OperationsFramework / modelModelAccessible

Decision trees

How can decision trees improve people, teams, or organisational effectiveness?

AccessibleOperationalTeam2 min read

Contents

Decision trees assist in the choice between two or more courses of action.

Decision trees support choices between two or more courses of action. By displaying decisions, uncertain events, outcomes, probabilities and values in one structure, they make the assumptions behind risk and reward explicit.

When to use it

Use a tree when a decision is complex enough that laying out every material option and outcome will improve judgement.

Use it when decision makers need to compare the expected costs and benefits of alternative paths transparently.

Origins

Tree-like reasoning has existed for centuries, and Bayes’ theorem provided an early formal basis for updating probabilities. Modern decision-tree analysis became widespread with operations research, decision theory and computer programming during the nineteen fifties. The same visual logic later became important in machine-learning classification, although a managerial decision tree represents choices and uncertainty rather than merely predicting a class.

What it is

A decision tree is a graphical model of a sequence of choices and uncertain events. It allows decision makers to attach probabilities, costs and benefits to each path and then compare the expected values. Standard symbols distinguish what management controls from what it cannot control:

Decision nodes, drawn as squares, mark a choice among mutually exclusive alternatives.

Decision branches extend from a decision node and should collectively cover the feasible alternatives.

Event nodes, drawn as circles, mark uncertainty resolved outside the decision maker’s control.

Event branches show the possible results of an uncertain event.

Terminal nodes, often drawn as triangles, contain the final value or outcome of a complete path.

How to use it

Campbell Ship Motor, or CSM, designs small ocean-going ship motors for a large South African manufacturer. Its researchers have developed a more efficient design using lower-cost modular parts and must decide whether to fund commercial development. Building and testing a prototype will cost $30,000, and the unfamiliar materials create a meaningful risk of failing stress or emissions tests.

If the prototype works, CSM can design it for manual assembly, third-party assembly or an automated North American line. Outsourcing could make the design worth as much as $100,000 because the manufacturer would not need to reconfigure its own operation. Successful automated assembly could make the design worth $250,000 because production could occur near customers without high labour cost. The team maps these choices, uncertainties and terminal values.

The rollback method evaluates the tree from right to left. At each event node, multiply every outcome value by its probability and add the products. At a decision node, select the best feasible branch.

Automated assembly: 50 per cent × $250,000 + 50 per cent × $30,000 = $140,000.

Outsourced assembly: 70 per cent × $100,000 + 30 per cent × $50,000 = $85,000.

Manual assembly: $75,000, with no event node.

Automated assembly has the highest expected value, so $140,000 becomes the rollback value for the next stage. The expected value of a successful research path is 30 per cent × $140,000 = $42,000. The unusable-prototype path is 70 per cent × −$30,000 = −$21,000. Combining them gives $42,000 + −$21,000 = $21,000. Because this exceeds the zero value of not investing, proceeding has an expected value of $21,000 at the initial decision.

Top practical tip

Keep the tree at the level where it changes the decision. Three or four critical variables are often more useful than a sprawling map of every imaginable detail. Document the evidence behind each probability and test how the recommendation changes when uncertain inputs move.

Top pitfall

A mathematically correct rollback cannot rescue an incomplete choice set. Before calculating, challenge whether the branches are mutually exclusive and collectively exhaustive. CSM, for example, may have omitted the option of selling the design to a Korean customer.