# Decision trees

A decision tree is a technique for identifying alternative courses of action and their implications (often in terms of cost). It shows decisions and consequences as lines between nodes (the circles in the diagram). If the object is to quantify costs, the expected cost of decisions and their possible outcomes can be calculated for any node in the tree.

The purpose is to calculate the full implications of a decision rather than just the initial cost.

For example: A project has the option to meet a stakeholder requirement in two different ways but it is unclear which one is the best solution. Whichever option is chosen there are two consequences, either:

X: The solution works and is integrated into the project at a cost of £3,000.

Y: The solution doesn’t work and the cost of retrospectively switching to the other solution is £10,000. At point A in the diagram above there are two possible courses of action: Option 1 and Option 2. Option 2 initially appears to be the cheaper option.

If Option 1 is chosen the chance of consequence X occurring is 90% and the chance of consequence Y occurring is 10%. With Option 2 the situation is reversed.

Therefore, the true cost of Option 1 is the initial cost plus the cost of the consequences, taking their probability into account.

 Option 1 initial cost £7,000 Consequence X £10,000 x 10% £1,000 Consequence Y £3,000 x 90% £2,700 Total cost £10,700

The same calculation for Option 2 gives a total cost of £13,300.

Based on the decision tree, option 1 is likely to be less expensive than option 2. The key word there is ‘likely’. The project manager may go for option 2 and get away with it. The option chosen will probably depend upon the risk context (attitude or appetite) of the project manager and stakeholders.