TreePlan 201 Guide

8/19/2019 TreePlan 201 Guide

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Decision TreesUsing TreePlan

16

16.1 TREEPLAN OVERVIEW

TreePlan is a decision tree add-in for Microsoft Excel 2010 & 2013 & 2016 (Windows) and

Microsoft Excel 2011 & 2016 (Macintosh).

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) press Ctrl+Shift+T (or Option+Cmd+T) 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 2010 & 2013 & 2016, you can start TreePlan either by choosing Add-ins >

TreePlan Decision Tree or by pressing Ctrl+Shift+T (hold down the Ctrl and Shift keys and press

T).

With Mac Excel 2011, you can start TreePlan either by choosing Tools > TreePlan Decision

Tree from the menu or by pressing Option+Cmd+T (hold down the Option and Command keys

and press T).

With Mac Excel 2016, you can start TreePlan by pressing Option+Cmd+T.

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


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198 Chapter 16 Decision Trees Using TreePlan

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 problems 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.

Branch Inputs Cell Formulas Defined Name

Optional

Optional

Cash Flow

Probability

Terminal Node

Endpoint Value

Event Node

Rollback Value

Decision Node

Choice Indicator

Decision Node

Rollback Value

RT (Risk Tolerance)

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Endpoint Valueat Terminal Node

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Rollback Value

at Event Node

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Rollback Value

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MAX or MIN of subsequent r ollback

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Choice Indicator

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16.5 Step-by-Step TreePlan Tutorial 199

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 thestorage 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 asa 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.


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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 SymbolsType of Node Written Symbol Computer Symbol Node Successor

Decision square square decision branchesEvent circle circle event branchesTerminal 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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Figure 16.15 Initial Event Branches

5. Select cell H2, and enter Awarded contract. Select cell H4, and enter 250000. Select cellH7, and enter Not awarded contract.

Figure 16.16 Event Branches With Names and Cash Flow

6. Select cell J3. Press Ctrl+Shift+T. In the TreePlan Terminal Node dialog box, select

Change To Decision Node, select Three Branches, and click OK. The tree is redrawn.

1

2

34

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Figure 16.17 Subsequent Decision Branches

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. Press Ctrl+Shift+T. In the TreePlan Terminal Node dialog box, select

Change To Event Node, select Two Branches, and click OK. The tree is redrawn.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1819

20

21

22

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0

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4

5

6

7

8

9

10

11

12

13

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15

16

17

18

19

20

21

22

23

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A B C D E F G H I J K L M N O

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80000

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13/22


Figure 16.19 Branches for Electronic Method Uncertainty

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. Press Ctrl+Shift+T. In the TreePlan Terminal Node dialog box, select

Change To Event Node, select Two Branches, and click OK. The tree is redrawn.

1

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45

67

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1213

14

1516

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19

2021

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00 0


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Figure 16.21 Branches for Magnetic Method Uncertainty

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.

12

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16

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150000

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30000

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Outcome 11120000

0 120000

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0 -50000


00 0


15/22


Figure 16.22 Complete Diagram Before Formatting

12. Double-click the sheet tab (or right-click the sheet tab and choose Rename from the

shortcut menu), and enter 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 –$50,000Event Awarded contract $250,000Decision Try electronic method –$50,000Event 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

12

34

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1112

13

1415

16

1718

1920

21

2223

24

2526

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80000-120000 80000


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2 -50000 90000 0.5250000 90000 Electronic failure

30000

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Try magnetic method 0 120000-50000 20000

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16/22

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ion.

the Tree

teps show ho

se other form

e Edit menu,

r Copy from

box, check the

et Original (2)

ift+T. In the

obabilities is

eft button.

eePlan Select

ell H12. Pres

button for Cel

w cells select

ose cells stillialog box, clic

or Decimal Pl

rs. Click OK.

Using TreePlan

, and 3, from t

he electronic

iagram

to use TreePl

ts for your ow

choose Move

the shortcut m

Create A Cop

, if the probab

reePlan Selec

elected, and cl

Dialog Box

Ctrl+Shift+T

s with Partial

ed, if the cash

selected, chook the Number

aces; select $ i

op to bottom)

ethod. A sub

an and Excel f

n tree diagra

or Copy Sheet

enu). In the lo

y box, and cli

lities are not l

t dialog box,

ick OK. With

. In the TreePl

Cash Flows is

flows are not l

e Home > Fotab. In the Cat

n the Symbol

s the optimal

sequent chapt

eatures to for

s.

(or right-click

er left corne

k OK.

eft-aligned, se

erify that the

all probability

an Select dial

selected, and

eft-aligned, cl

mat > Formategory list box

list box; select

choice. If awa

er provides m

at the tree dia

the sheet tab

of the Move

lect cell H9. P

ption button f

cells selected

g box, verify

lick OK. Wit

ick the Align

Cells. In the F choose Curre

-$1,234 for

ded the

re details

gram. You

nd choose

r Copy

ess

or Cells

, click the

hat the

all partial

eft button.

ormatcy; type 0

egative


17/22

F

igure 16.25 E

16. Select

option

rollbac

above.

17. Select

optionvalue c

above.

cel Format C

ell I12. Press

button for Cel

k cells selecte

ell S3. Press

button for Celells selected,

lls Dialog Bo

Ctrl+Shift+T.

s with Rollba

, choose For

trl+Shift+T. I

s with Terminhoose Format

In the TreePla

k EVs/CEs is

at > Cells. Re

n the TreePla

al Values is se> Cells. Repe

16.5 Step-by-

n Select dialo

selected, and

peat the Curre

Select dialog

lected, and clit the Currenc

tep TreePlan T

box, verify t

lick OK. Wit

ncy formattin

box, verify th

ck OK. Withformatting o

utorial 209

at the

all

of step 16

at the

ll terminalstep 16


18/22


Figure 16.26 Complete DriveTek Decision Tree

18. Double-click the Original (2) sheet tab (or right-click the sheet tab and 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. From the Edit menu, choose Move or Copy Sheet (or 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.

20. On sheet Formatted (2), select cell B1. Press Ctrl+Shift+T. In the TreePlan Select dialog

box, verify that the option button for Columns with Nodes is selected, and click OK.

With all node columns selected, choose Format > Cells > Number or Home > Format >

Format Cells > Number. In the Category list box, select Custom. Select the entry in theType edit box, and type ;;; (three semicolons). Click OK.

12

34

5

67

8

910

1112

13

1415

16

1718

1920

21

2223

24

2526

2728

29

3031

32

3334



$80,000-$120,000 $80,000


$150,000

0.5 Try electronic method $0 $150,000 Awarded contract

2 -$50,000 $90,000 0.5$250,000 $90,000 Electronic failure

$30,000

-$120,000 $30,000

0.7

Magnetic successPrepare proposal $120,000

Try magnetic method $0 $120,000-$50,000 $20,000

-$80,000 $84,000 0.3

Magnetic failure$0

-$120,000 $0

1 0.5

$20,000 Not awarded contract-$50,000

$0 -$50,000


$0$0 $0


19/22

F

E

s

v

d

t

f

f

igure 16.27 E

xplanation: A

parated by se

lues, and text

es not displa

e cell, but its

rmat without

rmats are sav

21. Select

option

rollbac

Cells >

list bo

22. Doubl

from t

rinting th

23. In the

24. To pri

& 201

Button

tab; fo

option

Heade

approp

cel Format C

custom numbe

icolons, and

, in that order.

positive num

esult is not di

aving to ente

d with the wo

ell A27. Pres

button for Cel

k values select

Number. In t

, and select th

-click the For

e shortcut me

Tree Dia

ame Box list

t the tree diag

& 2016, cho

or File > Prin

Orientation c

button for Fit

list box selec

riate headers a

lls Dialog Bo

r format has f

hey define the

When you spe

ers, negative

played. Later,

the formula a

kbook unless

Ctrl+Shift+T

s with Rollba

ed, choose Fo

e Category li

e three-semico

atted (2) she

u), and enter

ram

box, select Tr

am from Exc

se Page Layo

Preview > Pa

ick the option

o 1 Page Wi

None, and in

nd footers). Cl

ur sections of

formats for p

cify three sem

umbers, zero

if you want to

gain. Editing

you explicitly

. In the TreePl

k EVs/CEs is

mat > Cells >

t box, select C

lon entry. Cli

t tab (or right

odel Inputs

eDiagram (or

l, with the tre

t > Print Are

ge Setup. In th

button for La

e By 1 Page T

the Footer list

ick the Sheet

16.5 Step-by-

format codes.

sitive numbe

icolons witho

values, or tex

display the re

n existing for

delete a form

an Select dial

selected, and

Number or H

ustom. Scroll

k OK.

click the shee

. Save the wor

select cells A

diagram ran

> Set Print A

e Page Setup

dscape, and f

all. Click the

box select No

ab; clear the c

tep TreePlan T

The sections

s, negative nu

t format code

. The formula

sult, you can c

at does not d

t.

g box, verify

lick OK. Wit

ome > Format

to the bottom

t tab and choo

kbook.

1:S34).

e selected, in

rea. Then cho

ialog box, cli

or Scaling clic

eader/Footer

ne (or select o

heck box for

utorial 211

re

bers, zero

, Excel

remains in

hange the

elete it. All

hat the

all

> Format

f the Type

e Rename

xcel 2010

se Office

k the Page

the

tab; in the

her

ridlines,


20/22


and clear the check box for Row And Column Headings. Click OK. Choose File > Print

and click OK.

25. To print the tree diagram from Word, clear the check boxes for Gridlines and for Row

And Column Headings on Excel’s Page Setup dialog box Sheet tab. Select the tree

diagram range. In Excel 2010 & 2013 & 2016, choose Home > Paste > As Picture >

Copy as Picture. In the Copy Picture dialog box, click the option button As Shown When

Printed, and click OK. In Word select the location where you want to paste the tree

diagram and choose Edit > Paste.

Figure 16.28 DriveTek Without Rollback Values

Al ternative 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

0.5

Electronic success$150,000

0.5 Try electronic method $0 Awarded 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

0.5

Not awarded contract -$50,000$0

Don't prepare proposal$0

$0


21/22

F

1

T

e

u

f

F

F

a

e

T

f

igure 16.29 A

6.6 EXP

reePlan's defa

ent node and

ilities in Tree

rmulas for co

igure 16.30 T

or the Maximi

d CE = -LN((

ponential util

reePlan uses t

nction. The n

Prepare

-$50,000

Don't pr

$0

ternative Driv

NENTIA

lt is to rollbac

aximum of s

lan's Options

puting the uti

eePlan Option

e option with

A-EU)/B)*RT

ty, the formul

e name RT to

mes A and B

0.5 Awa

$25

proposal

0.5Not

$0

pare proposal

eTek Decisio

L UTILIT

k the tree usin

uccessor value

dialog box, Tr

lity and certai

s Dialog Box

exponential u

, where X and

s are U = A-

represent the

etermine scal

rded contract

,000

awarded contract

Tree

Y AND T

g expected val

s at a decision

eePlan will re

equivalent a

ility, the rollb

EU are cell re

*EXP(X/RT)

isk tolerance

ing. If the na


-$120,000

Try electronic method

-$50,000

Try magnetic method

-$80,000

16.6 Exponenti

REEPLA

ue (probabilit

node. If you

raw the decis

each node.

ck formulas a

ferences. For t

and CE = LN(

arameter of t

es A, B, and


$0

0.5Electronic failure

$0

0.7Magnetic success

$0

0.3Magnetic failure

$0

al Utility and Tre

N

-weighted av

hoose to use e

on tree diagra

re U = A–B*

he Minimize

(A-EU)/B)*R

e exponential

T don't exist

Use mechanical1

-$120,000

Use mechanical1

-$120,000

ePlan 213

rage) at an

xponential

with

XP(X/RT)

ption with

.

utility

n the

$80,000

$150,000

method$30,000

$120,000

method$0

-$50,000

$0


22/22


worksheet when you choose to use exponential utility, they are initially defined as A=1, B=1, and

RT=999999999999. You can change the values of the names using the Insert > Name > Define

command.

16.7 ACKNOWLEDGEMENT

TreePlan was developed by Professor Michael R. 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

2008–2016.

TreePlan 201 Guide

Documents