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Lesson 67

Building Decision Trees

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Hello! Welcome back to our exploration of Engineering Economics.

In our last lesson, we mastered the concept of Expected Monetary Value (EMV), a powerful tool for condensing a project's uncertain outcomes and their probabilities into a single, decision-guiding number. We saw how to use EMV to compare projects in a single-stage decision.

However, as you know from your experience managing complex software projects, decisions are rarely made in isolation. A choice made today often opens up new choices and exposes you to new uncertainties tomorrow. For instance, do you invest in building a scalable backend architecture now, or do you launch with a simpler solution and refactor later if user adoption is high? This is a sequence of decisions and chance events.

Today's lesson directly addresses this complexity. Our goal is to learn how to construct a decision tree to model a sequence of decisions and chance events. This is a visual and logical method for laying out all the possible paths a project can take, making it an indispensable tool for strategic planning. We'll focus on structuring the problem today, and in our next session, we'll learn how to analyze the tree to find the best path forward.

1. The Anatomy of a Decision Tree

At its core, a decision tree is a specialized flowchart designed for decision-making. It provides a clear, chronological map of a problem, starting from an initial decision and branching out to every possible conclusion.

The tree is built from a few simple components:

  • Decision Nodes (Squares ☐): These represent points in time where you, the decision-maker, must make a choice from a set of alternatives. For example, "Build New App" vs. "Upgrade Existing App". Branches leaving a decision node represent the different choices available.
  • Chance Nodes (Circles ◯): These represent points where an uncertain event occurs, and the outcome is outside your control. For example, after launching a product, demand might be "High" or "Low". Branches leaving a chance node represent the possible outcomes, each with an associated probability.
  • Branches (Lines ―): These are the connections between nodes. They represent either the actions you can take or the outcomes that can occur.
  • End Nodes (or Terminal Nodes): These represent the final outcome of a specific path through the tree. Each end node has a final value, or payoff, associated with it (e.g., total profit or loss for that sequence of events).

Here is a simple visualization of these components in action.

Decision Tree Template for Product Launch
This diagram shows the basic structure of a decision tree. A **decision node** (launch 'Yes' or 'No') is followed by a **chance node** (market 'Success' or 'Failure'), which leads to final **payoffs**.

To see these components explained in a simple example, please watch the first two minutes of the following video.

Introduction to Decision Trees

This video, 'Introduction to Decision Trees' by UTM MCS Math Videos, provides a concise definition of a decision tree and its fundamental components, using a straightforward manufacturing example.

Please watch from the beginning up to the timestamp 01:58. Focus on identifying the square decision node, the circular chance nodes, and the branches that represent alternatives and outcomes.

2. How to Build a Decision Tree: A Step-by-Step Process

Constructing a decision tree is a logical process of mapping a problem from left to right, in the order that events unfold.

Here is a systematic approach you can follow:

  1. Define the Problem and Start with the Initial Decision: Begin on the far left of your page. Draw a square decision node to represent the first choice you need to make.
  2. Draw Branches for Your Alternatives: From the decision node, draw a branch for each possible alternative. For example, if your decision is about IT infrastructure, your branches could be "Buy New Server," "Upgrade Existing Server," or "Migrate to Cloud."
  3. Add Subsequent Nodes: Follow each alternative branch to its conclusion. What happens next?
    • If it leads to another decision you must make, draw a square decision node.
    • If it leads to an uncertain outcome, draw a circular chance node.
  4. Branch Out from Chance Nodes: For each chance node, draw a branch for every possible outcome. Label each of these branches with its probability. Remember, the probabilities for all branches leaving a single chance node must sum to 1.0 (or 100%).
  5. Continue Until the End: Keep extending the tree to the right, adding nodes and branches until every path reaches its final logical conclusion. There are no more decisions to be made or uncertainties to resolve on that path.
  6. Assign Payoffs: At the very end of each terminal branch, write down the net payoff for that specific path. This is the cumulative financial result of all the decisions and outcomes along that branch.

This step-by-step guide is also available in the following resource, which you can use for future reference.

Decision Tree Analysis: 5 Steps to Better Decisions [2026]

The article 'Decision Tree Analysis: 5 Steps to Better Decisions' from Asana provides a clear, text-based guide to this process, which is a great supplement to the video material.

Please read the section 'How to create a decision tree', focusing on steps 1, 2, and 3. This reinforces the structured approach to building the visual model.

3. A Practical Example: IT Infrastructure Decision

Let's watch how this process is applied to a scenario highly relevant to your work: deciding whether to buy a new server or upgrade an existing one to handle anticipated traffic for an e-commerce platform.

Decision Tree Analysis for calculating Expected Monetary Value (EMV) | Decision Tree Example

This video from PMC Lounge, 'Decision Tree Analysis for calculating Expected Monetary Value', demonstrates the construction of a decision tree for a very practical IT decision.

Watch the segment from 05:14 to 09:14. Your focus should be on how the problem is structured: The initial decision node ('Buy' vs. 'Upgrade'). The costs associated with each decision branch. The chance nodes for traffic ('Heavy' vs. 'Low'). The probabilities and sales figures on the outcome branches. Don't worry about the EMV calculations for now; just observe how all the pieces of the problem are mapped onto the tree structure.

As you saw in the video, the tree provides a complete picture of the decision landscape. It clearly separates the choices you can control from the chance events you cannot, and it organizes all the relevant financial data (costs, revenues, probabilities) in a logical structure.

Test your understanding!

Imagine you are the General Manager of a software company planning to launch a new SaaS product. You face a strategic choice:

  1. Direct Launch: Go straight to a full market launch. The development cost is $500,000. If the launch is successful (60% probability), the profit will be $1,200,000. If it fails (40% probability), you will lose the entire development cost plus an additional $100,000 in marketing expenses.
  2. Pilot Program First: First, run a smaller pilot program at a cost of $80,000.
    • There's a 70% chance the pilot is successful. If it is, you then face a second decision: launch fully (at the same $500,000 cost) or scrap the project. If you launch, you are now much more confident of success (90% probability of that same $1,200,000 profit).
    • There's a 30% chance the pilot fails. If it fails, you will scrap the project, and your only loss is the cost of the pilot.

Your task is to draw the decision tree that models this entire scenario. You don't need to solve it. Just structure the problem by placing all the decision nodes, chance nodes, branches, and final payoffs in the correct places.

Show answer

Here is a description of how the decision tree should be structured:

  1. Initial Decision Node (Square): The tree starts on the left with a square node. Two branches emerge: "Direct Launch" and "Pilot Program First".

  2. Top Path ("Direct Launch"):

    • This branch leads to a Chance Node (Circle).
    • Two branches emerge from this chance node:
      • "Success" (labeled with 0.6 probability). This leads to a final payoff of $1,200,000 (profit) - $500,000 (cost) = $700,000.
      • "Failure" (labeled with 0.4 probability). This leads to a final payoff of -$500,000 (cost) - $100,000 (marketing loss) = -$600,000.

  3. Bottom Path ("Pilot Program First"):

    • This branch has the cost of the pilot program written on it (-$80,000). It leads to a Chance Node (Circle) representing the pilot's outcome.
    • Two branches emerge from this chance node:
      • "Pilot Success" (labeled with 0.7 probability). This leads to a Decision Node (Square) representing the choice after a successful pilot.
        • From this new decision node, a branch for "Launch Fully" leads to another Chance Node (Circle).
          • A "Market Success" branch (0.9 probability) leads to a final payoff of $1,200,000 - $500,000 - $80,000 = $620,000.
          • A "Market Failure" branch (0.1 probability) leads to a final payoff of -$500,000 - $80,000 = -$580,000.
        • From the same decision node, a branch for "Scrap Project" leads to a final payoff of -$80,000.
      • "Pilot Failure" (labeled with 0.3 probability). This leads directly to a final payoff of -$80,000.

This structure captures every decision point, uncertain outcome, and financial consequence in the problem statement.

Conclusion

In this lesson, we have laid the foundation for analyzing complex, multi-stage projects. You have learned how to translate a word problem describing a sequence of choices and uncertainties into a clear, logical diagram—a decision tree.

  • Key Takeaways:
    • Decision trees are visual models for problems involving a sequence of decisions and chance events.
    • The core components are decision nodes (squares) for choices, chance nodes (circles) for uncertainties, and branches for alternatives/outcomes.
    • Trees are constructed chronologically from left to right, starting with the initial decision.
    • Every path through the tree ends with a terminal payoff, representing the net financial result of that specific sequence.

Preview of the Next Lesson

Now that we know how to meticulously map out the problem, our next task is to solve it. In the next lesson, we will learn the rollback procedure. This powerful technique uses the Expected Monetary Value (EMV) concept we've already mastered to work backward from the final payoffs, allowing us to determine the optimal choice to make at the very first decision node.