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Decision trees and dealing with uncertainty

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# 4 Decision trees

Allow approximately 2 hours to complete this section.

Sometimes decisions can be complex and require a number of stages to arrive at a final outcome. Such a final outcome may be dependent on earlier, intermediate decisions. Alternatively, the final decision may be dependent on a series of uncertain, intermediate outcomes. Dealing with these types of decisions may appear, on the face of it, quite difficult. However, the technique of decision trees that you are going to explore in this section will help to simplify this process.

The best way to illustrate the technique is by a worked example in Activity 5. Before doing so, it is important to point out the meaning of two symbols that will be used in the decision trees.

Where a branch appears on your tree, this point will be called a node. A node may appear for one of two reasons. The first is that a decision is required. In other words, the node represents a series of choices. This type of node will be called a decision node and a square will be used to denote it. The second type of node is a chance node. Here, there is a range of possible events or outcomes of varying probabilities. Such nodes are denoted with a circle.

## Activity 5 Introduction to decision trees

Timing: Allow approximately 30 minutes to complete this activity

In Videos 3 and 4, you will be introduced to the powerful technique of decision trees. This technique allows you to incorporate probabilities into a range of potential outcomes, which may themselves be conditional on other outcomes.

You may wish to watch the videos a few times and make notes in the text boxes to ensure that you understand the concept of decision trees, as well as to answer the questions.

### Part 1

A company (MKOU) is assessing two outsourcing bids, A and B. Company A is more expensive but is reckoned to have a higher probability of delivering a high quality good than B. This is important as the higher the quality the more MKOU can charge and the less it will need to refund to dissatisfied customers. The data may be summarised as shown in Table 7.

Table 7 Possible financial benefits of using companies A and B
Company Probability of acceptable service level Net financial benefit if acceptable £M Net financial cost if not acceptable £M
A 80% 120 -30
B 55% 160 -10
Video 3 A worked example on decision trees
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### Part 2

A company is considering launching a new product. It can either launch immediately or in one year’s time. If it launches immediately there is a 0.75 chance of the launch being successful. If it is unsuccessful then the launch will be halted at a cost of £1M and relaunched in a year’s time. If the company launches immediately it may opt to also have a promotion, which has a 0.6 chance of success. If the promotion is successful the financial benefit is £10M, if not £2M. If the company does not do the promotion the benefit is £5M. If the company launches in a year’s time the benefit is £6M. What should the company do?

Video 4 A second worked example on decision trees
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#### Discussion

To summarise, you can use decision trees to break down a decision into a series of events that involve the decision-maker making a sub-decision (‘decision node’) or there being a chance event outside of the decision-maker’s control (‘chance node’). (Note that ‘sub-decision’ means a decision taken after the first, main, decision.)

By allocating probabilities to the chance nodes you can evaluate the expected value from the various combinations of sub-decisions and chance events.

This then informs which initial decision and then subsequent sub-decisions should be taken.

Now that you have watched the videos on decision trees, you will consider potential decisions faced by businesses. In the next section you will see some more applied examples of how decision trees are used in making business decisions.