# Decision Trees

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Decision Trees

Everyday businesses make decisions. Most, if not all, involves some risk. This could be because has the business has limited information on which to base the decision. Furthermore, the outcome of the decision may be uncertain. Launching a new product in a market abroad and be risky because a firm may not have experienced selling in that market. It may also be unsure about how consumers will react

When faced with a number of different is it gives the most return period what if a printing company have to decide whether to invest £750,000 then you printing press now or wait a few years? If it is bought now and a more efficient machine becomes available next year, then I may have been more profitable to wait. Alternatively, if they wait, they may find the older machine has problems and costs increase.

When the outcome is uncertain decision trees can be used to help a business decide which can minimise risk and gain the greatest return.

What are decision trees?

A decision tree is a method of tracing the alternative outcome of any decisions. The Likely result and then be compared so that the business and find the most profitable alternative. For example, the business may be faced with two alternatives to launch a new product in Europe or in the USA. A decision tree allows a business to be sure that launching a new product in Europe is likely to be more successful the launching a new product in the USA.

It is argued by some that decision-making is more effective if a quantitative approach is taken. This is where information on which decisions are based, and the outcomes of decision, are expressed as numbers. In a decision tree, numerical values given to such information. The decision tree also provides a pictorial approach decision making because a diagram is used which resemble the branches of a tree.  Answer the diagram maps of different courses of action possible outcomes of decisions and points where decisions have to be made. Calculations based on the decision tree can be used to determine the best likely outcome for the business and hence the most suitable decision.

Features of decision trees:

Decision trees have a number of features. These can be seen in figure 1 which shows a decision tree for a business that has decided to launch a new advertising campaign or retain an old one.

• Decision point: point where decisions have to be made in a decision tree are represented by a square and are called decision points. The decision maker has to choose between certain courses of action. In this example, the decision is whether to launch a new campaign or retain the old one.
• Outcomes:  point where there are different possible outcomes in the decision tree are represented by circles and are called chance Nodes. At these chance nodes it can be shown that the particular course of action might result in a number of outcomes. In this example at B there is a chance of failure or success of the new campaign.
• Probability or chance: the likelihood of possible outcomes happening is represented by probabilities in decision tree. The chance of a particular outcome happening is given a value. If the outcome is certain then the probability is 1. Alternatively, if there is no chance at all of the particular outcome occurring, the probabilities will be zero. In practice the value lies between 0 and 1. In figure 1, the chance of success here is 0.2 and the chance of failure is 0.8. Source of information we can be used to help estimate probabilities.
• Expected monetary value: this is the financial outcome of the decision. It is based on the predictive profit or loss of an outcome and the probability of an outcome. The profit or loss of any decision is shown on the right-hand side of figure one.

Decisions Outcomes and Costs:

In practice businesses may face many alternative decisions and possible outcomes. Take a farmer whose inherited some land and does not wish to use it with his existing farming business. There are three possible decisions for the farmers.

• Sell the land. The market is depressed, and this will earn him £0.6 million
• Wait for one year and hope that the market price improves. A land agent has told the Farmer the chance of an upturn in the market is 0.3, while the probability of it staying the same or declining is 0.5 and 0.2 respectively. The Likely proceeds from a sale in each circumstance £1 million, £0.6 million, and £0.5 million.
• Seek planning permission to develop the land. The legal and administration fees would be £0.5 million, the probability of being refused permission would be 0.8, which means a likelihood of obtaining permission is 0.2. If the latter the farmer will be left with the circumstances of option 2.

If planning permission is granted the Farmer has to decide at node E. If the Farmer to say to sell, the probability of getting a good price, i.e. 10 million pounds is it estimated to be 0.4, the probability of getting a low price i.e. 6 million pounds, 0.6. The farmer could also develop and sell for 5 million pounds. The probability of selling the development at a good price £25 million, is estimated to be 0.3 while the likelihood of getting a low price, i.e., 10 million pounds, is 0.7. Information about probability and earnings shown in figure 2