Decision Tree Analysis | worked example
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 layout the options clearly and decide the best course of action.
What is a decision tree?
A decision tree is a modeling 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 visualizing 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 in the 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 decion tree, we can represent the scenario by mapping out the routes by which different outcomes can be achieved.
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 circlular 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 consider. 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 out a new software tool that would be used by the sales team. But if it is successful, it could be rolled out across the organization, generating greater efficiencies and process alignment. Here’s what the decision tree looks like:
In this model, there are four possible outcomes, and two decision points. If we decide to kill the project, then we cut our losses, but we gain no benefit from the project. If we continue to invest in the project, then there is still a possibility that it will fail – leaving us even more out of pocket. But what if the project goes on to be successful and delivers the software? Then we face a further decision on whether to invest more in rolling out to the wider organization, or whether to 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 visualizing 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 conclude 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 the output of a recent risk assessment, the PMO indicates that even with additional investment, there is still a 40% chance of the project failing.
- If the system is implemented successfully, the sales team has forecast cost savings of $80,000pa.
- Delivering phase two of the project to roll the solution out across the organization is forecast to cost a further $100,000. This will take a further year to complete, after which the annual benefit across the organization is forecast to be $200,000pa
Adding this data to our decision tree allows us to view the data logically, enabling systemic analysis of the options, to enable better decision making.
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: this is the responsibility of portfolio managers and executive sponsors. But it does help decision-makers determine which choice will give the greatest benefit, given the alternative options 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 will help decision-makers understand the financial implications of their decisions. To help make things clearer, a process known as ‘rollback’ is used. With the rollback method, we start on the right-hand side of our tree and assess decision two. Proceeding with an organization-wide rollout will mean an extra investment of $100k. We will receive the $50k benefit in year 2 as the sales team starts to receive the benefit of the system, and we receive the full benefit of $200k in year three. Note. We have not used any discounting in this example, but flows can be discounted per your organization’s standard discounts. Our alternative option is leaving the software within the sales team only, which we calculate has a net benefit of $50k. Of course, this isn’t a decision we need to make for another twelve months, But we want to consider it now to identify the expected decision and outcome. Purely looking at the numbers, we see that the organization-wide rollout offers a better return, so we conclude this is the decision that would be most likely at decision point two. This is the path that we will use as a basis for calculating the best decision to make at decision point one.
From there, we can multiply our benefits by the probabilities of them actually occuring:
Invest (assuming org-wide rollout): 100k x 0.6 = 60k
Our decision tree is telling us clearly that the best decision, from a purely monetary perspective is to continue to invest in the project, rather than killing it off.
Use of Decision Trees in Artificial Intelligence
Decision tree analysis is a great too for financial analysis, but it plays an important role in machine learning and artificial neural networks.
Decision trees are used as a classification tool by many machine learning algorithms. Imagine you have a computer model designed to identify types of dogs in photographs. We provide the algorithm with our list of dog types and use a batch of images to train the algorithm. As we show the computer the images, it tries to predict which type of dog it is. We then provide the correct answers so that the machine can ‘learn.’ During this learning phase, the computer will develop a model which it can use to decide which type of dog is in the picture. This is usually in the form of a binary tree – a simple decision tree where each node has only two options – Yes or No. “Does the dog have long hair?” Yes/No etc. Such models require large amounts of training data – end even then, they can still get it wrong! One real-world attempt at building a dog classification model needed rework when the people supervising it realized that the model was deciding dogs were Siberian Huskys, not because of their size and fur, but because the photographs had snow in the background. Thus any dog playing in the snow was instantly classified as a Husky!
One of the ways machine learning gets around this misclassification problem is to use multiple decision tree algorithms – each having built its classification model independently. The group of decision trees are referred to as random forests, and the model will determine the most likely classification based on consensus across all of the decision trees.
But decision trees are used for more than classification. They can be used in a similar way to the project example we showed above to create real numbers. Such models are referred to as regression tree models. These models may be more complex than our example, but they follow the same basic principles. They are a vital component in Artificial Intelligence as they provide a structure by which a computer can make decisions based on an uncertain outcome. When humans make decisions, we often consider the range of possible outcomes before making a decision. Using classification and regression trees in machine learning allows computers to take a similar approach to decision making.
Trees with similar outcomes
Sometimes with decision tree analysis, you will find that you end up with decisions that have very similar outcomes. To help decide the best one to choose, it is helpful to remember why we undertake future planning. We assess a decision tree from right to left because everything comes back to the decisions we make today. None of us can tell exactly what the future has in store – who in 2019 would have predicted the tragic effects of Covid 19? But looking to the future in this way allows us to make decisions today that set the stage for what we do in the future. Therefore, whilst it is tempting to look at our trees purely in terms of monetary outcome, it is also worth considering flexibility. A good question to ask is, “Which decision will give us the most options and flexibility in the future?”. When all other factors look even, it is always best to allow your future self to be as flexible as possible.