### Decision Trees

```Decision Trees
Daisy Guevara
Gilberto Jiménez
Orlando Ruiz
Jan Salomón
What is a rooted tree?
 It
is a tree in which one vertex has been designated
as the root and every edge is directed away from
the root.
What are decision trees?
 It
is a rooted tree in which internal vertex
correspond to a decision, with a sub-tree at these
vertices for each possible outcome of the decision.
 The possible solution of the problem correspond to
the paths to the leaves of this rooted tree.
Elements of a Decision Tree
 The
set of decision (or strategies)
 The set of possible outcomes and/or the probabilities
of these outcomes.
 The results for the various combination and outcomes.
Once these elements are known, it is possible to find
the “optimal” solution or decision of the problem.
Types of Decision Trees
 Decision
Tree Forests
Types of Decision Trees
 Classification
and
Regression Trees
Types of Decision Trees
 Binary
Survival Tree
 Are
simple to understand and interpret.
 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.
 Possible scenarios can be added
 Worst, best and expected values can be
determined for different scenarios.
 Can be combined with other decision techniques.
Example: An application of decision trees
in Project Management
 A company
named SciTools Incorporated, is
invited to make a bid on a government contract.
The company with the lower bid obtain the
contract.
 The cost of prepared a bid is the \$5,000.
 The cost of the project is \$95,000.
 The total cost for the company is \$100,000. Then,
to obtain gain the company has to bid an amount
greater than \$100,000.
The first decision for SciTools is bid or not bid.
Bid?
Yes
No
End
The second decision for SciTools is
how much to bid?
Bid?
Yes
How much to
bid?
No
End
SciTools prepared the following analysis:
Amount of money
in the bid
Gain
Loss
\$115,000
\$15,000
\$5,000
\$120,000
\$20,000
\$5,000
\$125,000
\$25,000
\$5,000
The third decision is consider if there will be
other competitors in the bid?
Bid?
Yes
\$125k
How much
to bid?
End
\$115k
\$120k
Any
competing
bit?
Any
competing
bid?
No
Any
competing
bid?
 The
company, based on previous experience believes there is
a 30% chance that there will be no competing bids.
Bid?
Yes
How much
to bid?
\$125k
No
End
\$115k
\$120k
Any
competing
bit?
70%
Yes
Win bid?
Any
competing
bid?
30%
No
Win 25K
70%
Yes
Win bid?
Any
competing
bid?
30% No
Win \$20K
70%
Yes
Win bid?
30% No
Win \$15k
The fourth decision
is to consider the
probability to win
the bid.
Bid?
Yes
How much
to bid?
\$125k
No
End
\$115k
\$120k
Any
competing
bit?
70%
Yes
Win bid?
Any
competing
bid?
30%
No
Win 25K
70%
Yes
Win bid?
Any
competing
bid?
30% No
Win \$20K
70%
Yes
Win bid?
30% No
Win \$15k
SciTools prepared the following analysis:
Amount of money
in the bid
Probability of win
the bid
Probability of loss
the bid
\$115,000
80%
20%
\$120,000
40%
60%
\$125,000
10%
90%
The fifth decision is
how much SciTools
will gain or lose.
Bid?
Yes
How much
to bid?
\$125k
No
End
\$115k
\$120k
Any
competing
bit?
70%
Yes
30%
No
Win bid?
10%
Yes
Gain \$25K
Any
competing
bid?
70%
Yes
Win 25K
90%
No
Loss \$5K
Gain \$20k
70%
Yes
30% No
Win bid?
40%
Yes
Any
competing
bid?
Win \$20K
60%
No
Loss \$5k
30% No
Win bid?
80%
Yes
Gain \$15k
Win \$15k
20%
No
Loss \$5k
 Two
persons enter in a bid of whom will obtain two heads
or two tails. The options are presented in the following
decision tree:
H
H
Win H
T
Toss 1
H
T
Toss 2
H
Win
H
Toss 3
T
H
Win
T
Win
H
Toss 3
Toss 2
T
Win
T
T
Win T
Example of Green, Yellow, Red Card
Test 1
Test 2
Test 2
Test 3
Quiz
Test 3
Quiz
Quiz
Test 3
Quiz
Quiz
Test 3
Quiz
Quiz
Quiz
Example of Dinner’s Dilemma
A group of friends go out to dinner. They decided before
arriving to the restaurant to share the bill. They are
expecting to eat better and cheaper than paying individually.