Op Research Notes

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IndE 311: Stochastic Models and Decision Analysis

Winter 2007

Lab 1: Using spreadsheets to build and analyze decision trees

The objective of the lab is to familiarize you with two Excel add-ins (TreePlan & Sensit) to

build and analyze decision trees.

Part 0: Get ready

Go to class web page (http://courses.washington.edu/inde311 ), then select Labs. Download

the two add-ins (TreePlan and SensIt): Right-click on each link, select Save Target as and

save the two files on the desktop.

Open Microsoft Excel, select Tools -> Add-Ins Select Browse and point to the two add-ins

(on the desktop now) one by one. Verify that the add-ins are installed by checking if your

Tools menu contains Decision Tree and Sensitivity Analysis, i.e. as below:

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Part 1: Create a decision tree using TreePlan

Consider the first Goferbroke Co. problem in the text book (no seismic survey)

Step 1: In Microsoft Excel, select decision tree from the Tools menu and click on New Tree.See Figure 1.1.

Figure 1.1

This creates the default decision tree as shown in figure 1.2 with a single (square) decision

node with two branches.

Figure 1.2

Note: To change the type of any node in TreePlan, select the cell containing the node (B5 in

figure 2) and choose Decision Tree from the Tools menu. This brings up a dialogue box that

allows you to change the types of node.

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Step 2: Click on the cells to change the labels. Change labels for Decision 1 and Decision

2 (cells D2 & D7 in figure 2) to Drill and Sell respectively.

Step 3: Click on the cell containing the terminal node at the end of the drill branch (F3 in

Figure 1.2), and choose Decision Tree from the Tools menu. This brings up the

TreePlan dialog as shown in figure 1.3

Figure 1.3

Choose the change to event node option on the left and select two branches on the

right then click OK. This results in the decision tree with the nodes and branches

shown in Figure 1.4 (after replacing the default labels Event 1 and Event 2 with

Oil and Dry, respectively)

Figure 1.4

Step 4: Change the net cash flows and prior probabilities of each branch by click on the

default values and replace them with correct numbers.

Initially, each branch would show a default value of 0 for the net cash flow being

generated. Each of the two branches leading from event node would display default

values of 0.5 for their prior probabilities. They should be changed as following:

D6 = -100, D14 = 90, H1 = 0.25, H4 = 800, H6 = 0.75, H9 = 0

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At each stage in constructing a decision tree, TreePlan automatically solves for the optimal

policy with the current tree when using Bayes Decision rule. See figure 1.5. The number

inside each decision node indicates which branch should be chosen (assuming the branches

emanating from that node are numbered consecutively from top to bottom).

Figure 1.5

Part 2: Calculate posterior probabilities using Excel

Open a new sheet to practice calculating posterior probabilities using Bayes theorem.

Remember that we were given P(FSS|oil) and P(USS|dry), but wanted the posterior

probabilities. This can be done in Excel using the following template (formulas shown here).

Try building it yourself, while paying attention to how Bayes theorem is applied.

Figure 2.1

The result should look similar to this:

Figure 2.2

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Part 3: Create the decision tree for the full Goferbroke Co. problem (With the seismic

survey)

Practice what you learned on Part 1 on the full Goferbroke problem. Remember to use the

posterior probabilities you found in Part 2. Take your time.

The result should look like Figure 3.1.

Figure 3.1

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Part 4a: Prepare worksheet for sensitivity analysis

To perform the sensitivity analysis, we need to consolidate the problem data. That is, we

want to collect all problem parameters to one place and refer to them in the decision tree. So,

on the right side of your decision tree, you want to have your data entered in a format as in

Figure 4.1.

Figure 4.1

Now we want the data in the decision tree taken from these values, such that they are

updated any time a change is made in the consolidated data. Note that in Figure 4.1, the

posterior probabilities are functions of the prior probabilities (constructed as in Part 2) and will

be updated once a change is made in any of the prior probabilities.You should now have all cells shaded in Figure 4.2 as a function of your consolidated data.

0.142857

Oil

670

Drill 800 670

-100 -15.7143 0.857143

0.7 Dry

FSS -130

2 0 -130

0 60

Sell

60

90 60

Do Survey

0.5

-30 123 Oil

670

Drill 800 670

-100 270 0.5

0.3 Dry

USS -130

1 0 -130

0 270

1 Sell

123 60

90 60

0.25

Oil

700

Drill 800 700

-100 100 0.75

Dry

Don't do survey -100

1 0 -100

0 100

Sell

90

90 90

Figure 4.2

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Now you can also get the Expected Payoff (result of your decision tree) at the bottom of your

consolidated data, and summarize the optimal decision policy using a set of formulas, for

example as in Figure 4.3,

Figure 4.3

which would give, with the current data, the following result in Figure 4.4:

Now it should be very easy for you to try different values for the costs, probabilities and other

parameters and see how these affect your decision!

In the next part, well let a sensitivity analysis package, SensIt, test different values for us.

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Part 5: Use Sensit to create three types of sensitivity analysis graphs

Plot is used to generate a graph that shows how an output cell varies for different values of a

single data cell.

Select Sensitivity Analysis Plot from the Tool Menu, brings up the Plot dialogue box shown

in Figure 5.1. The left side of the Plot dialogue box is used to specify the data cell that will bevaried (the prior probability of oil in cell V9) and the o utput cell of interest (the expected

payoff in cell X5). The right side of the Plot dialogue box is used to specify the range of values

to be considered for the single data cell (the prior probability of oil). Clicking OK generates the

graph shown in Figure 5.2.

Figure 5.1

SensIt - Sensitivity Analysis - Plot

0

100

200

300400

500

600

700

0 0.2 0.4 0.6 0.8 1

Prior Probability of oil

Expecte

d

Pay

Figure 5.2

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Spider Graph can be used investigate how a cell value changes (e.g. the expected payoff)

under percentage changes of a certain set of cells (e.g. costs or revenues in cells V4:V7).

Select Sensitivity Analysis -> Spider from the Tool Menu. In the dialog box shown in Figure

5.3, fill in the values of interest. Click OK.

.

Figure 5.3

The resulting spider graph would look similar to Figure 5.4

Sensit - Sensitivity Analysis - Spider

90100110120130140150160170180190200

40% 60% 80% 100

%

120

%

140

%

160

%

% Change in Input Value

Expected

Payoff

Cost of survey

Cost of drill

Revenue if oil

Revenue if sell

Revenue if dry

Figure 5.4

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Tornado graph: add three columns for the data set that defines the range (low, base, and

high) to test for the data cells as shown in Figure 5.5

Figure 5.5

Selecting Sensitivity Analysis ->Tornado from the Tool menu, which brings up the dialog

box shown in Figure 5.6. After filling in the values of interest, click OK

Figure 5.6

The resulting tornado graph is shown in Figure 5.7.

Figure 5.7

Investigate the three charts generated. We will talk about what they represent during the lab.

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