We all have decisions to make. Sometimes we go with our gut. Sometimes we go with what our moral compass tells us is right. But some decisions require a more structured approach. Decision trees are a great management tool to have in your PMO and Project Management arsenal. Decision tree analysis helps you lay out the options clearly and decide the best course of action.
What is a decision tree?
A decision tree is a modelling tool that enables you to decide a course of action. It works by creating tree diagrams, where each option represents a different branch. Sometimes, simply visualising the options in this way is enough to stimulate conversation and drive decisions. But there’s more to decision trees than laying out data in a visually appealing way. Decision tree analysis is also a financial analysis tool. By assigning monetary values to each leaf node and assigning probabilities to each outcome, you can quickly map out advanced statistical models that can serve as predictive models or tools to help with complex decisions.
Example of a decision tree
Let’s consider a very important project: planning a wedding. You have a large garden. Ideally you would like to set up food and drink in the garden, and have space for the formal part of the ceremony. The only problem is that your large garden is near Seattle, WA. And one thing everyone knows about Seattle is that it rains. A lot. You could set everything up for a wedding outdoors and hope for the best. Or you could hire a marquee. The marquee would keep everyone dry, but it would be more claustrophobic.
With a decision tree, we can represent the scenario by mapping out the routes by which different outcomes can be achieved.
A simple decision tree with one decision node and one chance node on each branch.
Drawing a decision tree
To draw a decision tree, we put the first node on the far left. In our example above, it is the choice of renting a marquee, or having an outdoor wedding. Branches are then drawn representing each course of action. These courses of action could be decisions that are made, or they could be chance events. In our example above we have represented decisions with a square node, and chance events, in our case the weather, with a circular node.
The tree can carry on branching as many times as is necessary to capture the possible outcomes. At the end of each branch, we have a terminating node that shows the outcome, or payoff.
Complex decision trees
The wedding example above was a simple one, with only one decision. But your real-life examples may be more complex. So let’s consider a more complex example that a PMO may face. Consider the scenario where you have a project in your portfolio that is not doing so well. You have to decide whether to kill the project or invest more to let it continue. The project was to build a new software tool for the sales team. But if it succeeds, it could be rolled out across the organisation, generating greater efficiencies and process alignment. Here’s what the decision tree looks like:
The same kind of decision, this time with two decision points and a chance node in between.
In this model, there are four possible outcomes and two decision points. If we decide to kill the project, we cut our losses, but we gain no benefit from it. If we continue to invest in the project, there is still a possibility that it will fail, leaving us even more out of pocket. But what if the project goes on to succeed and delivers the software? Then we face a further decision on whether to invest more in rolling it out to the wider organisation, or keep the software for use within the sales team only.
Adding financial data to a decision tree
By adding financial data to our decision trees, we shift from merely visualising the chain of decisions and chance events to constructing a financial basis for decision making. We are going to stick with the project scenario above, but now let’s look at how we can add data to the tree. Our decisions will be based on three factors: the probabilities, the costs, and the likely return on our investment. The PMO reviews the available data and concludes the following:
- The cost to deliver the project, up to the point where the sales team has the tool operational, is £50,000. It will take one year to complete.
- Based on the history of running similar projects within the company, the track record of the project manager, and a recent risk assessment, the PMO estimates a 40% chance of the project failing even with the additional investment: a 60% chance of success.
- If the project succeeds and the tool is kept for the sales team only, it is forecast to deliver a net benefit of £50,000 over three years.
- Rolling the solution out across the whole organisation instead is forecast to cost a further £100,000 on top of the original spend, and to deliver a net benefit of £100,000 over three years.
Adding this data to our decision tree lets us view it logically, enabling a systematic comparison of the options.
The same decision, with probabilities and financial values added to every branch.
Deciding what to do
Once we have a decision tree, we can consider the impact of our decisions. It is important to note that the decision tree will never tell you exactly what to do: that is the responsibility of portfolio managers and executive sponsors. But it does help decision-makers work out which choice gives the greatest benefit, given the alternatives available.
Decisions will be made considering a wider range of factors than those shown in our tree: how well does this project align with our strategic goals? Will it boost morale? Does delivering this project open up more future options for us? But laying out the financial argument in a decision tree helps decision-makers understand the financial implications of their choice. To make things clearer, a process known as ‘rollback’ is used. With the rollback method, we start on the right-hand side of the tree and assess decision point two first. Rolling out across the whole organisation costs a further £100,000 and delivers a net benefit of £100,000 over three years. Keeping the tool for the sales team only costs nothing further and delivers a net benefit of £50,000 over three years. Purely on the numbers, the organisation-wide rollout wins, so that is the path we carry back to decision point one.
From there, we weight each option at decision point one by its probability of occurring:
Invest (taking the organisation-wide rollout if it succeeds): 0.6 × Â£100,000, minus 0.4 × Â£50,000 for the amount already spent if the project fails, giving an EMV of £40,000.
Kill: £0.
Our decision tree is telling us clearly that the best decision, from a purely monetary perspective, is to continue investing in the project rather than killing it off now.
EMV averages away the extremes. Two options can share the same expected monetary value and still be different choices. If one carries a small chance of a loss the organisation cannot absorb, the average hides it. A sensitivity check, or a simple best case and worst case range alongside the EMV, catches what the average alone misses.
Decision trees in artificial intelligence
Decision tree analysis is a strong financial analysis tool, but it also plays an important role in machine learning and artificial neural networks.
Decision trees are used as a classification tool by many machine learning algorithms. A well-known illustration from the machine learning literature involves an image classifier trained to tell huskies from wolves. The model performed well on its training images, but researchers found it had actually learned to detect snow in the background rather than any feature of the animal, so any dog photographed in the snow was classified as a wolf. This came to light only once the researchers inspected which pixels the model was actually using to make its decision (Ribeiro, Singh and Guestrin, 2016). It is a useful reminder that a model can look accurate and still be learning the wrong thing.
One of the ways machine learning gets around this kind of misclassification is to use multiple decision tree algorithms, each built independently. This group of trees is known as a random forest, and the model determines the most likely classification based on consensus across all of them.
Decision trees are used for more than classification. They can be used in a similar way to the project example above to predict real numbers rather than a category; such models are known as regression trees. They follow the same basic principles as our example, and they are a key part of how a computer can make decisions based on an uncertain outcome, in much the same way a person weighs up a range of possible outcomes before deciding.
Trees with similar outcomes
Sometimes with decision tree analysis, you will find you end up with options that have very similar outcomes. To help decide between them, it is worth remembering why we do this kind of planning in the first place. We assess a decision tree from right to left because everything comes back to the decisions we make today, and none of us can say exactly what the future holds. Looking ahead in this way lets us make decisions today that set the stage for what we do next. So whilst it is tempting to judge our trees purely on monetary outcome, it is also worth considering flexibility. A good question to ask is: which decision gives us the most options and flexibility in future? When all other factors look even, it is always best to leave your future self as much room to manoeuvre as possible.
Further reading
- Magee, J. F. (1964). ‘Decision Trees for Decision Making.’ Harvard Business Review, July–August 1964. Read on hbr.org
- Magee, J. F. (1964). ‘How to Use Decision Trees in Capital Investment.’ Harvard Business Review, September–October 1964.
- Raiffa, H. (1968). Decision Analysis: Introductory Lectures on Choices under Uncertainty. Addison-Wesley.
- Project Management Institute (2017). A Guide to the Project Management Body of Knowledge (PMBOK Guide), 6th edition, section 11.4, Figure 11-16.
- Ribeiro, M. T., Singh, S. and Guestrin, C. (2016). ‘“Why Should I Trust You?”: Explaining the Predictions of Any Classifier.’ Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135–1144. doi.org/10.1145/2939672.2939778
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