Decision-tree

In decision theory and decision making a decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. If in practice decisions have to be taken online with no recall under incomplete knowledge, a decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm. Another use of decision trees is as a descriptive means for calculating conditional probabilities.

General
In decision analysis, a "decision tree" — and the closely related influence diagram — is used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated.

A decision tree consists of 3 types of nodes:-

1. Decision nodes - commonly represented by squares

2. Chance nodes - represented by circles

3. End nodes - represented by triangles



Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). Therefore, used manually, they can grow very big and are then often hard to draw fully by hand. Traditionally, decision trees have been created manually - as the aside example shows - although increasingly, specialized software is employed.

Commonly a decision tree is drawn using flow chart symbols as it is easier for many to read and understand.



Analysis can take into account the decision maker's (e.g., the company's) preference or utility function, for example:



The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $400K—in that range of risk aversion, the company would need to model a third strategy, "Neither A nor B").

Influence diagram
A decision tree can be represented more compactly as an influence diagram, focusing attention on the issues and relationships between events.



The squares represent decisions, the ovals represent action, and the diamond represents results.

Uses in teaching
Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods.

Advantages
Amongst decision support tools, decision trees (and influence diagrams) have several advantages:

Decision trees:
 * Are simple to understand and interpret. People are able to understand decision tree models after a brief explanation.
 * 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.
 * Use a white box model. If a given result is provided by a model, the explanation for the result is easily replicated by simple math.
 * Can be combined with other decision techniques. The following example uses Net Present Value calculations, PERT 3-point estimations (decision #1) and a linear distribution of expected outcomes (decision #2):

Disadvantages
Decision trees:
 * For data including categorical variables with different number of levels, information gain in decision trees are biased in favor of those attributes with more levels.
 * Calculations can get very complex particularly if many values are uncertain and/or if many outcomes are linked.

Example
Decision trees can be used to optimize an investment portfolio. The following example shows a portfolio of 7 investment options (projects). The organization has $10,000,000 available for the total investment. Bold lines mark the best selection 1, 3, 5, 6, and 7, which will cost $9,750,000 and create a payoff of 16,175,000. All other combinations would either exceed the budget or yield a lower payoff.