11/29/2021

Example of Decision Tree Structure

 Decision tree models
Decision Tree include such concepts
such as nodes, branches,
Event 1 terminal values, payoff
distribution, certain
equivalent , and the roll
Decision Event 2 back method.
node
Three Types of Nodes:
Event 3
DISCOUNTED DECISION  Decision Nodes
 Chance Nodes

TREE ANALYSIS  Terminal Nodes

(optional)

Chance node

Decision Nodes
What is a Decision Tree?
Notation used in Decision Tree
 A point where a choice must be made; it is shown as a
square or a box. The branches extending from a
decision node are decision branches
A square/ box
 Each branch representing one of the possible
alternatives or courses of action available at that point
 Used to show a choice that the manager has to make
• It is a visual It is a way of
representatio breaking down
n of choices, complicated  The set of alternatives must be mutually exclusive (if
consequence situations
s, down to one is chosen, the others cannot be chosen) and
probabilities, easier-to-
and collectively exhaustive (all possible alternatives must
opportunities understand
scenarios be included in the set).

Chance Nodes
 Is a point where uncertainty is resolved (a point where
A circle the decision maker learns about the occurrence of an
event);it is shown as a circle.
 It is sometimes called a ‘‘CHANCE NODE’’
 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.

Purpose of Decision Tree  The set of events must be mutually exclusive (if one occurs, the others cannot
occur) and collectively exclusive (all possible events must be included in the
set). Each event is assigned a subjective probability; the sum of probabilities
Can be used as a model for a sequential for the events in a set must equal one.
 Used to show that a probability outcome will occur
decision problems under uncertainty
 In general, decision nodes and branches represent the controllable factors in a
It describes graphically the decisions to be decision problem; event nodes and branches represent uncontrollable factors.
made, the events that may occur and the  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
outcomes associated with combinations of maker learns the outcome of the event(not necessarily when the event occurs).
decisions and events
Terminal Node
Probabilities are assigned to the events and  Representing the final result of a combination
values are determined for each outcome A Triangle
of decisions and events.
 It is the endpoints of a decision tree, shown as
A major goal of the analysis is to determine the end of a branch on hand-drawn diagrams
the best decisions and as a triangle or vertical bar on a computer-
generated diagram.

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Expected Value
 For an alternative is often a good measure of the value of an
 Solving the tree involves pruning all the best decisions at decision nodes, alternative since over the long run this is the average amount that you
and finding the expected values of all possible states of nature at chance expect to make from selecting the alternative.
nodes.  For an uncertain alternative is calculated by multiplying each possible
 Create the tree from left to right outcome of the uncertain alternative by its probability, and summing
 Solve the tree from right to left. the results. The expected value decision criterion selects the
alternative that has the best expected value. In situations involving
NODES AND SYMBOLS profits where ‘‘more is better’’, the alternative with the highest
expected value is best and in situations involving costs where ‘‘less is
Type of Node Written Computer Node better’’, the alternative with the lowest expected value is best.
Symbol Symbol Successor Decision Tree Rollback
 The process of successively calculating expected values from the
Decision square Square Decision endpoints of the decision tree to the root node, as demonstrated and
branches called a decision tree rollback.
Event Circle Circle Event Decision Strategy
branches  The complete specification of all the preferred decisions in a sequential
decision problem.
Terminal Endpoint Triangle or Terminal  The complete specification of the alternatives that should be selected
bar value at all decision nodes in a decision tree called a decision strategy.

Decision Tree
Development Cost Development Sales Revenue Net Profit
Outcome

success $1, 000, 000 $900, 000

(0.5)
Temperature $100, 000
Sensor (0.5) failure $0 -$100, 000 Easy Example
Pressure
Sensor (0.8) success $400, 000 $390, 000

(0.2) failure $0 $10, 000

Neither

$0

A Decision Tree of two choices

Decision Tree Notation
A diagram of a decision, as illustrated in the figure, is
called a DECISION TREE. This diagram is read from left to right. Go to Graduate What should I do?
The leftmost node in a decision tree is called the ROOT NODE. In School to get my
the figure, this is a small square called DECISION NODE. The
master in Civil
branches emanating to the right from a decision node represent
the set of decision alternatives that are available. One, and only Engineering
one, of this alternatives (that are available) can be selected. The
small circles in the tree are called CHANCE NODES. The number
shown in parentheses on each branch of a chance node is the
probability that the outcome shown on the branch will occur at
the chance node . The right end of each path through the tree is
called an ENDPOINT and each endpoint represents the final Go to work “in
outcome of following a path from the root node of the decision
tree to that endpoint. the real world”

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Example – Joe’s Garage

Joe’s garage is considering hiring another mechanic. The

mechanic would cost them an additional $50,000 / year in
salary and benefits. If there are a lot of accidents in Iowa
What are some of the costs we City this year, they anticipate making an additional $75,000
in net revenue. If there are not a lot of accidents, they
should take into account when could lose $20,000 off of last year’s total net revenues.
deciding whether or not to go to Because of all the ice on the roads, Joe thinks that there
graduate school? will be a 70% chance of “a lot of accidents” and a 30%
chance of “fewer accidents”. Assume if he doesn’t expand
he will have the same revenue as last year.
Draw a decision tree for Joe and tell him what he should
do.

Example - Answer

70% chance of an increase

in accidents
Hire new
mechanic Profit = $70,000
30% chance of a
Cost = $50,000 decrease in accidents
Profit = - $20,000

Tuition Fees Rent/ Food/ etc. Opportunity cost of Anticipated future Don’t hire new
salary earnings mechanic
Cost = $0

• Estimated value of “Hire Mechanic” =

NPV =.7(70,000) + .3(- $20,000) - $50,000 = - $7,000
• Therefore you should not hire the mechanic

Simple Decision Tree Model

1.5 years of tuition: $30, 000
1.5 years of room/ board: $20, 000
Benefits of Decision Tree
1.5 years of opportunity cost of salary:

Go to
$100, 000
Total: $150, 000
1. The impact of possible future decisions
Graduate Plus: 2. The impact of uncertainty on confidence
School to get anticipated 5 years salary after
graduate school: $600, 000
3. The impact of varying commitments of payoff
my master in
Civil Eng’g NPV (graduate school): $600, 000-$150, 4. The sequencing and interrelations of tasks and events
000=$450, 000
5. The measurement of risk
Go to work First 1.5 year salary: $100, 000 (from
“in the real above), minus expenses of $20, 000
world” Final 5 year salary: $330, 000
NPV (no graduate school): $410, 000

Choice= Go to Graduate School

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Why Use decision tree analysis?

• First, a decision tree is a visual representation

of a decision situation (and hence aids
Advantages and communication).
Disadvantages of Using • Second, the branches of a tree explicitly show
Decision Tree all those factors within the analysis that are
considered relevant to the decision (and
implicitly those that are not).

DISADVANTAGES • Third, and more subtly, a decision tree generally

captures the idea that if different decisions were to
be taken then the structural nature of a situation
1. Instability-the quality or state of being (and hence of the model) may have changed
unstable dramatically. This is in contrast to an Excel model
with sensitivity analysis (or a Monte Carlo simulation
2. Complexity model) in which a change of parameters in the model
3. Unwieldy-not easily managed, handled does not represent any structural change to the
situation. Capturing the logic and conditionality that
4. Costs is present in a tree would be complex to do in such
5. Too Much Information modelling environments.

6. Analysis Limitations

ADVANTAGES • Fourth, and arguably the most powerful, a

decision tree allows for forward and backward
1. Decision trees implicitly perform variable calculation paths to happen (taken care of
screening or feature selection automatically when using the PrecisionTree
2. Decision trees require relatively little effort from decision tree software) and hence the choice
users for data preparation of the correct decision to take (optimality of
3. Nonlinear relationships between parameters do decision making, or optimal exercise if
not affect tree performance embedded real options) is made
4. The best feature of using trees for analytics - easy automatically.
to interpret and explain to executives!

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