Using Decision Trees
June 1, 2012 Leave a comment
Making decisions is part in parcel with any project or program manager’s day-to-day duties. Decisions can come in all forms, from deciding which resources to use for specific tasks, to changes to project scope. As humans, we are more than familiar with the notion of having multiple alternatives and making a decision as to which alternative is the ‘best’ course of action. Not all decisions will always have the desired outcome and certainly, not all choices available are obvious from the standpoint of which path to take.
Within the corporate world, certain decisions are more benign in nature while others carry considerably more weight and potential downside risks for the company, if that decision yields an unexpected or less than stellar result. As such, corporations often take great pains in performing thorough and rigorous analysis on the various decisions they need to make, evaluating alternatives in a systematic and methodical nature.
While generally speaking, very important decisions are often left up to the executives of a company to decipher, it is not unusual for the program manager to either have to make complex and potentially high risk decisions or to provide input to executives pertaining to various alternatives and paths of action.
The actual scrutiny around the decision making process is often part of the broader realm of risk assessment and risk mitigation. As many project managers know, projects themselves will often have a set of predefined ‘risks’ that have been categorized at project inception. More often than not, the manner in which risks are assessed can have intangible attributes associated with them (schedule slippage, loss of customers, etc). But more often than not, the primary ‘tangible’ measure for assessing risks would be a monetary one. i.e. the perceived upside and downside monetary amounts associated with a particular project.
Whenever a decision is meant to be made, often times, the most obvious metric that executives want to utilize is the monetary reference. They want to know which decisions would lead to which potential monetary outcomes. And it is with this in mind that Decision Trees become a practical and effective way of categorizing decisions based on monetary outcome.
What are Decision Trees?
Decision Trees are a graphical and mathematical method of determining the most viable decision path to take based on various monetary and probability estimates. They can actually become quite complex, with multiple branches and varying outcome possibilities, to the point that some of these more intricate structures require a computer to resolve.
Shown below, is a simple representation of a common decision tree structure:
The above example is demonstrating a simple thought experiment pertaining to the decision of whether or not an individual should take a particular bet involving a coin toss. When examining the above image, the key take-aways are as follows:
- This decision tree is evaluating two specific possibilities, ‘Bet‘ or ‘Don’t Bet‘
- The ‘Don’t Bet‘ option carries with it no upside or downside risk; if you choose not to accept the bet, no further evaluation is required
- The ‘Bet‘ option is broken down further into two probabilistic outcomes, each with an inherent upside and downside; in this case, the probability of the outcomes is identical at 50%, since this is a simple coin toss
So from a visual perspective, the decision tree is providing the individual with a graphical display of the decisions and outcomes along with probability calculations on upside and downside monetary risks
How do Decision Trees Work?
The main premise behind a decision tree is to categorize decisions into functional options and assess the upside and downside potential of those decisions mathematically. Depending on the situation, a decision can often be followed by subsequent decisions that also have specific attributes associated with them. As alluded to earlier, these trees can often become quite complex depending on how intricate the decision is or how many permutations are involved. The ultimate goal of a decision tree is to provide a tangible basis to each decision to give those in charge something more concrete from which to base their ultimate selection.
Shown below is an example (provided by Wikipedia) that demonstrates just how complex and multi-tiered certain decision trees can become:
In this case, a very complex decision tree with multiple levels of outcome has been drafted (by hand no less!) to calculate the best possible outcome.
Decision Tree Example
To show a full example (with calculations), we are going to step through a simple decision tree analysis. Consider the following decision tree:
The above graphic demonstrates two options being presented, Option 1 and Option 2. Both options have identical probabilities associated with their success or failure, all being set to 50% for simplicity.
For Option 1, a successful outcome will yield a net result of $100 dollars and a failure will result in a net loss of -$30 dollars.
For Option 2, a successful outcome will yield a net result of $90 dollars and a failure will result in a net loss of -$10 dollars.
With the above being said, which is the ‘best’ choice? In order to determine that, one must calculate the ‘EV‘ or ‘Expected Value‘ of each option. Calculations are provided in the graphic, but will also be repeated here:
Option 1 EV = (0.5)(100) + (0.5)(-30) = $35
Option 2 EV = (0.5)(90) + (0.5)(-10) = $40
Based on the EV calculations, Option 2 is the better selection since it’s EV is higher than that of Option 1. As such, the better course of action in this example would be Option 2. This is also denoted in the above graphic.
Decision Trees can be a handy resource when one is presented with different tracks and the individual doing the analysis wants to perform some level of due diligence on the best expected outcomes. Note that even with the calculations at hand, decision trees can often be somewhat subjective since expected monetary outcomes or the probabilities for success and failure of certain outcomes are not always straightforward to assert. Often times, these can amount to guesses. Nevertheless, the usage of a decision tree can be a good asset, especially when dealing with senior or executive management that prefers tangible monetary amounts as the baseline for their decision making process.