Chapter 5
There is no more miserable human being
than one in whom nothing is habitual but
indecision.—William James
Decision-Making
Concepts
1
Elements of Decisions
Every decision has acts. These are the
possible choices.
Outcomes are the consequences.
Decisions made under uncertainty involve
events.
When there is uncertainty, outcomes are
determined partly by choice (acts) and partly
by chance (events). Decisions are portrayed:
2
With a decision table or a payoff table.
Or by a decision tree.
The Payoff Table
 The payoff table has a column for each act
and a row for each event.
 The payoff value expresses how closely an
outcome brings the decision maker to his or
her goal.
3
The Decision Tree
 The decision tree shows acts and events on separate forks,
sequenced chronologically. Each outcome has a path.
4
Payoffs and Probabilities
 Here the payoffs for outcomes are found adding partial
cash flows on branches. Event branches have probabilities.
5
Making the Decision
Using a Payoff Table




Decision makers want to maximize payoff.
But, the outcome is uncertain.
Various criteria exist for making the choice.
Maximizing expected payoff is commonly
used to make choices.
 First, compute expected payoff for each act.
 An act’s expected payoff is the weighted average
value for its column found by multiplying payoffs
by the row’s probability and summing the products.
 Second, choose the act having the maximum.
6
Computing Expected Payoffs
 The Tippi-Toes expected payoffs are:
 For simplicity, the pneumatic movement act was first
eliminated. It is an inadmissible act because it is
dominated by one or more acts.
 Inadmissible acts will never be selected because there is a single
act that is always at least as good and in one case strictly better.
 Weights and pulleys (see previous slide) dominates pneumatic.
7
Maximizing Expected Payoff
is the Bayes Decision Rule
 It is not a perfect criterion because it can
lead to the less preferred choice.
 Consider the Far-Fetched Lottery decision:
ProbaEVENTS bility
Head
.5
Tail
.5
ACTS
Gamble
Don’t Gamble
+$10,000
-5,000
Would you gamble?
8
$0
0
The Far-Fetched Lottery
Decision
 The expected payoffs are:
ACTS
EVENTS
Head
Tail
Probability
Gamble
Don’t Gamble
Payoff × Prob.
Payoff × Prob
.5
+$5,000
$0
.5
-2,500
0
$2,500
$0
Expected Payoff:
 Most people prefer not to gamble!
9
 That violates the Bayes decision rule.
 But the rule often indicates preferred choices even
though it is not perfect.
Other Decision Criteria
 Maximin Payoff: Choose best of possible worsts
(take MAXImum of MINimums).
 Way too conservative for business decisions.
 Focuses totally on downside. Ignores upside.
 Uses less information than Bayes decision rule.
10
Other Decision Criteria
 Maximum Likelihood: Identify most likely
event, ignore others, and pick act with
greatest payoff.
 Personal decisions often made that way.
 Collectively, other events may be more likely.
 Ignores lots of information.
11
Decision Tree Analysis
 Each node is evaluated in terms of its
expected payoff.
 Event forks: expected payoffs are computed.
 Act forks: the greatest value is brought back.
 The decision tree is folded back by
maximizing expected payoff.
 Inferior acts are pruned from the tree.
 The pruned tree indicates the best course of
action, the one maximizing expected payoff.
12
 The process works backward in time.
Folding Back the Decision Tree
13
Opportunity Loss
 Another perspective on decision making is
provided by the opportunity loss.
 It is the reduction in payoff between the best
outcome and what would be achieved.
14
Using Opportunity Loss
 Criteria may be based on opportunity loss,
which is a measure of regret. It is a
quantity to be minimized.
 Choosing the act minimizing expected
opportunity loss is the preferred criterion.
 It is equivalent to Bayes decision rule.
 This sometimes involves easier calculations.
15
Expected Value of
Perfect Information
 Although perfect information is an ideal, it
says a lot about less-than-perfect predictors.
EVPI = Expected payoff under certainty
- Maximum Exp. Payoff (no Info.)
 The expected payoff under certainty is
computed assuming best act will be chosen
regardless of the event that occurs.
16
Expected Value of
Perfect Information
 The expected payoff under certainty is just
an ideal. (Perfect predictors are unrealistic.)
 For Tippi-Toes, the maximum expected
payoff (no information) is $455,000 and
EVPI = $460,500 - 455,000 = $5,500
 The above expresses “on the average” how
much better we are with the information.
 We should reject less-than-perfect predictors (real ones) costing more than the EVPI.
17
Templates and Software
 Payoff Table templates
 Palisade Decision Tools PrecisionTree 1.0
18
Simple Payoff Table for
Exchecker Decision (Figure 5-2)
1. Enter problem
name in B3.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
4. Expected payoffs 14
15
16
2. Enter data in B9:F12 and labels
in A9:A12 and C8:F8.
B
C
D
E
F
PAYOFF TABLE EVALUATION
PROBLEM:
Exchecker Marketing Strategy
Problem Data
Act 1
Act 2
Act 3
Act 4
Events
Probability Direct Mail Targ. Ad. Telemark Mass Mkt
1 Premature
0.1
85.0%
50.0%
40.0%
40.0%
2 Lackluster
0.3
80.0%
70.0%
65.0%
50.0%
3 Quick Accept.
0.4
40.0%
50.0%
30.0%
70.0%
4 Wildly Enthus.
0.2
25.0%
35.0%
40.0%
60.0%
Expected Payoff
53.5%
53.0%
43.5%
59.0%
C
13 =SUMPRODUCT($B$9:$B$12,C9:C12)
3. If more events or acts are required, expand the table by inserting
additional rows and/or columns. Make sure the formulas for the Expected
19
Payoffs in the last row include all the rows of the expanded table.
1. Enter problem
name in B3. 1
2. Enter
data in
B9:F12 and
labels in
A9:A12 and
C8:F8.
4. Answers :
exp. payoff,
exp.
opportunity
loss, max.
exp. payoff,
min. exp.
opportunity
loss, EVPI.
20
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Expanded Payoff Table for
Exchecker Decision (Figure 5-3)
A
B
C
D
F
G
PAYOFF TABLE EVALUATION
PROBLEM:
Exchecker Marketing Strategy
Problem Data
1
2
3
4
E
Act 1
Events
Probability Direct Mail
Premature
0.1
$ 85.00
Lackluster
0.3
$ 80.00
Quick Accept.
0.4
$ 40.00
Wildly Enthus.
0.2
$ 25.00
Act 2
Targ. Ad.
$ 50.00
$ 70.00
$ 50.00
$ 35.00
9
10
11
12
G
=MAX(C9:F9)
=MAX(C10:F10)
=MAX(C11:F11)
=MAX(C12:F12)
Act 3
Telemark
$ 40.00
$ 65.00
$ 30.00
$ 40.00
Act 4
Mass Mkt
$ 40.00
$ 50.00
$ 70.00
$ 60.00
Row
Maximum
$ 85.00
$ 80.00
$ 70.00
$ 60.00
Act Summary
Expected Payoff
Exp. Opportunity Loss
Act 1
Act 2
Act 3
Act 4
Direct Mail Targ. Ad. Telemark Mass Mkt
$53.50
$53.00
$43.50
$59.00
$19.00
$19.50
$29.00
$13.50
Overall Summary
Maximum Expected Payoff:
Minimum Expected Opportunity Loss:
Expected Value of Perfect Information:
$59.00
$13.50
$13.50
Act 4 Mass Mkt
Act 4 Mass Mkt
D
23 =MAX(C18:F18)
C
24 =MIN(C19:F19)
18 =SUMPRODUCT($B$9:$B$12,C9:C12)
25 =D24
19 =SUMPRODUCT($B$9:$B$12,$G$9:$G$12-C9:C12)
E
=CONCATENATE("Act
F
23 ",MATCH(D23,C18:F18,0))
23 =HLOOKUP(E23,$C$16:$F$17,2)
=CONCATENATE("Act
24 =HLOOKUP(E24,$C$16:$F$17,2)
24 ",MATCH(D24,C19:F19,0))
3. If more
events or acts
are required,
expand the table
by inserting
additional rows
and/or columns.
Make sure the
formulas in the
Act Summary
table include all
the rows of the
expanded table.
Make sure that
the formulas in
D23:E24 include
all the columns
in the expanded
table.
Palisade Decision Tools
PrecisionTree
The PrecisionTree 1.0 software program on
the CD-ROM accompanying this book is an Excel
Add-In that solves decision trees. It has a number
of options for analyzing and graphing results.
21
PrecisionTree
To start PrecisionTree, click on the Windows Start
button, select Programs, Palisade Decision Tools,
then PrecisionTree 1.0 for Excel
Both Excel and PrecisionTree will open. You
will see the normal Excel screen with two new
tool bars, one for Palisade Decision Tools and
the other for PrecisionTree, as shown next.
22
The PrecisionTree Tool Bar
The PrecisionTree tool bar will show
along with the Excel tool bars.
Click on the New Tree icon and click in a cell
in the spreadsheet to start a new tree. Or click
on PrecisionTree on the menu bar, select the
Create New option, and click on Tree.
23
Initial PrecisionTree
Decision Tree
Clicking in cell A1 yield this initial tree.
A
1
2
B
1
tree #1
0
Figure 5-8
To name the tree, click in the tree #1
box. This brings to the screen the Tree
Settings dialog box shown next.
24
Tree Settings Dialog Box for
Naming Decision Tree (Figure 5-9 )
Enter the name Ponderosa Record Company in the
Tree Name line and click OK.
25
Initial Ponderosa Record Co.
Decision Tree (Figure 5-10)
A
1
2
P on d er os a R ec or d C o m p an y
B
1
0
To expand the decision tree move the cursor
over the end nod and click. This yields the
Nodes Settings dialog boxes shown next.
26
Node Settings Dialog Box
(Figure 5-11)
Under node type click on the decision node
27
.
The Node Settings dialog box changes to that shown
on the right. There enter 2 in the # of Branches line
and click OK.
Extended PrecisionTree Decision
(Figure 5-12)
A
1
2
3
4
5
6
B
branch
C
TRUE
1
0
0
FALSE
0
0
0
Ponderosa Record Company
0
branch
The costs associated with the branches are
entered directly onto the spreadsheet, $15,000
in cell B2 and $0 in cell B6.
28
To name the branches click inside one of the
boxes named branch. This brings to the screen
the Branch Settings dialog box shown next.
Branch Settings Dialog Box for
Naming Decision Branches (Figure 5-13 )
Enter the name of the branch in the Branch Name
line and click OK.
29
Extended Decision Tree with Decisions
and Partial Cash Flows (Figure 5-14 )
The 1 and 0 in C1 and C5 are the probabilities
and the $15,000 and $0 in C2 and C6 are the net
payoffs for the respective branches. The $15,000
in B4 is the expected payoff for the decision.
A
1
2
3
4
5
6
30
B
Test market
C
TRUE
1
$15,000
$15,000
FALSE
0
$0
$0
Ponderosa Record Company
$15,000
Don't test market
Clicking on the end node in cell C1:C2 continues the
tree expansion. The Node Settings dialog box
appears as previously. Only this time under Node
Type select the chance button
.
Second Expanded Decision Tree
(Figure 5-15)
The tree has two new branches, Favorable
and Unfavorable.
A
1
2
3
4
5
6
7
8
9
10
B
C
Favorable
D
50.0%
$0
Test market
0.5
$15,000
TRUE
$15,000
$15,000
Unfavorable 50.0%
$0
0.5
$15,000
Ponderosa Record Company
$15,000
Don't test market
31
FALSE
0
$0
$0
Probabilities of 50% and 0% are in C1 and C5.
Partial cash flows, both $0, appear in C2 and C6.
Expanding the tree once more yields the next tree.
Third Expanded Decision Tree
(Figure 5-16)
Two new branches, Market nationally and Abort,
have been added to the tree. Their respective cash
flows, -$50,000 and $0, are in D2 and D6.
A
B
C
D
1
M ar k et n atio n ally
2
FA LS E
- $ 50 ,0 0 0
3
F av or ab le
4
$0
T R UE
A b or t
$0
T e s t m ar k et
8
-$ 3 5,0 0 0
$ 15 ,0 0 0
6
7
0
5 0.0 %
5
0 .5
$ 1 5 ,0 0 0
TR UE
$ 1 5,0 0 0
9
$ 1 5 ,00 0
U n fav o ra bl e
10
11
E
5 0.0 %
$0
0 .5
$ 15 ,0 0 0
P on d er os a R ec or d C o m p an y
12
$ 15 ,0 0 0
13
D o n 't te s t m ar k et
14
F ALS E
$0
32
0
$0
Continuing to add branches yields the final tree
shown next.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
TRUE on a
branch
indicates a
branch is
selected and
FALSE means
it is not.
Final Decision Tree
(Figure 5-17)
B
C
D
Success
33
20.0%
$0
$10,000
$17,000
FALSE
$0
0
-$5,000
TRUE
-$15,000
$1,000
Success
20.0%
$90,000
Market nationally
-$47,000
Failure
80.0%
$0
Unfavorable
50.0%
$0
-$15,000
TRUE
Abort
$0
0.5
-$15,000
$1,000
50.0%
Success
$100,000
Market nationally
-$10,000
50.0%
Failure
$0
FALSE
$0
$0
Abort
0
$40,000
FALSE
-$60,000
TRUE
0
$0
$0
0.0
$25,000
FALSE
-$50,000
Don't test market
0.1
-$55,000
50.0%
Favorable
Abort
4. The
expected
payoff is
$1,000 (cell
B24).
$35,000
$17,000
Failure
Test market
0.4
TRUE
-$50,000
1. Test market
3. If the test
market is not
successful,
Ponderosa Record Company
abort.
F
80.0%
$90,000
Market nationally
The optimal
strategy is:
2. If the test
market is
successful,
market
nationally.
E
0
-$60,000
0.0
-$65,000
Risk Profile
Clicking on the Decision Analysis icon
gives the risk profile.
The risk profile is the probability
distribution of the possible outcomes if
the optimal strategy is followed.
34
Risk Profile
for Ponderosa Record Co. (Figure 5-18)
Risk Profile For Ponderosa Record Company
0.6
Probability
0.5
0.4
0.3
0.2
0.1
0
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
Expected Value, $
35
10000
20000
30000
40000
50000
Sensitivity Analysis
Determining Important Factors
 The optimal solution depends on many
factors. Which is the most important? A
sensitivity analysis answers this question.
To perform a sensitivity analysis,
click on the Sensitivity Analysis icon.
36
Sensitivity Analysis
Determining Important Factors
How does the $1,000 payoff change if
±10% changes occur in:
 the $90,000 partial cash flow in cell E2
37
 the 0.80 success probability in cell E1
 the $15,000 test marketing cost in cell
B12
Clicking on the Sensitivity Analysis Icon
yields the Sensitivity Analysis
dialog box shown next.
Sensitivity Analysis Dialog Box
(Figure 5-19)
1. In the Cell to
Analyze line
enter B24, the
location of the
$1,000 expected
payoff
2. Under the
Input Editor
section, input E2
in the Cell line
as the location
of the $90,000
partial cash
flow.
38
3. Click the
Suggest Values
button and enter
the ±10% variation
and click on the
Add button and
Success/Ponderosa
!$E$2 (-10%,90000,
10%) appears in the
first line in the Cells
to Vary box.
4. Repeat these
steps for the other
items to vary.
5. Click on the
Run Analysis
button.
Tornado Diagram
(Figure 5-20)
Effect of a Ten Percent Change on the Expected Payoff
(Tornado Diagram)
Successful Outcome
Sales
Successful Outcome
Probability
Test Marketing Cost
-200.0%
-100.0%
0.0%
100.0%
200.0%
300.0%
400.0%
Expected Value Change from Base Value
39
Each horizontal bar shows the effect on the $1,000
expected payoff of a ±10% change in original levels of
(1) $90,000 successful sales outcome, (2) 0.80 success
probability, (3) the $15,000 test marketing cost.
Spider Graph
(Figure 5-21)
The Effect of Ten Percent Changes on the Expected Value
(Spider Graph)
Expected Value, $
5000
4000
Sucess probability
3000
Test marketing cost
2000
Sucess sales
1000
-10.0%
-5.0%
0
0.0%
5.0%
10.0%
15.0%
Percent Change from Base Value
40
1. The steeper the slope of the line, the larger the effect of a
factor on the $1,000 expected payoff.
2. The success probability and sales lines coincide indicating
that they have equal effects on the $1,000 expected payoff.