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Decision Trees Using TreePlan 16

16.1 TREEPLAN OVERVIEW TreePlan is a decision tree add-in for Windows Excel 2010 & 2013 & 2016 & 2019 & 365 and Mac Excel 2016 & 2019 & 365.

TreePlan helps you build a decision tree diagram in an Excel worksheet using dialog boxes. Decision trees are useful for analyzing sequential decision problems under uncertainty. Your decision tree model may include various controllable alternatives (e.g., whether to introduce a new product, whether to bid on a new project) and uncontrollable uncertainties (e.g., possible demand for a product, whether you're awarded a contract), arranged in chronological order. TreePlan automatically includes formulas for summing cash flows to obtain outcome values and for calculating rollback values for determining the optimal strategy.

To use TreePlan, you (1) open a new worksheet, (2) choose TreePlan > TreePlan to build a new decision tree diagram, (3) select a node to change the structure of your decision tree, (4) enter branch names, cash flows, and probabilities, and (5) determine the optimal strategy from TreePlan's results.

All of TreePlan’s functionality, including its built-in help, is a part of the TreePlan XLAM file. There is no separate setup file or help file. When you use TreePlan on a Windows computer, TreePlan does not create any Windows Registry entries (although Excel may use such entries to keep track of its add-ins).

16.2 BUILDING A DECISION TREE IN TREEPLAN With Windows Excel or Mac Excel, you can start TreePlan by choosing the TreePlan ribbon and clicking the TreePlan button. In these instructions we write “TreePlan > TreePlan.”

An alternative is to use the shortcut key: Control+Shift+T on Windows Excel, or Option+Command+t on Mac Excel.

If the worksheet doesn't have a decision tree, TreePlan prompts you with a dialog box with three options; choose New Tree to begin a new tree. TreePlan draws a default initial decision tree with its upper left corner at the selected cell. For example, the figure below shows the initial tree when cell C3 is selected before creating the new tree.

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16.4 TREEPLAN INPUTS AND FORMULAS

Figure 16.7 Influence Chart of TreePlan Inputs and Formulas

Figure 16.8 Explanation of Formulas

16.5 STEP-BY-STEP TREEPLAN TUTORIAL A decision tree can be used as a model for a sequential decision problem under uncertainty. A decision tree describes graphically the decisions to be made, the events that may occur, and the outcomes associated with combinations of decisions and events. Probabilities are assigned to the events, and values are determined for each outcome. A major goal of the analysis is to determine the best decisions.

Decision tree models include such concepts as nodes, branches, terminal values, strategy, payoff distribution, certain equivalent, and the rollback method. The following problem illustrates the basic concepts.

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16.5 Step-by-Step TreePlan Tutorial 203

DriveTek Problem

DriveTek Research Institute discovers that a computer company wants a new storage device for a proposed new computer system. Since the computer company does not have research people available to develop the new storage device, it will subcontract the development to an independent research firm. The computer company has offered a fee of $250,000 for the best proposal for developing the new storage device. The contract will go to the firm with the best technical plan and the highest reputation for technical competence.

DriveTek Research Institute wants to enter the competition. Management estimates a cost of $50,000 to prepare a proposal with a fifty-fifty chance of winning the contract.

However, DriveTek's engineers are not sure about how they will develop the storage device if they are awarded the contract. Three alternative approaches can be tried. The first approach is a mechanical method with a cost of $120,000, and the engineers are certain they can develop a successful model with this approach. A second approach involves electronic components. The engineers estimate that the electronic approach will cost only $50,000 to develop a model of the storage device, but with only a 50 percent chance of satisfactory results. A third approach uses magnetic components; this costs $80,000, with a 70 percent chance of success.

DriveTek Research can work on only one approach at a time and has time to try only two approaches. If it tries either the magnetic or electronic method and the attempt fails, the second choice must be the mechanical method to guarantee a successful model.

The management of DriveTek Research needs help in incorporating this information into a decision to proceed or not.

[Source: The storage device example is adapted from Spurr and Bonini, Statistical Analysis for Business Decisions, Irwin.]

Nodes and Branches

Decision trees have three kinds of nodes and two kinds of branches. A decision node is a point where a choice must be made; it is shown as a square. The branches extending from a decision node are decision branches, each branch representing one of the possible alternatives or courses of action available at that point. The set of alternatives must be mutually exclusive (if one is chosen, the others cannot be chosen) and collectively exhaustive (all possible alternatives must be included in the set).

There are two major decisions in the DriveTek problem. First, the company must decide whether or not to prepare a proposal. Second, if it prepares a proposal and is awarded the contract, it must decide which of the three approaches to try to satisfy the contract.

An event node is a point where uncertainty is resolved (a point where the decision maker learns about the occurrence of an event). An event node, sometimes called a "chance node," is shown as a circle. The event set consists of the event branches extending from an event node, each branch representing one of the possible events that may occur at that point. The set of events must be mutually exclusive (if one occurs, the others cannot occur) and collectively exhaustive (all possible events must be included in the set). Each event is assigned a subjective probability; the sum of probabilities for the events in a set must equal one.

The three sources of uncertainty in the DriveTek problem are: whether it is awarded the contract or not, whether the electronic approach succeeds or fails, and whether the magnetic approach succeeds or fails.


In general, decision nodes and branches represent the controllable factors in a decision problem; event nodes and branches represent uncontrollable factors.

Decision nodes and event nodes are arranged in order of subjective chronology. For example, the position of an event node corresponds to the time when the decision maker learns the outcome of the event (not necessarily when the event occurs).

The third kind of node is a terminal node, representing the final result of a combination of decisions and events. Terminal nodes are the endpoints of a decision tree, shown as the end of a branch on hand-drawn diagrams and as a triangle on computer-generated diagrams.

The following table shows the three kinds of nodes and two kinds of branches used to represent a decision tree.

Figure 16.9 Nodes and Symbols Type of Node Written Symbol Computer Symbol Node Successor Decision square square decision branches Event circle circle event branches Terminal endpoint triangle or bar terminal value

Terminal Values

Each terminal node has an associated terminal value, sometimes called a payoff value, outcome value, or endpoint value. Each terminal value measures the result of a scenario: the sequence of decisions and events on a unique path leading from the initial decision node to a specific terminal node.

To determine the terminal value, one approach assigns a cash flow value to each decision branch and event branch and then sum the cash flow values on the branches leading to a terminal node to determine the terminal value. In the DriveTek problem, there are distinct cash flows associated with many of the decision and event branches. Some problems require a more elaborate value model to determine the terminal values.

The following diagram shows the arrangement of branch names, probabilities, and cash flow values on an unsolved tree.

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5. Select cell H2, and enter Awarded contract. Select cell H4, and enter 250000. Select cell H7, and enter Not awarded contract.

Figure 16.16 Event Branches With Names and Cash Flow

6. Select cell J3. Choose TreePlan > TreePlan. In the TreePlan Terminal Node dialog box, select Change To Decision Node, select Three Branches, and click OK. The tree is redrawn.

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7. Select cell L2, and enter Use mechanical method. Select cell L4, and enter –120000. Select cell L7, and enter Try electronic method. Select cell L9, and enter –50000. Select cell L12, and enter Try magnetic method. Select cell L14, and enter –80000.

Figure 16.18 Subsequent Decision Branches With Names and Cash Flows

8. Select cell N8. Choose TreePlan > TreePlan. In the TreePlan Terminal Node dialog box, select Change To Event Node, select Two Branches, and click OK. The tree is redrawn.

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9. Select cell P7, and enter Electronic success. Select cell P12, and enter Electronic failure. Select cell P14, and enter –120000.

Figure 16.20 Branch Names and Cash Flows for Electronic Method Uncertainty

10. Select cell N18. Choose TreePlan > TreePlan. In the TreePlan Terminal Node dialog box, select Change To Event Node, select Two Branches, and click OK. The tree is redrawn.

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11. Select cell P16, and enter .7. Select cell P17, and enter Magnetic success. Select cell P21, and enter .3. Select cell P22, and enter Magnetic failure. Select cell P24, and enter –120000.

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12. Rename the sheet tab Original. Save the workbook.

Interpreting the Results

The $30,000 terminal value on the far right of the diagram in cell S13 is associated with the following scenario:

Figure 16.23 Evaluation of a Scenario Branch Type Branch Name Cash Flow Decision Prepare proposal –$50,000 Event Awarded contract $250,000 Decision Try electronic method –$50,000 Event Electronic failure (Use mechanical method) –$120,000

Terminal value $30,000

TreePlan put the formula =SUM(P14,L11,H12,D20) into cell S13 for determining the terminal value.

Other formulas, called rollback formulas, are in cells below and to the left of each node. These formulas are used to determine the optimal choice at each decision node.

In cell B26, a formula displays 1, indicating that the first branch is the optimal choice. Thus, the initial choice is to prepare the proposal. In cell J11, a formula displays 2, indicating that the second branch (numbered 1, 2, and 3, from top to bottom) is the optimal choice. If awarded the

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Figure 16.26 Complete DriveTek Decision Tree

18. Right-click the sheet tab, choose Rename from the shortcut menu, and enter Formatted. Save the workbook.

Displaying Model Inputs

When you build a decision tree model, you may want to discuss the model and its assumptions with co-workers or a client. For such communication it may be preferable to hide the results of formulas that show rollback values and decision node choices. The following steps show how to display only the model inputs.

19. Right-click the sheet tab, and choose Move Or Copy from the shortcut menu. In the lower left corner of the Move Or Copy dialog box, check the Create A Copy box, and click OK.

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click the sheet . Save the wor

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our sections of e formats for poecify three semnumbers, zero if you want togain. Editing ayou explicitly

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16.5 Step-by-S

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Tutorial 215

are mbers, zero s, Excel remains in

change the elete it. All

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25. To print the tree diagram from Word, in Excel select the tree diagram range. On Excel’s Page Layout ribbon, uncheck Gridlines View. On Excel’s Home ribbon, click (Clipboard) Copy. In Word, select the insertion point, and on Word’s Home ribbon, click the (Clipboard) Paste dropdown arrow, and click Paste as Picture.

Figure 16.28 DriveTek Without Rollback Values

Alternative Model

If you want to emphasize that the time constraint forces DriveTek to use the mechanical approach if they try either of the uncertain approaches and experience a failure, you can change the terminal nodes in cells R13 and R23 to decision nodes, each with a single branch.

Use mechanical method$80,000

-$120,000


$150,0000.5 Try electronic method $0Awarded contract

-$50,000 0.5$250,000 Electronic failure

$30,000-$120,000

0.7Magnetic success

Prepare proposal $120,000Try magnetic method $0

-$50,000-$80,000 0.3

Magnetic failure$0

-$120,000


-$50,000$0

Don't prepare proposal$0

$0

F

1Trevutfo

F

FoU

FoU

igure 16.29 Al

6.6 EXPOreePlan's defauvent node and mtilities in TreePormulas for com

igure 16.30 Tr

or the MaximizU = A–B*EXP(

or the MinimizU = A-B*EXP(X

Prepare

-$50,000

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lternative Driv

ONENTIAult is to rollbacmaximum of sPlan's Options mputing the uti

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ze option with X/RT) and CE

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proposal

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epare proposal

veTek Decision

AL UTILITYck the tree usinuccessor valuedialog box, Trility and certain

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exponential uti= LN((A-EU)

arded contract

0,000

awarded contract

n Tree

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es at a decisionreePlan will redn equivalent at

tility, the rollbaU)/B)*RT, whe

ility, the formu/B)*RT.

Use mechanical method

-$120,000

Try electronic method

-$50,000

Try magnetic method

-$80,000

16.6 Exponenti

REEPLANlue (probabilityn node. If you cdraw the decisit each node.

ack formulas aere X and EU a

ulas are


$0

0.5Electronic failure

$0

0.7Magnetic success

$0

0.3Magnetic failure

$0

ial Utility and Tre

N y-weighted avechoose to use eion tree diagram

are are cell referen

Use mechanical 1

-$120,000

Use mechanical 1

-$120,000

eePlan 217

erage) at an exponential m with

nces.

$80,000

$150,000

method$30,000

$120,000

method$0

-$50,000

$0


TreePlan uses the name RT to represent the risk tolerance parameter of the exponential utility function. The names A and B determine scaling. When you choose to use exponential utility, if the names A, B, and RT do not already exist in the worksheet or workbook, they are initially defined as A=1, B=1, and RT=999999999999.

In Windows Excel you can change the values of defined names using Formulas > Name Manager > Edit.

In Mac Excel you can change the values of defined names by choosing (from the topmost menu) Insert > Name > Define Name or by choosing Formulas > Define Name. In the Define Name dialog box, after you select a name in the “Names in workbook” list box, enter a new value in the “Select the range of cells” edit box, and click the OK button.

16.7 ACKNOWLEDGEMENT TreePlan was developed by Professor Michael Rory Middleton at the University of San Francisco (using the Excel 4 XLM macro programming language) and modified for use at Fuqua (Duke University) by Professor James E. Smith. Mike Middleton rewrote portions using VBA during 2008–2020.

20200723-1827-decan · 2020. 9. 29. · ded in the spre to that termina and by maxim xpected value is optimal for ptimal to prep ld try the elect an the mechan TreePlan wit t button

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