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8/19/2019 TreePlan 201 Guide
1/22
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
8/19/2019 TreePlan 201 Guide
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1
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16.
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f you want to
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and everythin
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Building a Dec
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decision or ev
press OK. To
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branch labels:
nds. To help
ision Tree in Tre
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1
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ision tree is sh
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PLAN D
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8/19/2019 TreePlan 201 Guide
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F
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igure 16.6 Te
reePlan has a
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16.3
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ay calculatio
reePlan's dial
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choose to Ma
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se options.
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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)
Location Formula
Endpoint Valueat Terminal Node
SUM of branch cash flo ws
Rollback Value
at Event Node
IF probabilities SUM to
approximately on e, then SUM the
products of probabilities times
subsequent rollback values
Rollback Value
at Decision Node
MAX or MIN of subsequent r ollback
values
Choice Indicator
at Decision Node
Nested IF function s
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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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200 Chapter 16 Decision Trees Using TreePlan
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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F
T
b
t
F
igure 16.10 D
o build the de
anch name, b
e left side of e
uilding th
1. Start w
is ope
2. Select
in Mac
press
instruc
box, cl
igure 16.11 T
Prepare prop
Don't prepare
iveTek Decisi
ision tree, you
anch cash flo
ach branch. A
e Tree Dia
ith a new wor
, choose Inser
ell A1. In Ex
Excel 2011, c
trl+Shift+T. I
tions refer onl
ick the New T
eePlan New T
0.5 Aw
sal
0.5
Not
proposal
on Tree Diagr
use TreePlan
, and branch
s you build the
ram
sheet. (If no
> Worksheet.
el 2007 & 20
hoose Tools >
Mac Excel 2
to the Windo
ee button. A
ree Dialog Bo
arded contract
awarded contract
am
s dialog boxe
robability (fo
tree diagram,
orkbook is o
)
0 & 2013, ch
TreePlan Dec
011 & 2016, p
ws shortcut k
ecision node
x
Use mechan
Try electroni
Try magneti
16.5 Step-by-
to develop th
an event) in t
TreePlan ente
en, choose Fil
ose Add-ins
ision Tree. Or
ress Option+
y. In the Tree
ith two branc
ical method
0.El
method
0.El
0.M
method
0.M
tep TreePlan T
e structure. Y
he cells above
rs formulas in
e > New. If a
TreePlan De
, in any Windo
md+T. Subse
lan New Tre
hes appears.
ctronic success
ctronic failure
gnetic success
gnetic failure
utorial 201
u enter a
and below
other cells.
orkbook
ision Tree;
ws version,
uent
dialog
$80,000
$150,000
$30,000
$120,000
$0
-$50,000
$0
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2
F
F
F
2 Chapter 16
igure 16.12 In
3. Select
D7, an
igure 16.13 B
4. Select
Chang
igure 16.14 T
1
23
456
789
A B
10
1
234
56
789
A B
20
Decision Trees
itial Decision
ell D2, and e
enter Don't
anch Names a
ell F3. Press
To Event No
eePlan Termi
C D
Alternative 1
0
Alternative 2
0
C D
Prepare propo
-50000
Don't prepare
0
Using TreePlan
ree Diagram
ter Prepare p
repare prop
nd Cash Flow
trl+Shift+T. I
de, select Two
al Node Dial
E F G
0
0
E F G
al-50
-50000
roposal
0
roposal. Sele
sal.
n the TreePla
Branches, an
g Box
0
0
00
0
t cell D4, and
Terminal No
click OK. Th
enter –50000.
de dialog box,
e tree is redra
Select cell
select
n.
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16.5 Step-by-Step TreePlan Tutorial 203
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
56
7
8910
11
1213
14
A B C D E F G H I J K0.5
Outcome 3
-50000Prepare proposal 0 -50000
-50000 -50000 0.5
Outcome 4
-500002 0 -50000
0
Don't prepare proposal0
0 0
12
34
5
67
89
1011
121314
A B C D E F G H I J K
0.5 Awarded contract
200000Prepare proposal 250000 200000
-50000 75000 0.5Not awarded contract
-500001 0 -50000
75000
Don't prepare proposal0
0 0
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204 Chapter 16 Decision Trees Using TreePlan
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
23
24
A B C D E F G H I J K L M N O
Alternative 5
200000
0 200000
0.5
Awarded contract Alternative 6
1 200000
250000 200000 0 200000
Prepare proposal Alternative 7
200000
-50000 75000 0 200000
0.5
Not awarded contract
1 -5000075000 0 -50000
Don't prepare proposal
0
0 0
12
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
A B C D E F G H I J K L M N O
Use mechanical method
80000
-120000 80000
0.5
Awarded contract Try electronic method
2 150000
250000 150000 -50000 150000
Prepare proposal Try magnetic method
120000
-50000 50000 -80000 120000
0.5
Not awarded contract
1 -50000
50000 0 -50000
Don't prepare proposal
0
0 0
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16.5 Step-by-Step TreePlan Tutorial 205
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
23
45
67
89
1011
1213
14
1516
1718
19
2021
2223
2425
26
2728
29
A B C D E F G H I J K L M N O P Q R S
Use mechanical method80000
-120000 80000
0.5Outcome 8
0.5 150000 Awarded contract Try electronic method 0 150000
2250000 150000 -50000 150000 0.5
Outcome 9150000
0 150000
Prepare proposal
-50000 50000 Try magnetic method120000
-80000 120000
0.5
1 Not awarded contract50000 -50000
0 -50000
Don't prepare proposal0
0 0
1
234
56
7
89
1011
1213
1415
1617
1819
20
2122
2324
25
2627
2829
A B C D E F G H I J K L M N O P Q R S
Use mechanical method80000
-120000 80000
0.5
Electronic success
0.5 150000 Awarded contract Try electronic method 0 150000
3250000 120000 -50000 90000 0.5
Electronic failure30000
-120000 30000Prepare proposal
-50000 35000 Try magnetic method
120000-80000 120000
0.51 Not awarded contract
35000 -500000 -50000
Don't prepare proposal
00 0
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206 Chapter 16 Decision Trees Using TreePlan
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
34
5
67
8
910
1112
13
1415
16
1718
1920
21
2223
24
2526
2728
29
3031
32
3334
A B C D E F G H I J K L M N O P Q R S
Use mechanical method
80000-120000 80000
0.5Electronic success
150000
0.5 Try electronic method 0 150000 Awarded contract
3 -50000 90000 0.5250000 120000 Electronic failure
30000
-120000 30000
0.5
Outcome 10Prepare proposal 120000
Try magnetic method 0 120000-50000 35000
-80000 120000 0.5
Outcome 11120000
0 120000
1 0.5
35000 Not awarded contract-50000
0 -50000
Don't prepare proposal
00 0
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16.5 Step-by-Step TreePlan Tutorial 207
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
5
67
8
910
1112
13
1415
16
1718
1920
21
2223
24
2526
2728
29
3031
3233
34
A B C D E F G H I J K L M N O P Q R S
Use mechanical method
80000-120000 80000
0.5Electronic success
150000
0.5 Try electronic method 0 150000 Awarded contract
2 -50000 90000 0.5250000 90000 Electronic failure
30000
-120000 30000
0.7
Magnetic successPrepare proposal 120000
Try magnetic method 0 120000-50000 20000
-80000 84000 0.3
Magnetic failure0
-120000 0
1 0.5
20000 Not awarded contract-50000
0 -50000
Don't prepare proposal0
0 0
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2
s
c
a
F
T
F
8 Chapter 16
cond branch (
ntract, Drive
out interpreta
ormatting
he following s
ay choose to
13. From t
Move
dialog
14. On she
Ctrl+S
with P
Align
igure 16.24 T
15. Select
option
cash fl
With tCells d
(zero)
Numb
Decision Trees
numbered 1, 2
ek should try
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
8/19/2019 TreePlan 201 Guide
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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
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210 Chapter 16 Decision Trees Using TreePlan
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
A B C D E F G H I J K L M N O P Q R S
Use mechanical method
$80,000-$120,000 $80,000
0.5Electronic success
$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
Don't prepare proposal
$0$0 $0
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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,
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212 Chapter 16 Decision Trees Using TreePlan
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
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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
Use mechanical method
-$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
0.5Electronic success
$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
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214 Chapter 16 Decision Trees Using TreePlan
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.