Chapter 5

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Chapter 5

There is no more miserable human being than one in whom nothing is habitual but indecision.—William James

Decision-Making

Concepts

2

Elements of DecisionsEvery 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:With a decision table or a payoff table.Or by a decision tree.

3

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.

4

The Decision Tree

The decision tree shows acts and events on separate forks, sequenced chronologically. Each outcome has a path.

5

Payoffs and Probabilities

Here the payoffs for outcomes are found adding partial cash flows on branches. Event branches have probabilities.

6

Making the DecisionUsing 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.

7

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.

8

Maximizing Expected Payoffis 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:

Would you gamble?

EVENTSProba-bility

ACTS

Gamble Don’t Gamble

Head .5 +$10,000 $0

Tail .5 5,000 0

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The Far-Fetched Lottery Decision

The expected payoffs are:

Most people prefer not to gamble! That violates the Bayes decision rule. But the rule often indicates preferred choices even

though it is not perfect.

EVENTSProba-bility

ACTS

Gamble Don’t Gamble

Payoff × Prob. Payoff × Prob

Head .5 +$5,000 $0

Tail .5 2,500 0

Expected Payoff: $2,500 $0

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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.

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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.

12

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.

The process works backward in time.

13

Folding Back the Decision Tree

14

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.

15

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.

16

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.

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Expected Value ofPerfect 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 predict-

ors (real ones) costing more than the EVPI.

18

Templates and Software

Payoff Table templates

Palisade Decision Tools PrecisionTree 1.0

19

Simple Payoff Table forExchecker Decision (Figure 5-2)

123456789

10111213141516

A B C D E F

PROBLEM: Exchecker Marketing Strategy

Act 1 Act 2 Act 3 Act 4Events 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%

PAYOFF TABLE EVALUATION

Problem Data

13C

=SUMPRODUCT($B$9:$B$12,C9:C12)

1. Enter problem name in B3.


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 Payoffs in the last row include all the rows of the expanded table.

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 Payoffs in the last row include all the rows of the expanded table.

2. Enter data in B9:F12 and labels in A9:A12 and C8:F8.


4. Expected payoffs4. Expected payoffs

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Expanded Payoff Table for Exchecker Decision (Figure 5-3)

123456789

1011121314151617181920212223242526272829303132

A B C D E F G

PROBLEM: Exchecker Marketing Strategy

Act 1 Act 2 Act 3 Act 4 RowEvents Probability Direct Mail Targ. Ad. Telemark Mass Mkt Maximum

1 Premature 0.1 85.00$ 50.00$ 40.00$ 40.00$ 85.00$ 2 Lackluster 0.3 80.00$ 70.00$ 65.00$ 50.00$ 80.00$ 3 Quick Accept. 0.4 40.00$ 50.00$ 30.00$ 70.00$ 70.00$ 4 Wildly Enthus. 0.2 25.00$ 35.00$ 40.00$ 60.00$ 60.00$

Act 1 Act 2 Act 3 Act 4Direct Mail Targ. Ad. Telemark Mass Mkt

Expected Payoff $53.50 $53.00 $43.50 $59.00Exp. Opportunity Loss $19.00 $19.50 $29.00 $13.50

Maximum Expected Payoff: $59.00 Act 4 Mass MktMinimum Expected Opportunity Loss: $13.50 Act 4 Mass MktExpected Value of Perfect Information: $13.50

PAYOFF TABLE EVALUATION

Act Summary

Overall Summary

Problem Data

9101112

G=MAX(C9:F9)=MAX(C10:F10)=MAX(C11:F11)=MAX(C12:F12)

232425

D=MAX(C18:F18)=MIN(C19:F19)=D24

2324

F=HLOOKUP(E23,$C$16:$F$17,2)=HLOOKUP(E24,$C$16:$F$17,2)

23

24

E

=CONCATENATE("Act ",MATCH(D23,C18:F18,0))

=CONCATENATE("Act ",MATCH(D24,C19:F19,0))

1819

C=SUMPRODUCT($B$9:$B$12,C9:C12)=SUMPRODUCT($B$9:$B$12,$G$9:$G$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 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.

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.

4. Answers : exp. payoff, exp. opportunity loss, max. exp. payoff, min. exp. opportunity loss, EVPI.

4. Answers : exp. payoff, exp. opportunity loss, max. exp. payoff, min. exp. opportunity loss, EVPI.

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Palisade Decision ToolsPrecisionTree

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.

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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.

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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.

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Initial PrecisionTreeDecision Tree

12

A B1

0tree #1

Clicking in cell A1 yield this initial tree.

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.

25

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.

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Initial Ponderosa Record Co. Decision Tree (Figure 5-10)

12

A B1

0Ponderosa Record Company

To expand the decision tree move the cursor over the end nod and click. This yields the Nodes Settings dialog boxes shown next.

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Node Settings Dialog Box (Figure 5-11)

Under node type click on the decision node .

The Node Settings dialog box changes to that shown on the right. There enter 2 in the # of Branches line and click OK.

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Extended PrecisionTree Decision (Figure 5-12)

123456

A B CTRUE 1

0 0

0

FALSE 0

0 0

Ponderosa Record Company

branch

branch

The costs associated with the branches are entered directly onto the spreadsheet, $15,000 in cell B2 and $0 in cell B6.

To name the branches click inside one of the boxes named branch. This brings to the screen the Branch Settings dialog box shown next.

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Branch Settings Dialog Box forNaming Decision Branches (Figure 5-13 )

Enter the name of the branch in the Branch Name line and click OK.

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Extended Decision Tree with Decisionsand Partial Cash Flows (Figure 5-14 )

123456

A B CTRUE 1

$15,000 $15,000

$15,000

FALSE 0

$0 $0


Test market

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 .

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.

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Second Expanded Decision Tree (Figure 5-15)

123456789

10

A B C D50.0% 0.5

$0 $15,000

TRUE

$15,000 $15,000

50.0% 0.5

$0 $15,000

$15,000

FALSE 0

$0 $0


Test market

Don't test market

Favorable

Unfavorable

The tree has two new branches, Favorable and Unfavorable.

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.

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Third Expanded Decision Tree (Figure 5-16)

123456789

1011121314

A B C D EFALSE 0

-$50,000 -$35,000

50.0%

$0 $15,000

TRUE 0.5

$0 $15,000

TRUE

$15,000 $15,000

50.0% 0.5

$0 $15,000

$15,000

FALSE 0

$0 $0


Test market

Don't test market

Favorable

Unfavorable

Market nationally

Abort

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.

Continuing to add branches yields the final tree shown next.

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123456789

10111213141516171819202122232425262728293031323334

A B C D E F80.0% 0.4

$90,000 $35,000

TRUE

-$50,000 $17,000

20.0% 0.1

$0 -$55,000

50.0%

$10,000 $17,000

FALSE 0

$0 -$5,000

TRUE

-$15,000 $1,000

20.0% 0.0

$90,000 $25,000

FALSE

-$50,000 -$47,000

80.0% 0.0

$0 -$65,000

50.0%

$0 -$15,000

TRUE 0.5

$0 -$15,000

$1,000

50.0% 0

$100,000 $40,000

FALSE

-$60,000 -$10,000

50.0% 0

$0 -$60,000

FALSE

$0 $0

TRUE 0

$0 $0


Test market

Don't test market

Favorable

Unfavorable

Market nationally

Abort

Success

Failure

Market nationally

Abort

Success

Failure

Market nationally

Abort

Success

Failure

Final Decision Tree (Figure 5-17)

TRUE on a branch indicates a branch is selected and FALSE means it is not.

TRUE on a branch indicates a branch is selected and FALSE means it is not.

The optimal strategy is:

1. Test market

2. If the test market is successful, market nationally.

3. If the test market is not successful, abort.

4. The expected payoff is $1,000 (cell B24).

The optimal strategy is:

1. Test market

2. If the test market is successful, market nationally.

3. If the test market is not successful, abort.

4. The expected payoff is $1,000 (cell B24).

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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.

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Risk Profilefor Ponderosa Record Co. (Figure 5-18)

Risk Profile For Ponderosa Record Company

0

0.1

0.2

0.3

0.4

0.5

0.6

-70000 -60000 -50000 -40000 -30000 -20000 -10000 0 10000 20000 30000 40000 50000

Expected Value, $

Pro

bab

ilit

y

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Sensitivity AnalysisDetermining 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.

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Sensitivity AnalysisDetermining Important Factors

How does the $1,000 payoff change if

±10% changes occur in: the $90,000 partial cash flow in cell E2 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.

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Sensitivity Analysis Dialog Box(Figure 5-19)

1. In the Cell to Analyze line enter B24, the location of the $1,000 expected payoff

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.

2. Under the Input Editor section, input E2 in the Cell line as the location of the $90,000 partial cash flow.

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.

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.

4. Repeat these steps for the other items to vary.

5. Click on the Run Analysis button.

5. Click on the Run Analysis button.

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Tornado Diagram (Figure 5-20)

Effect of a Ten Percent Change on the Expected Payoff(Tornado Diagram)

-200.0% -100.0% 0.0% 100.0% 200.0% 300.0% 400.0%

Test Marketing Cost

Successful OutcomeProbability

Successful OutcomeSales

Expected Value Change from Base Value

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.

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Spider Graph (Figure 5-21)

The Effect of Ten Percent Changes on the Expected Value(Spider Graph)

0

1000

2000

3000

4000

5000

-10.0% -5.0% 0.0% 5.0% 10.0% 15.0%

Percent Change from Base Value

Exp

ecte

d V

alu

e, $

Sucess probability

Test marketing cost

Sucess sales

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.

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