Decision TreesDecision Trees

Introduction

Decision trees enable one to look at decisions:

• with many alternatives and states of nature

• which must be made in sequence

Decision Trees

A graphical representation where:

a decision node from which one of several alternatives may be chosen

a state-of-nature node out of which one state of nature will occur

Thomson Case

• Thomson lumber a profitable company located in Portland, Oregon.

• Step 1: John Thomson to identify whether to expand his product line. He then try to find alternatives to define a course of action or strategy that a decision maker can use.

Thomson Case (Cont.)

• Step 2: Thomson decides that there are 3 alternatives. 1. to build a large new plant 2. a small plant 3. no plant at all.

• Step 3: He determines that there are only 2 possible outcomes : The market for new product could be favorable (high demand for the new product) or unfavorable (low demand).

• Step 4: Thomson wants to maximize his profit to evaluate each consequence. He evaluated the potential profits with the various outcomes. For favorable market, the new large plant will yield a net profit of $200,000 while if the market unfavorable will turn to a net loss of $180,000. A small plant will yield a net profit of $100,000 under favorable market and a net loss of $20,000 for unfavorable market. Finally if he does nothing would result in $0 profit in either market.

Thomson Case (Cont.)

• Step 5 &6 : The last two steps are to select a decision theory model and apply it to the data to help making decision. Selecting the model depends on the environment in which you are operating and the amount of risk and uncertainty involve.

Thomson Case (Cont.)

State of Nature

Alternative Favorable market

Unfavorable market

Construct a large plant

200,000 -180,000

Construct a small plant

100,000 -20,000

Do nothing 0 0

Thompson’s Decision Tree Fig. 4.1

1

2

A Decision Node

A State of Nature Node Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

Constr

uct

Large

Pl

ant

Construct Small Plant

Do Nothing

Five Steps toDecision Tree Analysis

1. Define the problem2. Structure or draw the decision tree3. Assign probabilities to the states of nature4. Estimate payoffs for each possible combination of

alternatives and states of nature5. Solve the problem by computing expected

monetary values (EMVs) for each state of nature node.

Thompson’s Decision Tree Fig. 4.2

A Decision Node

A State of Nature Node Favorable

Market (0.5)

Unfavorable Market (0.5)

FavorableMarket (0.5)

Unfavorable Market (0.5)

Constr

uct

Large

Plan

t

Construct Small PlantDo Nothing

$200,000

-$180,000

$100,000

-$20,000

0

EMV =$40,000

EMV=$10,000

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2