# Decision Tree

A **decision tree** is a graphical representation of a multistage decision-making system. It comprises of a set of decision variables that are arranged in the form of a tree, with each variable representing a decision and branching out to one or more decision variables. Decision trees are widely used in the field of Operations Research for decision analysis.

A typical decision tree uses standard flowchart symbols. As shown in the figure below, a decision tree has nodes (circular, in this case) to represent decision variables. These nodes have arcs originating from them that lead to all possible decision outcomes.

There is a starting node at the base of the tree which represents the central **input**, or the central idea/decision – this is known as the ** root node**. We have represented it with a blue circle. In Stage 1, there are two possible decision outcomes (coloured green and blue) emanating from the root node. In the second stage of decision-making, each of these two nodes has two decision nodes emanating from it, and so on.

Now, with respect to the starting node, the two nodes at Stage 1 are the two possible **outputs**. These two outputs are known as ** chance nodes** and serve as

**inputs**for Stage 2 and the process continues until we have arrived at all possible inputs and outputs.

Now, we will notice that there are several **paths **that can be taken from the central input to reach either of the possible outcomes in the final stage – these are known as ** endpoints** (in our case, there are eight endpoints in Stage 3). Each of these paths is known as a

**.**

*feasible path*The primary purpose behind this whole exercise is to find the best possible path from the root node to the endpoints. This is known as the ** optimal path**. To obtain the

**optimal solution**, it is essential to find an optimal path that picks the best outcome at every stage.

Decision trees are the most effective when:

- There is uncertainty in predicting outcomes for a decision.
- There is a large number of factors influencing decisions or many possible outcomes for every decision.
- There is a possibility that newer outcomes might be added later.

**Advantages of decision trees**

**Ease of Construction and Interpretation:**Decision trees are very simple to construct and equally easy to understand and interpret. While it is a humongous and time-consuming task to convey the idea of multistage decisions to an audience without a graphical representation to support the theories, the same becomes vastly effortless with the aid of a properly-structured decision tree.**Dynamic Nature:**Decision trees are dynamic in the sense that they permit the addition of newer decision nodes and paths.**Versatile:**Decision trees are versatile. They can be used in conjunction with a wide range of other decision-making techniques and tools like decision matrices, T-charts and Pareto analyses. Also, the structure of a decision tree allows non-linear variables in its decision nodes, which is not feasible in the case of most other decision-making tools.**Step-by-step Evaluation:**Decision trees allow a step-by-step evaluation of scenarios, thus making it possible to evaluate the optimum values of the decision variables at each stage.

**Disadvantages of decision trees**

**Variance:**In decision trees, the values assigned to the decision variables are based on expectations and as such, outcomes may vary from the expected values.**Unnecessary Complexities:**Over-simplification of the decision tree will result in the addition of unnecessary nodes to the tree. This will have an adverse impact on the accuracy of the final outcome.