Business 260: Managerial Decision Analysis

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Business 260 Managerial Decision
Analysis Professor David Mease Lecture
4 Agenda 1) Go over Midterm Exam 1
solutions 2) Assign Homework 2 (due Thursday
4/2) 3) Decision Analysis (QBA Book Chapter 4)
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Homework 2 Homework 2 will be due Thursday
4/2 We will have an exam that day after we
review the solutions The homework is posted on
the class web page http//www.cob.sjsu.edu/mease
_d/bus260/260homework.html Questions 3 and 4
will be added as the due date gets closer The
solutions will be posted so you can check your
answers http//www.cob.sjsu.edu/mease_d/bus260/2
60homework_solutions.html
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Quantitative Business Analysis
Decision Analysis (Chapter 4)
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Chapter Topics

• Problem Formulation
• Decision Making without Probabilities
• Decision Making with Probabilities
• Decision Analysis with Sample Information

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Problem Formulation
The first step in the decision analysis process
is problem formulation. We begin with a verbal
statement of the problem. Then we identify -
the decision alternatives - the states of nature
(uncertain future events) - the payoff
(consequences) associated with each specific
combination of the decision alternatives and the
state of natures
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Problem Formulation
Example Burger Prince Restaurant is
considering opening a new restaurant on Main
Street. The company has three different building
designs (A, B, and C), each with a different
seating capacity. Burger Prince estimates that
the average number of customers arriving per hour
will be 40, 60, or 80.
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Problem Formulation
Decision Alternatives States of Nature
d1 use building design A d2 use building
design B d3 use building design C
s1 an average of 40 customers arriving per
hour s2 an average of 60 customers arriving per
hour s3 an average of 80 customers arriving per
hour
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Problem Formulation
Payoff Table - The consequence resulting from
a specific combination of a decision alternative
and a state of nature is a payoff. - A table
showing payoffs for all combinations of decision
alternatives and states of nature is a payoff
table. - Payoffs can be expressed in terms of
profit, cost, time, distance or any other
appropriate measure.
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Problem Formulation
Payoff Table Example (Payoffs are Profit Per
Week)
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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In class exercise 59 A food vendor can sell
either ice cream or hot chocolate but not both.
If it is warm, selling ice cream will make 250
and hot chocolate will make 40. If it is not
warm, selling ice cream will make 90 and hot
chocolate will make 200. There is a 40 chance
it will be warm. Make a payoff table for this
problem.
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In class exercise 60 The Islander Fishing
Company purchases clams for 1.50 per pound from
Peconic Bay fisherman and sells them to various
New York restaurants for 2.50 per pound. Any
clams not sold to the restaurants by the end of
the week can be sold to a local soup company for
0.50 per pound. The probabilities of the
various levels of demand are as follows Make
a payoff table for purchase levels 500, 1000 and
2000 pounds using profit as the payoff.
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Problem Formulation
Decision Tree - A decision tree is a
chronological representation of the decision
problem. - A decision tree has two types of
nodes 1) round nodes correspond to chance
events 2) square nodes correspond to decisions -
Branches leaving a round node represent the
different states of nature branches leaving a
square node represent the different decision
alternatives. - At the end of a limb of the tree
is the payoff attained from the series of
branches making up the limb.
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In class exercise 61 Make a decision tree for
the Burger Prince example.
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In class exercise 61 Make a decision tree for
the Burger Prince example.
(ANSWER)
40 customers per hour (s1)
10,000
Design A (d1)
60 customers per hour (s2)
2
15,000
80 customers per hour (s3)
14,000
40 customers per hour (s1)
8,000
Design B (d2)
60 customers per hour (s2)
3
1
18,000
80 customers per hour (s3)
12,000
40 customers per hour (s1)
6,000
Design C (d3)
60 customers per hour (s2)
4
16,000
80 customers per hour (s3)
21,000
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Decision Making Without Probabilities
Three commonly used criteria for decision making
when probability information regarding
the likelihood of the states of nature is
unavailable are - the optimistic (maximax)
approach - the conservative (maximin)
approach - the minimax regret approach
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Decision Making Without Probabilities
Optimistic (Maximax) Approach - The optimistic
approach would be used by an optimistic decision
maker - The decision with the overall largest
payoff is chosen - If the payoff table is in
terms of costs, the decision with the overall
lowest cost will be chosen (hence, a minimin
approach)
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In class exercise 62 What decision would the
optimistic approach favor for the Burger Prince
Restaurant example?
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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(ANSWER)
In class exercise 62 What decision would the
optimistic approach favor for the Burger Prince
Restaurant example?
States of Nature Decision (Customers
Per Hour) Alternative 40 s1 60 s2
80 s3 Design A d1 10,000 15,000
14,000 Design B d2 8,000 18,000
12,000 Design C d3 6,000 16,000
21,000
Maximaxdecision
Maximax payoff
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In class exercise 63 What decision would the
optimistic approach favor for the ice cream/hot
chocolate example?
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Decision Making Without Probabilities
Conservative (Maximin) Approach -The
conservative approach would be used by a
conservative decision maker. -For each
decision the minimum payoff is listed. The
decision corresponding to the maximum of these
minimum payoffs is selected. -If payoffs are in
terms of costs, the maximum costs will be
determined for each decision and then the
decision corresponding to the minimum of these
maximum costs will be selected. (Hence, a
minimax approach)
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In class exercise 64 What decision would the
conservative approach favor for the Burger Prince
Restaurant example?
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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In class exercise 64 What decision would the
conservative approach favor for the Burger Prince
Restaurant example?
(ANSWER)
Maximin payoff
Maximindecision
Decision Minimum Alternative
Payoff Design A d1 10,000 Design B d2
8,000 Design C d3 6,000
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In class exercise 65 What decision would the
conservative approach favor for the ice cream/hot
chocolate example?
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Decision Making Without Probabilities
Minimax Regret Approach -The minimax regret
approach requires construction of a regret table
or an opportunity loss table. -This is done by
calculating for each state of nature the
difference between each payoff and the largest
payoff for that state of nature. -Then, using
this regret table, the maximum regret for each
possible decision is listed. -The decision
corresponding to the minimum of the maximum
regrets is chosen.
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In class exercise 66 What decision would the
minimax regret approach favor for the Burger
Prince Restaurant example?
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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In class exercise 66 What decision would the
minimax regret approach favor for the Burger
Prince Restaurant example? Regret table
(ANSWER)
States of Nature Decision (Customers
Per Hour) Alternative 40 s1 60 s2
80 s3 Design A d1 0
3,000 7,000 Design B d2 2,000
0 9,000 Design C d3 4,000
2,000 0
Decision Maximum Alternative
Regret Design A d1 7,000 Design B d2
9,000 Design C d3 4,000
Minimaxdecision
Minimaxregret
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In class exercise 67 What decision would the
minimax regret approach favor for the ice
cream/hot chocolate example?
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Decision Making With Probabilities
Up until now we have ignored probabilities for
the states of nature But usually you should have
some reasonable estimate of these
probabilities
P(sj) gt 0 for all states of nature
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Decision Making With Probabilities
We can use these probabilities to compute the
expected value for each decision
alternative Then the expected value approach
to decision making is to choose the alternative
solution that gives you the largest expected
value
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In class exercise 68 Assuming probabilities of
.4, .2 and .4 for 40, 60 and 80 customers
respectively, what decision would the expected
value approach favor for the Burger Prince
Restaurant example? Show the simplified decision
tree with the expected values.
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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(WORK)
In class exercise 68 Assuming probabilities of
.4, .2 and .4 for 40, 60 and 80 customers
respectively, what decision would the expected
value approach favor for the Burger Prince
Restaurant example? Show the simplified decision
tree with the expected values.
40 customers (s1) P(s1) .4
10,000
Design A (d1)
60 customers (s2) P(s2) .2
2
15,000
80 customers (s3) P(s3) .4
14,000
40 customers (s1) P(s1) .4
8,000
Design B (d2)
60 customers (s2) P(s2) .2
3
1
18,000
80 customers (s3) P(s3) .4
12,000
40 customers (s1) P(s1) .4
6,000
Design C (d3)
60 customers (s2) P(s2) .2
4
16,000
80 customers (s3) P(s3) .4
21,000
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In class exercise 68 Assuming probabilities of
.4, .2 and .4 for 40, 60 and 80 customers
respectively, what decision would the expected
value approach favor for the Burger Prince
Restaurant example? Show the simplified decision
tree with the expected values.
(ANSWER)
EV(d1) .4(10,000) .2(15,000)
.4(14,000) 12,600
Design A d1
2
EV(d2) .4(8,000) .2(18,000)
.4(12,000) 11,600
Design B d2
3
1
EV(d3) .4(6,000) .2(16,000)
.4(21,000) 14,000
Design C d3
4
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In class exercise 69 What decision would the
expected value approach favor for ice cream/hot
chocolate example?
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Decision Making With Probabilities
When choosing among alternative decisions with
very similar expected values, often people will
use the variance or standard deviation to help
make their decisions. The alternative with
the smaller variance or standard deviation is
generally preferred. This is a form of risk
analysis, but it differs from the type discussed
in your text.
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In class exercise 70 Compute the standard
deviation for only the ice cream alternative in
the ice cream/hot chocolate example.
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Expected Value of Perfect Information
- Frequently information is available which can
improve the probability estimates for the states
of nature. - The expected value of perfect
information (EVPI) is the increase in the
expected profit that would result if one knew
with certainty which state of nature would occur.
- The EVPI provides an upper bound on the
expected value of any sample or survey
information.
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Expected Value of Perfect Information
Expected value of perfect information is defined
as where EVPI expected value of
perfect information EVwPI expected value
with perfect information about the states of
nature EVwoPI expected value without perfect
information about the states of nature
EVPI EVwPI EVwoPI
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Expected Value of Perfect Information
EVPI Calculation Step 1 Determine the optimal
return corresponding to each state of
nature. Step 2 Compute the expected value of
these optimal returns. Step 3 Subtract the EV
of the optimal decision from the amount
determined in step (2).
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In class exercise 71 Compute the EVPI for the
Burger Prince Restaurant example. What does the
EVPI mean in this context?
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
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In class exercise 71 Compute the EVPI for the
Burger Prince Restaurant example. What does the
EVPI mean in this context?
(ANSWER)
Average Number of Customers Per Hour
s1 40 s2 60 s3 80
Design A Design B Design C
10,000 15,000 14,000
8,000 18,000 12,000
6,000 16,000 21,000
EVPI .4(10,000) .2(18,000) .4(21,000) -
14,000 2,000
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In class exercise 72 Compute the EVPI for the
ice cream/hot chocolate example. What does the
EVPI mean in this context?
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Decision Analysis With Sample Information
Knowledge of sample (survey) information can be
used to revise the probability estimates for the
states of nature. Prior to obtaining this
information, the probability estimates for the
states of nature are called prior
probabilities. The updated probabilities are
called posterior probabilities or branch
probabilities for decision trees.
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Decision Analysis With Sample Information
You can choose decision alternatives in the
decision tree based on the outcome of the sample
information using the expected value
approach. The expected value based on this is
called the Expected Value with Sample Information
(EVwSI). Finally, you can compute the expected
value of sample information (EVSI) as the
additional expected profit possible through
knowledge of the sample information.
EVSI EVwSI EVwoSI
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Decision Analysis With Sample Information
EVSI expected value of sample information
EVwSI expected value with sample information
about the states of
nature EVwoSI expected value without sample
information about the states of
nature
EVSI EVwSI EVwoSI
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In class exercise 73 A market research survey
is available for the Burger Prince Restaurant
example. It will report either favorable or not
favorable. There is a 54 chance it will be
favorable. Based on this, the posterior
probabilities are given below. Using these
numbers, compute the expected value of sample
information and explain its meaning in this
context.
P(40 customers per hour favorable) .148
P(60 customers per hour favorable) .185
P(80 customers per hour favorable) .667
P(40 customers per hour unfavorable) .696
P(60 customers per hour unfavorable) .217
P(80 customers per hour unfavorable) .087
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In class exercise 73 Decision Tree (top half)
(WORK)
s1 P(s1I1) .148
10,000
d1
s2 P(s2I1) .185
4
15,000
s3 P(s3I1) .667
14,000
s1 P(s1I1) .148
8,000
d2
s2 P(s2I1) .185
5
2
18,000
s3 P(s3I1) .667
P(I1) .54
12,000
I1
s1 P(s1I1) .148
6,000
d3
s2 P(s2I1) .185
6
16,000
1
s3 P(s3I1) .667
21,000
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In class exercise 73 Decision Tree (bottom
half)
(WORK)
s1 P(s1I2) .696
10,000
1
d1
s2 P(s2I2) .217
7
15,000
s3 P(s3I2) .087
14,000
I2
s1 P(s1I2) .696
8,000
P(I2) .46
d2
s2 P(s2I2) .217
8
3
18,000
s3 P(s3I2) .087
12,000
s1 P(s1I2) .696
6,000
d3
s2 P(s2I2) .217
9
16,000
s3 P(s3I2) .087
21,000
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In class exercise 73
(ANSWER)
d1
13,593
4
17,855
d2
12,518
5
2
I1 (.54)
d3
17,855
6
EVwSI .54(17,855) .46(11,433)
14,900.88
1
d1
7
I2 (.46)
11,433
d2
10,554
8
3
11,433
d3
9,475
9
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In class exercise 74 Show the complete decision
tree for the Burger Prince Restaurant example
(including a decision node for whether or not to
obtain the survey information).