Decision TreesDaisy 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

Advantages of Decision TreesAre 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 addedWorst, 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?

End

Yes No

The second decision for SciTools is how much to bid?

Bid?

End

Yes No

How much to bid?

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?

Any competing

bid?

End

Yes No

Any competing

bit?

How much to bid?

Any competing

bid?

$125k

$120k

$115k

The company, based on previous experience believes there is a 30% chance that there will be no competing bids.

Bid?

Any competing

bid?

End

Yes No

Any competing

bit?

Win 25K Win bid? Win $15kWin bid? Win $20K

How much to bid?

Win bid?

Any competing

bid?

$125k

$120k

$115k

70% Yes 30% No70%

Yes70% Yes

30% No 30% No

The fourth decision is to consider the probability to win the bid.

Bid?

Any competing

bid?

End

Yes No

Any competing

bit?

Win 25K Win bid? Win $15kWin bid? Win $20K

How much to bid?

Win bid?

Any competing

bid?

$125k

$120k

$115k

70% Yes 30% No70%

Yes70% Yes

30% No 30% No

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?

Any competing

bid?

End

Yes No

Any competing

bit?

Win 25K Win bid? Win $15kWin bid? Win $20K

How much to bid?

Win bid?

Any competing

bid?

$125k

$120k

$115k

Loss $5kLoss $5K Gain $20kGain $25K Loss $5kGain $15k

70% Yes 30% No70%

Yes70% Yes

30% No 30% No

10% Yes

90% No

40% Yes

60% No

80% Yes

20% No

Example of Heads or Tails Two persons enter in a bid of whom will obtain two heads

or two tails. The options are presented in the following decision tree:

Toss 1

Toss 2

H

Toss 2

T

Win H Toss 3 Toss 3 Win T

H T H T

Win H

Win T

Win H

Win T

H T H T

Example of Green, Yellow, Red Card

Test 1

Test 2 Test 2

Test 3 Test 3 Test 3 Test 3

Quiz Quiz Quiz Quiz Quiz Quiz Quiz Quiz

Example of Dinner’s Dilemma

Menu Price

Mofongo with Lobster $25

Rice and Crab $18

Rice with Meat Stew $12

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.