DECISION TREES
Activity:
Sarah King, president of King Electronics, Inc., has two design options for her new line of highresolution cathode-ray tubes (CRTs) for computer-aided design workstations. The life cycle
sales forecast for the CRT is 100.000 units.
Design option A has a 0.90 probability of yielding 59 good CRTs per 100 and a .
10 probability of yielding 64 food CRTs per 100.
This design will cost $1.000.000.
Design option B has 0.80 probability of yieldin 64 good units per 100 and a 0.20 probability of
yielding 59 good units per 100. This design will cost $1.350.000.
Good or bad, each CRT will cost $75. Each good CRT will sell for $150. Bad CRTs are
destroyed and have no salvage value. Because units break up when thrown in the trash, there
is little disposal cost. Therefore, we ignore any disposal costs in this problem.
Solution:
$425.000
59
0.9
Good CRT
$ 7.965.000
CAD cost $1.000.000
Prod. Cost $7.500.000
Total Cost $8.500.000
Net Result -350.000
A
Total Cost $8.500.000
0.1
64
Good CRT
$ 960.000
$600.000
64
0.8
Good CRT
$ 7.680.000
Net Result $1.100.000
CAD cost $1.350.000
Prod. Cost $7.500.000
Total Cost $8.850.000
Net Result -750.000
B
Total Cost $8.850.000
0.2
59
Good CRT
$ 1.770.000
Net Result $110.000
$0
General Info ( from wikipedia):
In operations research, specifically in decision analysis, a decision tree (or
tree diagram) is a decision support tool that uses a graph or model of
decisions and their possible consequences, including chance event
outcomes, resource costs, and utility. A decision tree is used to identify the
strategy most likely to reach a goal. Another use of trees is as a descriptive
means for calculating conditional probabilities.
In data mining and machine learning, a decision tree is a predictive model;
that is, a mapping from observations about an item to conclusions about its
target value. More descriptive names for such tree models are
classification tree (discrete outcome) or regression tree (continuous
outcome). In these tree structures, leaves represent classifications and
branches represent conjunctions of features that lead to those
classifications. The machine learning technique for inducing a decision tree
from data is called decision tree learning, or (colloquially) decision trees.
Contents
[hide]
1 General
2 Influence diagram
3 Uses in teaching
4 Creation of decision
nodes
5 Advantages
6 See also
7 References
8 External links
General
In decision analysis, a "decision tree" — and a closely related model form,
an influence diagram — is used as a visual and analytical decision support
tool, where the expected values (or expected utility) of competing
alternatives are calculated.
For example a factory makes product B. The manager has to decide to
invest in development for a new product - product A or product C. (She
cannot do both due to budget constraints.) Product A is estimated to require
two million dollars of R&D investment, but only has a 50% chance of the
research being successful and a product being obtained. It will have a 30%
chance of selling $5M profit, a 40% chance of selling $10M profit, and a 30%
chance of no sales. Product C, on the other hand, will also cost $2M in R&D
but has an 80% chance of selling $5M profit and a 20% chance of no sales.
$1M is the manufacturing cost for either product.
If the company has a policy of maximising expected values, which is the
preferred strategy? The alternatives, probabilities, payoffs, and resulting
expected value calculations are shown in the example tree below. In this
case either Product A or Product C are expected to turn a profit but product
C has the higher expected value of $1 million:
The same example again, this time taking account of the time value of
money by discounting to Net Present Values, for this scenario it can be seen
that Product C is clearly the winning choice with a payout of $0.36 million.
Product A is not expected to turn a profit.
Analysis can take into account the decision maker's (e.g., the company's)
preference or utility function, for example:
The basic interpretation in this situation is that the company prefers B's risk
and payoffs under realistic risk preference coefficients (greater than $400K -in that range of risk aversion, the company would need to model a third
strategy, "Neither A nor B").
Influence diagram
A decision tree can be represented more compactly as an influence
diagram, focusing attention on the issues and relationships between events.
Uses in teaching
Decision trees, influence diagrams, utility functions, and other decision
analysis tools and methods are taught to undergraduate students in schools
of business, health economics, and public health, and are examples of
operations research or management science methods.
Creation of decision nodes
Three popular rules are applied in the automatic creation of classification
trees. The Gini rule splits off a single group of as large a size as possible,
whereas the entropy and twoing rules find multiple groups comprising as
close to half the samples as possible. Both algorithms proceed recursively
down the tree until stopping criteria are met.
Advantages
Amongst decision support tools, decision trees (and influence diagrams)
have several advantages:
Decision trees:
are simple to understand and interpret. People are able to
understand decision tree models after a brief explanation.
have value even with little hard data. Important insights can be
generated based on experts describing a situation (its alternatives,
probabilities, and costs) and their preferences for outcomes.
use a white box model. If a given result is provided by a model, the
explanation for the result is easily replicated by simple math.
can be combined with other decision techniques. The following
example uses Net Present Value calculations, PERT 3-point estimations
(decision #1) and a linear distribution of expected outcomes (decision
#2):
can be used to optimize an investment portfolio. The following
example shows a portfolio of 7 investment options (projects). The
organization has $10,000,000 available for the total investment. Bold
lines mark the best selection 1, 3, 6 and ,7 which will cost $7,740,000 and
create a payoff of 2,710,000. All other combinations would either exceed
the budget or yield a lower payoff: