Screenshot 2024-09-26 at 2.22.58 PM.png

## 11 Decision Trees ### Learning Objectives * Construct and interpret simple decision tree diagrams * Understand the calculations and interpretations of figures generated by these techniques * Understand the limitations of using decision trees ### Getting Started When making a business decision...

## 11 Decision Trees ### Learning Objectives * Construct and interpret simple decision tree diagrams * Understand the calculations and interpretations of figures generated by these techniques * Understand the limitations of using decision trees ### Getting Started When making a business decision it is helpful to use a quantitative decision-making technique if possible. This involves the application of numerical values, which can be compared easily. For example, Latika Naidu runs a successful import business, Gujurat Craftwork, based in Paris, buying craft products from India. The company sells the items to a network of retailers in the EU. Latika wants to expand the business and has identified two clear options: * Begin importing products from the Middle East to expand the product range * Set up an online operation to sell more widely. Latika paid a business consultant €1000 to help make the decision. This was quite helpful. The consultant said the probability of success for the first option was 0.5, or 50 per cent. In contrast, the probability of success for the second option was 0.72, or 72 per cent. The cost of both options is very similar, but Latika will only choose one option. ### Making Decisions Every day, businesses make decisions. Most, if not all, involve some risk. This could be because 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 can be risky because a firm may not have experience of selling in that market. It may also be unsure about how consumers will react. When faced with a number of different decisions a business will want to choose the course of action which gives the most return. What if a printing company had to decide whether to invest $750,000 in a new printing press now or wait a few years? If it bought now and a more efficient machine became available next year, then it might have been more profitable to wait. Alternatively, if it waits it may find the old machine has problems and costs increase. When the outcome is uncertain, decision trees can be used to help a business reach a decision which could minimise risk and gain the greatest return. ### What are Decision Trees? A decision tree is a method of thinking about the alternative outcomes of any decision and presenting these in a diagram. The results can then be compared so that the business can find the most profitable alternative. For example, a business may be faced with two alternatives – to launch a new product in Europe or in the USA. A decision tree may show that launching a new product in Europe is likely to be more successful than 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 decisions, are expressed as numbers. In a decision tree, numerical values are given to such information. The decision tree also provides a pictorial approach to decision making because a diagram is used which resembles the branches of a tree. The diagram maps out 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 find the ‘best’ likely outcome for the business and therefore the most suitable decision. ### Features of Decision Trees Decision trees have a number of features. These can be seen in Figure 1, which shows the decision tree for a Japanese business that has to decide whether to launch a new advertising campaign or retain an old one. > **Figure 1** A simple decision tree, based on a decision whether to retain an existing advertising campaign or begin a new one | | | | |-------------------|-------------------------------------------|-------------------------------------------| | **A** | **Launch new campaign** | **Retain old campaign** | | **B** | Success - 0.2 - ¥15m | Failure - 0.8 | | | Failure - 0.8 | Success - 0.4 - ¥7m | | **C** | | Failure - 0.6 - ¥1m | * **Decision points:** Points where decisions have to be made in a decision tree are represented by squares 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. The square labelled ‘A’ represents this point. * **Outcomes:** Points where there are different possible outcomes in a decision tree are represented by circles and are called chance nodes. At these chance nodes it can be shown that a 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 a possible outcome happening is represented by probability in a decision tree. The chance of a particular outcome occurring is given a value. If the outcome is certain then the probability is 1. Alternatively, if there is no chance at all of a particular outcome occurring, the probability will be O. In practice, the value will lie between 0 and 1. In Figure 1, at ‘B’ the chance of success for the new campaign is 0.2 and the chance of failure is 0.8. It is possible to estimate the probability of events occurring if information about these events can be found. There are two sources of information which can be used to help estimate probabilities. * **Back data:** For example, if a business has opened 10 new stores in recent years, and 9 of them have been successful, it might be reasonable to assume that the chances of another new store being successful are 9/10 or 0.9. * **Another source is research data:** For example, a business might carry out market research to find out how customers would react to a new product design – 80 per cent of people surveyed may like the product and 20 per cent may dislike it. ### Expected Monetary Values This is the financial outcome of a decision. It is based on the predicted profit or loss of an outcome and the probability of that outcome occurring. The profit or loss of any decision is shown on the right-hand side of Figure 1. For example, if the launch of a new campaign is a success, a ¥15 million profit is expected. If it fails, a loss of ¥2 million is expected. ### Calculating Expected Monetary Values (EMV) What should the firm decide? It has to work out the expected values of each decision, taking into account the expected profit or loss and the probabilities. So, for example, the expected value of a new campaign is: | | | |----------------------|-------------| | **Success** | 0.2 x ¥15m | | | = ¥3m - ¥1.6m| | | = 1.4m | | **Failure** | +0.8 x (-¥2m)| | | = -¥1.6m | The expected value of retaining the current campaign is: | | | |----------------------|-------------| | **Success** | 0.4 x ¥7m | | | = ¥2.8m - ¥0.6m | | | = 2.2m | | **Failure** | +0.6 x (-¥1m) | | | = -¥0.6m | From these figures the firm should continue with the existing campaign because the expected value is higher.