 To specify a Decision Tree,
you need to enter the KNOWLEDGE BASE you've assembled into two tables:
- The DECISION TREE TABLE, and
- The PROBABILITIES AND PAYOFFS TABLE.
Let's start with the DECISION TREE TABLE. For
each node:
- Enter a short description in the DESCRIPTION
column. The nodes are labeled N1, N2, N3, etc.
- Specify whether it is a decision node
or an outcome node. By default, all nodes are initially set
to decision nodes. To switch to outcome node, click on the node's Outcome
radio button.
- List its successor nodes in the node's Next field.
Consider the analysis of
the Promotional Campaign (from S.M. Lee et al., 1985, with modifications).1
The first six nodes in the decision
tree are as follows:
|
NODE |
DESCRIPTION |
COST OR BENEFIT |
|
N1 |
Start |
|
|
N2 |
We Introduce the Product |
R&D Cost of $80K |
|
N3 |
We Do Not Introduce the Product |
|
|
N4 |
Our Competitor Introduces a Competing Product |
|
|
N5 |
Our Competitor Does Not Introduce a Competing Product |
|
|
N6 |
We Launch a Major Promotional Campaign, etc. |
|
Nodes N1, N4, N5 are decision nodes. Nodes N2,
N3, and N6 through N11 are outcome nodes. Nodes N12
through N24 are final outcome nodes.
Only node N2 involves a cost.
The first three nodes can be specified as follows:
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Now, let's focus on the PROBABILITIES
AND PAYOFFS TABLE. For each node:
If the node is an outcome node, enter its
probability or likelihood, as a percentage, in the node's Probability column. If
it is a decision node, leave the node's Probability column blank.
Enter the associated payoff, if any, in the
node's From column. If the node has no cost, benefit, or payoff associated with
it, leave the node's From and To columns blank.
If the payoff is a cost or
loss, enter a negative number. If the payoff is a benefit or profit, enter a positive
number.
If the payoff is uncertain
or variable, enter the limits of the payoff's range in the node's From and To
columns. For example, if the payoff of the 12th node can increase from $50K to $80K, enter
50 and 80 in N12's From and To columns, respectively. Conversely, if the
payoff can decrease from $80K to $50K, enter 80 and 50 in the From and To
columns, respectively.
Use the same currency unit
for benefits, costs, and payoffs (e.g., $K or $Million).
Where monetary values cannot
be used, use utility values instead. For example, in a clinical decision
analysis, you can use quality-adjusted life years.
Consider
the above Promotional Campaign. Suppose that the probabilities and the costs,
benefits, or payoffs for nodes N1-N5 and N12-N13 where as follows:
|
NODE |
DESCRIPTION |
PROB. |
COST, BENEFIT, OR PAYOFF |
|
From |
To |
|
N1 |
Start |
-- |
-- |
-- |
|
N2 |
We Introduce the Product |
|
$80K |
|
|
N3 |
We Do Not Introduce the Product |
|
|
|
|
N4 |
Our Competitor Introduces a Competing Product |
70% |
|
|
|
N5 |
Our
Competitor Does Not Introduce a Competing Product |
30% |
|
|
|
N12 |
We
Launch a Big Promotional Campaign |
60% |
$50K |
$80K |
|
N13 |
We
Launch a Medium Promotional Campaign |
30% |
$80K |
$100 |
|
N14 |
We
Launch a Small Promotional Campaign |
10% |
$140 |
$180 |
Note that the
probabilities of N4 and N5 add to 100%, and those of N12, N13, and N14 also add to 100%.
The product R&D cost associated with N2 is assumed to be $80K. N12, N13, and N14 are
three of 13 possible final outcomes. The payoffs (profits) of the promotional campaign are
assumed to range between $50K and $80K for N12, between $80K and $100K for N13, and
between $140K and $180K for N14. The probabilities and payoffs for nodes N15 through N24
are not shown.
Then, the probabilities and payoffs can be
entered as follows:
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Sources:
1 See Sang M. Lee, Laurence J. Moore, and Bernard W. Taylor III, Management
Science, 2nd ed. Dubuque, IA: Wm. C. Brown Publishers, 1981, 1985, at 431-434
[Decision Tree for Promotion of New Product].
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