Decision tree

A decision tree (or tree diagram) 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. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. 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.

Decision trees have traditionally been created manually, as the following example shows:

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.

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.

Uses in teaching

This section requires expansion.

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):

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.^[1]

Perhaps the most common online interaction with decision trees is in the form of online navigation. For example, online shopping sites (Amazon.com, BestBuy.com, SurLaTable.com, Shopping.com and nearly all others) have a 'top-level' or 'primary' navigation bar visible from the home page and usually from all pages on the site. On BestBuy.com, this top-level menu includes the major categories: "TV & Video, Audio, Car & GPS, Cameras & Camcorders, Computers..." Click on a top-level category of the decision tree, and you see a secondary navigation menu. For computers: "Laptops, Netbooks, Desktops..." Each leads to a set of tertiary-level or third-level menus which also act as 'filters', as well as featured products.

See also

External links

Wikimedia Commons has media related to: decision diagrams

• Decision Tree Analysis mindtools.com
• Decision Analysis open course at George Mason University
• Tutorial on decision tree
• Extensive Decision Tree tutorials and examples
• Cha, Sung-Hyuk; Tappert, Charles C (2009). "A Genetic Algorithm for Constructing Compact Binary Decision Trees". Journal of Pattern Recognition Research 4 (1): 1–13. 

References