Chapter 3
Decision Analysis
The Six Steps in Decision Making
1. Clearly define the problem at hand
2. List the possible alternatives
3. Identify the possible outcomes or states
of nature
4. List the payoff or profit of each
combination of alternatives and
outcomes
5. Select one of the mathematical decision
theory models
6. Apply the model and make your decision
Case of Maria Rojas
Maria Rojas is considering the possibility of opening a small
dress shop on Fairbanks Avenue, a few blocks from the
university. She has located a good mall that attracts students.
Her options are to open as mall shop, a medium-sized shop,
or no shop at all. The market for a dress shop can be good,
average, or bad. The probabilities is 1/3 for each market.
The net profit or loss for the medium-sized and small shops
for the various market conditions are given in the following
table. Building no shop at all yields no loss and no gain.
Case of Maria Rojas
Types of Decision-Making
Environments
Type 1: Decision making under certainty
 Decision maker knows with certainty the
consequences of every alternative or
decision choice
Type 2: Decision making under uncertainty
 The decision maker does not know the
probabilities of the various outcomes
Type 3: Decision making under risk
 The decision maker knows the
probabilities of the various outcomes
Decision Making Under
Uncertainty
There are several criteria for making decisions
under uncertainty
1. Maximax (optimistic)
2. Maximin (pessimistic)
3. Criterion of realism (Hurwicz)
4. Equally likely (Laplace)
5. Minimax regret
Maximax
Used to find the alternative that maximizes
the maximum payoff
 Locate the maximum payoff for each alternative
 Select the alternative with the maximum
number
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
MAXIMUM
IN A ROW
($)
75,000
25,000
-40,000
75,000
100,000
35,000
-60,000
100,000
0
0
0
Maximax
0
Maximin
Used to find the alternative that maximizes
the minimum payoff
 Locate the minimum payoff for each alternative
 Select the alternative with the maximum
number
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
MINIMUM IN
A ROW ($)
75,000
25,000
-40,000
-40,000
100,000
35,000
-60,000
-60,000
0
0
0
0
Maximin
Criterion of Realism (Hurwicz)
A weighted average compromise between
optimistic and pessimistic
 Select a coefficient of realism

 Coefficient is between 0 and 1
 A value of 1 is 100% optimistic
 Compute the weighted averages for each
alternative
 Select the alternative with the highest value
Weighted average = (maximum in row)
+ (1 – )(minimum in row)
Criterion of Realism (Hurwicz)
 For the small shop alternative using
 = 0.8
(0.8)(75,000) + (1 – 0.8)(–40,000) = 52,000
 For the medium-sized shop alternative using  = 0.8
(0.8)(100,000) + (1 – 0.8)(–60,000) = 68,000
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
CRITERION OF
REALISM
( = 0.8)$
75,000
25,000
-40,000
52,000
100,000
35,000
-60,000
68,000
0
0
0
Realism
0
Equally Likely (Laplace)
Considers all the payoffs for each alternative
 Find the average payoff for each alternative
 Select the alternative with the highest average
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
ROW
AVERAGE ($)
75,000
25,000
-40,000
20,000
100,000
35,000
-60,000
25,000
0
0
Equally likely
0
0
Minimax Regret
Based on opportunity loss or regret, the
difference between the optimal profit and
actual payoff for a decision
 Create an opportunity loss table by determining
the opportunity loss for not choosing the best
alternative
 Opportunity loss is calculated by subtracting
each payoff in the column from the best payoff
in the column
 Find the maximum opportunity loss for each
alternative and pick the alternative with the
minimum number
Minimax Regret
STATE OF NATURE
GOOD MARKET
($)
 Opportunity
Loss Tables
BAD
MARKET
($)
AVERAGE
MARKET
($)
100,000 - 75,000
35,000 - 25,000
0 – (- 40,000)
100,000 - 100,000
35,000 - 35,000
0 – (- 60,000)
100,000 - 0
35,000 - 0
0
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
25,000
10,000
40,000
0
0
60,000
100,000
35,000
0 Table 3.7
Minimax Regret
STATE OF NATURE
ALTERNATIVE
Small shop
Medium-sized
shop
Do nothing
Table 3.8
GOOD
MARKET
($)
25,000
AVERAGE
MARKET
($)
10,000
BAD
MARKET
($)
MAXIMUM IN A
ROW
($)
40,000
40,000
Minimax
0
0
60,000
60,000
100,000
35,000
0
100,000
Decision Making Under Risk
 Decision making when there are several possible
states of nature and we know the probabilities
associated with each possible state
 Most popular method is to choose the alternative
with the highest expected monetary value (EMV)
EMV(alternative i) = (payoff of 1st state of nature) x (prob. of 1st state of nature)
+ (payoff of 2nd state of nature) x (prob. of 2nd state of nature)
+…
+ (payoff of last state of nature) x (prob. of last state of nature)
EMV for Maria Rojas
 Each market has a probability of 1/3
 Which alternative would give the highest EMV?
 The calculations are
EMV (small shop)
= (1/3)($75,000) + (1/3)($25,000) + (1/3)($-40,000)
= $20,000
EMV (medium shop) = (1/3)($100,000) + (1/3)($35,000) + (1/3)($-60,000)
= $25,000
EMV (do nothing)
= (1/3)($0) + (1/3)($0) + (1/3)($0)
= $0
EMV for Maria Rojas
STATE OF NATURE
ALTERNATIVE
Small shop
GOOD
MARKET
($)
AVERAGE
MARKET
($)
BAD
MARKET
($)
ROW
AVERAGE ($)
75,000
25,000
-40,000
20,000
100,000
35,000
-60,000
25,000
Do nothing
0
0
0
0
Probability
1/3
1/3
Medium-sized
shop
1/3
Largest EMV
EMV (small shop)
EMV (medium shop)
EMV (do nothing)
= (1/3)($75,000) + (1/3)(25,000) + (1/3)(-40,000)
= $20,000
= (1/3)($100,000) + (1/3)(35,000) + (1/3)($-60,000)
= $25,000
= (1/3)($0) + (1/3)($0) + (1/3)($0)
= $0
Expected Value of Perfect
Information (EVPI)
 EVwPI (Expected Value with Perfect Information) is the long
run average return if we have perfect information before a
decision is made
EVwPI = (best payoff for 1st SoN)x P1st SoN
+ (best payoff for 2nd SoN)x P2nd SoN
+ … + (best payoff for nth SoN)x Pnth SoN
 EVPI (Expected Value of Perfect Information) places an
upper bound on what you should pay for additional
information
EVPI = EVwPI – Maximum EMV
Expected Value of Perfect
Information (EVPI)
 Scientific Marketing, Inc. offers analysis
that will provide certainty about market
conditions (favorable)
 Additional information will cost $25,000
 Is it worth purchasing the information?
Expected Value of Perfect
Information (EVPI)
STATE OF NATURE
ALTERNATIVE
Small shop
BAD
MARKET
($)
25,000
-40,000
20,000
100,000
35,000
-60,000
25,000
Do nothing
0
0
0
0
Probability
1/3
1/3
1/3
Best alternative for good state of nature is opening a medium shop with a payoff of
$100,000
Best alternative for average state of nature is opening a medium shop with a payoff of
$35,000
Best alternative for bad state of nature is to do nothing with a payoff of $0
EVwPI = ($100,000)(1/3) + ($35,000)(1/3) + ($0)(1/3) = $45,000
2.
ROW AVERAGE
($)
75,000
Medium-sized
shop
1.
GOOD
MARKET ($)
AVERAGE
MARKET
($)
The maximum EMV without additional information is $25,000
EVPI = EVwPI – Maximum EMV
= $45,000 - $25,000 = $20,000
Expected Value of Perfect
Information (EVPI)
1. Best alternative for good state of nature is opening a
medium shop with a payoff of $100,000
Best alternative for average state of nature is opening a
medium shop with a payoff of $35,000
So the maximum
Maria
Best alternative
for bad state
of nature is to do nothing
should
pay for the additional
with a payoff
of $0
information is $20,000
EVwPI = ($100,000)(1/3) + ($35,000)(1/3) + ($0)(1/3) =
$45,000
2. The maximum EMV without additional information is
$25,000
EVPI = EVwPI – Maximum EMV
= $45,000 - $25,000 = $20,000
Expected Opportunity Loss
 Expected opportunity loss (EOL) is the




cost of not picking the best solution
First construct an opportunity loss table
For each alternative, multiply the opportunity
loss by the probability of that loss for each
possible outcome and add these together
Minimum EOL will always result in the same
decision as maximum EMV
Minimum EOL will always equal EVPI
Expected Opportunity Loss
Opportunity loss table
STATE OF NATURE
ALTERNATIVE
GOOD
MARKET
($)
Small shop
AVERAGE
MARKET
($)
BAD
MARKET
($)
MAXIMUM IN A
ROW
($)
25,000
10,000
40,000
25,000
0
0
60,000
20,000
Do nothing
100,000
35,000
0
45,000
Probability
1/3
Medium-sized
shop
EOL (small shop)
1/3
1/3
Minimum EOL
= (1/3)($25,000) + (1/3)($10,000) + (1/3)($40,000)
= $25,000
EOL (medium shop) = (1/3)($0) + (1/3)($0) + (1/3)($60,000)
= $20,000
EOL (do nothing)
= (1/3)($100,000) + (1/3)($35,000) + (1/3)($0)
= $45,000
Homework 03
 Prob. 3.16, 3.18, 3.19, 3.22, 3.26, 3.27