Topic 4: Decision Tree Analysis

Introduction

Decision Theory is an analytic and systematic approach to the study of decision making

Good decision is one that is based on logic, considers all available data and possible alternatives, and the quantitative approach described here

What is involved in making a good decision?

5 Steps in Decision Making

  1. Define the problem
  1. Structure or draw the decision tree
  1. Assign probabilities to the state of nature
  1. Estimate payoffs for each possible combination of alternatives and states of nature
  1. Solve the problem by computing expected monetary values (EMV) for each state of nature node

Thompson Lumber Company is considering expanding by manufacturing and marketing a new product – backyard storage sheds.

The company can choose to:

Construct a large new plant.

Construct a small new plant.

Do not develop the new product line at all.

The possible outcomes (states of nature) are:
The market could be favorable or unfavorable.

Trees start from left to right

Trees represents decisions and outcomes in sequential order

Squares represent decision nodes

Circles represent states of nature nodes(outcomes)

Lines or Branches connect the decision nodes and the states of nature

This is decision making when there are several possible states of nature, and the probabilities associated with each possible state are known

Suppose each market outcome has a probability of occurrence of 0.50(50%).

Decision Making under risk:

Expected Value of Sample Information

EVSI= [Expected Value with sample information, assuming no cost to gather it] - [Expected value of best decision without** sample information]

= (Expected Value with sample information + cost) - (Expected Cost without sample information

Utility

(Probability)(Utility Score)+(Probability)(Utility Score)