## Decision tree

A decision tree is a diagrammatic approach to making a decision on the basis of the statistical concept of probability. The diagram is called a decision tree as the branches of the diagram are spread in the form of a tree. Different branches of the tree present different outcomes or decisions on account of different probabilities and expectations of the outcomes.

It’s a sound tool for decision-making used around the globe for making a decision about not only complex investing and financing issues but issues related to the personal lives of the people.

The concept of the decision tree is more useful in a situation that involves a series of decisions with a number of outcomes at each step of the decision-making.

For instance, the project to expand in a new country can contain a number of variables that need to be considered before making any final decision.

The strength of the decision tree is the division of the decision-making process into chunks that provide a base for analytical thinking and assertive exercise to come up with the most suitable decision easily. Sometimes, variables of the decision are dependent on each other.

For instance, with an increase in sales up to a certain threshold there may be a decrease in the cost of sales, the company may have the policy to allocate 20% of the revenue for sales and marketing. Hence, the situation becomes complex and a human memory may not be able to process the information easily.

Hence, diagrammatic presentation of the variables helps in understanding flow for the process of decision making. Let’s understand that how a decision tree works.

## Steps of decision tree

There are two steps of using tree decision that include construction of decision tree and making evaluation and recommendation based on the constructed decision tree.

### 1) Construction of decision tree

The process of construction starts with a rectangle on the left-hand side of the paper. A rectangle is a place where the main idea/criteria are written that leads to a final decision at the end. The circles are assigned for the outcomes, there can be two outcomes for certain situations either good or bad.

These outcomes may depend on other outcomes and further leaves need to be drawn. Systematic construction of tree based on outcomes provide an excellent approach to reaching a rational decision.

An important point to note is that the outcomes are not under the control of managers and external information needs to be taken to close the circles in the rectangle.

It’s like taking information in the form of circles and reaching the rectangles in the form of a decision. This provides a logical flow and visual approach for a decision to be reached.

Consider a decision tree with two branches. The two branches mean two outcomes are possible for the decision under consideration. The upper branch does not have a point of the outcome, it means there is certainty regarding the decision on the upper side of the branch.

However, the lower branch has an outcome point that divides into further outcome points. This indicates that there are different variables of the outcomes that need to be considered in reaching the point of a rectangle or the decision.

### 2) Evaluation of the decision

The evaluation of the decision tree starts from the right side. It moves from right to left by considering expected values and all the calculations for the probabilities. If there are different branches in the tree, all of them are solved from right to left and the decision is reached in the final.

The first step of evaluation is the labeling of the leaves and all other parts of the tree. Expected values and probability are written on the tree.

Once the decision tree is labeled, start with the extreme right and keep on multiplying expected values with probability. It will provide a decision when all of the branches are closed.

However, the prediction of expected values and probability is judgmental and the real figures may not even be close to the expected values. Further, the use of a decision tree does not consider risk appetite, and all the decision-making is based on probability and expected values.

It’s important to note that a comprehensive understanding of the factors affecting decisions and a strong understanding of the factors is required to reach an optimum decision using a decision tree, otherwise, it may not be of much use.

## Example of decision tree

The given example illustrates that how a decision tree helps in deciding on a situation about expected values and probabilities.

The square at the left shows that we need to decide on the development of the software. We have two branches/options. The first option is to not go for the development and have no revenue and no cost. The second option is to incur the cost of USD 2,000 and earn revenue.

However, success and failure are probable with 0.3 and 0.7. If the business gets the success it will be able to USD 7,000 as calculation show {(5000*0.7) + (10,000*0.2) + (15000*0.1)}. On the other side, the expected cash flows are USD 1,500 {(1500*0.5) + (1500*0.5)}.

The probability of success and failure is 0.3 and 0.7 respectively. If we allocate the expected amount in case of success, we get USD 2,100 (7,000*0.3) and in case of failure, we get USD 1,050 as (1500*0.7).

Hence, to reach the triangle we get USD 3,150 as (2,100+1050) which is more than the cost of development amounting to USD 2,000, and the business is expected to generate a return.

Hence, based on given cost, expected revenue, and probabilities, the decision can be made to opt for software development.

However, the use of a decision tree requires a comprehensive understanding of the market, external factors, internal capabilities, management competence, and a sound sense of judgment to allocate the probabilities to certain outcomes.

The changes in the variables may lead to a change in the decision. Hence, due care needs to be exercised in estimating input variables for a decision tree.