Transcript

NARRATOR:

In this video, we're going to introduce decision trees. A decision tree is a really useful tool for visualising and solving problems where there are various choices involved and we don't know which choices to make. So we're going to bring in probabilities with this.

Decision trees consist of nodes. These are where the branches of the decision tree split. And there are two types of nodes. A square node is where a decision is being taken, something that is our choice. And the other type of node we show is a circle, where there is some kind of chance element. This is where we apply probabilities, where things happen outside our control.

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 dissatisfied customers.

So we need to assess two bids to make a decision between A or B. Let's set up a branch for A and a branch for B. There's a chance on each of them - will they deliver a good service or not? So let's look at A's first. It's a chance. So it's a circle node. Will the service of A be acceptable? And that's a 'Yes' or a 'No' branch. There's an 80% probability, or 0.8, of it being 'Yes'. So, therefore, there must be 0.2 of it being 'No'.

You'll recall from the beginning of this section that all probability must total 1. So if it's 'Yes', it has a final value of 120 million pounds, whereas if it's a 'No', it's minus 30 million pounds. And we're going to have to give refunds, and there's going to be costs incurred.

Coming down to B, is it acceptable? 'Yes' or 'No'? There is a 0.55 probability, or 55% chance of it being 'Yes'. So the 'No' must be 0.45 because probabilities have to equal 1. And the values here are 160 million pounds and minus 10 million pounds.

And what we do now is we just work out which of these two nodes - 1 or 2 - have the highest expected value. The expected value of 1 is going to be 0.8 times 120 plus 0.2 times minus 30, which is 90 million pounds. And the value of node 2 is going to be 0.55 times 160 plus 0.45 times minus 10. And that works out to be 83.5 million pounds. 90 million pounds goes here, and 83.5 million pounds goes here.

In this fairly simple decision tree, the root with the highest expected value is A. We would expect, on average, A to get 90 million pounds, whereas B only 83.5 million pounds. Therefore, on this basis, we would go with A.

Notice that although this is a simple decision tree, we can already see the technique. When we're setting up the model, we work from left to right, going through putting down what each of the various branches will do. And then we work backwards to get the expected value of each node.