For Whom?
• Equally Likely method is for the
decision maker who does not have
particular preference on taking or
avoiding risks.
Criterion 5: Minimax Regret
• Step 1. Construct a ‘regret table’,
• Step 2. Pick maximum regret of each
row in regret table,
• Step 3. Pick minimum of those
maximums in Step 2, its corresponding
alternative is the decision.
Regret
• Regret is amount you give up due to
not picking the best alternative in a
given state of nature.
• Regret = Opportunity cost =
Opportunity loss
Payoff Table for Thompson Lumber
and Column Maximums
States of Nature
Decision
Alternatives
Favorable
Unfavorable
market
market
Large plant
$200,000
$100,000
$0
$200,000
-$180,000
-$20,000
$0
$0
Small plant
Doing nothing
Column Max
Regret Table for Thompson Lumber
States of Nature
Decision
Alternatives
Favorable
Unfavorable
market
market
Large plant
$0
$100,000
$200,000
$180,000
$20,000
$0
Small plant
Doing nothing
Minimax Regret Decision
for Thompson Lumber
Regret Table
Decision
Alternatives
Large plant
Small plant
Do nothing
States of Nature
Favorable Unfavorable
market
market
0
180,000
100,000
20,000
200,000
0
Row
Maximum
180,000
100,000
200,000
Min(Row max’s) = Min{180,000, 100,000, 200,000}
= 100,000.
So, the minimax regret decision is ‘small plant’.
For Whom?
• MiniMax Regret is an approach for the
decision maker who hates the feeling
of having regrets.
Decision Making under Risk
• The outcome of a decision alternative
is not known, but its probability is
known.
Max EMV Approach
• Step 1. Calculate EMV for each
alternative.
• Step 2. Pick the alternative with
highest EMV as the decision.
EMV – expected monetary value
• EMV of an alternative is the expected value of
possible payoffs of that alternative.

• EMV
n
X
i 1
i*
P( X i )
n=number of states of nature
P(Xi)=probability of the i-th state of nature
Xi=payoff of the alternative under the i-th state of
nature
Example of Thompson Lumber
States of Nature
Decision
Alternatives
Favorable Unfavorable
market
market
0.5
0.5
Large plant
$200,000 -$180,000
Small plant
$100,000 -$20,000
Doing nothing
$0
$0
EMV
10,000
40,000
0
Minimum EOL Approach
Step 1. Generate the opportunity loss table.
Step 2. Calculate the expected value (EOL)
for each alternative in the opportunity loss
table.
Step 3. Pick up the alternative with the
minimum EOL.
Opportunity Loss Table
• Opportunity loss = Regret = Opp. cost
• Opportunity loss table = Regret Table
Payoff Table for the Thompson
Lumber Example
States of Nature
Decision Alternatives
Favorable
Market
Unfavorable
Market
Build a large plant
$200,000
-$180,000
Build a small plant
$100,000
-$20,000
Doing nothing
$0
$0
Opportunity Loss table and EOL
for Thompson Lumber
States of Nature
Decision
Alternatives
Favorable Unfavorable
market
0.5
Large plant
$0
Small plant
$100,000
Doing nothing $200,000
market
0.5
$180,000
$20,000
$0
EOL
Expected Value of Perfect
Information (EVPI)
• It is value of additional information for
better decision making.
• It is an upper bound on how much to pay
for the additional information.
Calculating EVPI
• EVPI
= (Exp. payoff with perfect information) –
(Exp. payoff without perfect information)
= EVwPI
– EVw/oPI
EVw/oPI
• EVw/oPI is the average payoff you
expect to get based only on the
information given in the decision
table without the help of
additional information.
• EVw/oPI = Max (EMV)
EVw/oPI = Maximum EMV
States of Nature
Decision
Alternatives
Favorable Unfavorable
market
market
0.5
0.5
Large plant
$200,000 -$180,000
Small plant
$100,000 -$20,000
Doing nothing
$0
$0
Since Max EMV = 40,000,
EVw/oPI = 40,000.
EMV
10,000
40,000
0
EVwPI
• EVwPI is the average payoff you can get
if following the perfect information about
the state ofn nature in the future.
• EVwPI   bi Pi
i 1
where n=number of states of nature
bi=best payoff of i-th state of nature
Pi=probability of i-th state of nature
EVwPI for the Example of Thompson
States of Nature
Decision
Alternatives
Favorable Unfavorable
market
market
0.5
0.5
Large plant
$200,000 -$180,000
Small plant
$100,000 -$20,000
Doing nothing
$0
$0
bi
$200,000
$0
EVwPI = 200,000*0.5+0*0.5 = 100,000
EMV
10,000
40,000
0
EVPI for Thompson Lumber
• EVwPI = 200,000*0.5 + 0*0.50 = $100,000
• EVw/oPI = Maximum EMV = $40,000
• EVPI = EVwPI – EVw/oPI
= $100,000 – $40,000
= $60,000
EVPI is a Benchmark in Purchasing
Additional Information
• EVPI is the maximum $ amount the
decision maker would pay to
purchase the additional information
about the states of nature (from a
consulting firm, for example).
What if Information Is Not
Perfect?
• In most cases, information about future
is not “perfect”. We need to discount
EVwPI properly in those cases.
• If you have 80% of confidence on the
information, then
Expected Value of Additional
Information = EVAI
= EVwPI * 80% - EVw/oPI
Maximum EMV, Minimum
EOL, and EVPI
• The decision selected by the Maximum
EMV approach is always the same as
the decision selected by the Minimum
EOL approach. (why?)
• The value of EVPI is equal to the value
of minimum EOL. (why?)
An Example
Land on ‘Head’ Land on ‘Tail’
Guess ‘Head’
$100
- $60
Guess ‘Tail’
- $80
$150
• You can play the game for many times.
• Someone offers you perfect information about
“landing” at the price of $65 per time. Do you
take it? If not, how much would you pay?
• (See the handout of class work)
In the Tossing Coin Example
•
•
•
•
•
•
EMV for “guess Head” = $20.
EMV for “guess Tail” = $35* (Max EMV).
EOL for “guess Head” = $105
EOL for “guess Tail” = $90* (Min EOL)
EVwPI = $125, EVw/oPI=$35
EVPI = $90
$
Maximum average payoff per game
average
payoff
35
average
payoff
20
EMV
EOL
regret
EOL
regret
125
EMV
Alt. 2,
Guess “Tail”
Alt. 1,
Guess “Head”
Alternatives
How to Set Up a Decision Table
• A decision table is set up by the decision
maker.
• Determine decision alternatives and states
of nature.
• Determine the payoffs of each alternative
under the states of nature.
• See case “Garden Salad” in class work.