Making decisions the easy way - a Decision Tree overview

The decision tree allows the decision maker to follow along each potential decision path to its' predicted conclusion, evaluate the expected outcomes against other potential paths on the tree, and determine the overall expected outcome.

One thing I come across pretty often is the need to reduce complex challenges into "bite-sized" pieces in order to facilitate informed decision-making. There are a number of different frameworks that can be applied depending on the particular situation, but one that I am particularly fond of is something called a "decision tree". This approach to decision making is extremely helpful for people who understand the factors that could impact their decisions, but who are unsure of how to quantify them in a manner that provides a clear, dollar-based, indication of the expected outcomes.

In a nutshell, a decision tree is a tool that helps you visualize the main components in a decision making process (decisions, uncertainties, & consequences), laid out in the shape of a tree lying on its side. Each time a branch splits, it occurs at either a point of decision or uncertainty, referred to as "nodes." A decision node would be one where the decision maker decides which path to take based on the highest expected outcome between the choices, and an uncertainty (or "chance") node is one where outside forces determine the best path to take based on the likelihood of a particular event. The decision tree allows the decision maker to follow along each potential decision path to its' predicted conclusion, evaluate the expected outcomes against other potential paths on the tree, and determine the overall expected outcome.

While there are a number of great decision and analysis tools that offer seemingly limitless options to help you understand and frame a variety of problems (Palisade's DecisionTools Suite is one that I have used in the past), they can be expensive to the point of off-putting for individuals and small businesses unless there is expected regular use of the tools. So, for this example, I am using screenshots from an input-limited Decision Tree template I downloaded for free from Word Templates Online, but modified for my example. You can also build your own decision trees from scratch in Excel if you're okay with the extra time required and don't need all the bells and whistled offered in the developed versions.

Let's go through a basic example to illustrate what a decision tree is and how it might be employed in a decision making process.

Premise: You are the CEO of a fledgling manufacturing company that is developing an innovative new product, the likes of which the buying public has never seen. Your product requires a dedicated manufacturing facility due to specialized equipment and storage needs. You are tasked with determining what size of manufacturing facility you should build.

This product will only be sold for one year, and the facility will be abandoned at that point. (not realistic, I know, but trying to simplify the example by limiting the time view to defined time period... there are other obvious areas of simplification as well - just go with it).

Here is what we know about this project:

- Unit sale price of new product = $20.00

- Unit manufacturing cost of new product = $4.75

- Market research says you will sell between 4.75M and 10M units annually

Here are the initial facility specs your engineering firm has presented you:

Large facility

- Construction cost = $82.5M

- Annual output capacity = 10.0M units

Small Facility

- Construction cost = $55M

- Annual output capacity = 6.5M units

Pretty simple so far: If you operate each facility at its maximum capacity, the construction cost allocation for the small facility is $8.46/unit vs. $8.25/unit for the large facility (note: the key phrase here is "maximum capacity").

"But wait," you say. "...we only have one customer pool and, therefore, we will only have one demand number. Is it 4.75M units, or 10M units?" Your crack marketing squad clues you in to the fact that nobody can be certain what demand will be for an unknown and untested product. However, they have put their heads together and determined a likely range of demand that spans 4.75M units on the low end and 10M units on the high end. The best they are able to tell you is that there is a 40% likelihood that demand will be at the low end of their initial projection and 60% likelihood that it will be at the top end of their projection.

Now you have questions:

1/ If we build the small facility to protect ourselves against the potential of demand at the low end of the forecast, what can we do to increase capacity should demand come in at the high end of the forecast?

2/ If we build the large facility to have capacity for the high end of the demand forecast, what can we do to mitigate against the potential catastrophe of a low demand environment?

Your team has answers:

1/ The engineering firm has come up with a way to expand the output of the small facility, should you so choose to scale up for higher demand after you have completed initial construction, by 1.5M units at an incremental cost of $20M.

2/ Your marketing team is advising you that they could develop an emergency advertising campaign to deploy should you have low demand after building the large facility. They project that it will cost $5M, with a 75% chance that they will be able to bolster demand by 30%, but the resulting 25% chance that it will only have a 10% effect on demand.

If you think your head is about to explode, have no fear - decision tree is here! Let's look at the structure of our challenge:

- Primary question: "Should we build a small facility or a large facility?"

- Should we proceed with the small facility: we have a chance node (is demand going to be high or low?), followed by a decision node on the high demand side (should we expand the facility?).

- Should we proceed with the large facility: we have the same demand chance node, followed by a decision node on the low demand side to either advertise or not, and a chance node on the "advertise" side with either a modest or sizable response.

I've set up some input cells in my Excel spreadsheet to make the decision tree easier to work with - here they are for quick reference:

Here's what our decision tree looks like (decision nodes are depicted as squares, and chance nodes as circles):

Based on the inputs we provided, the highest expected outcome follows the decision to build the large facility.

Each branch of the tree ultimately ends with a value for expected gross margin (far right column). Accordingly, you can see that the best individual outcome of $70M would occur if you built the large facility and demand was high (calculated by taking Sale Price per Unit of $20 - Direct Cost per Unit of $4.75, multiplying the result by 10M units, and subtracting out the $82.5M facility construction cost). The worst individual outcome of -$10,062,500 would occur if you built the large facility, demand was low, and you decided not to advertise.

The blue numbers next to the chance nodes (circles) represent the expected outcome given the likelihood of the event. As an example, the effectiveness of advertising node results in an expected outcome of -$7,818,750 should there be a modest response, and $6,668,750 should there be a sizable response. Taking the weighted outcome based on the expected likelihood (-$7,818,750 * 25% chance, plus $6,668,750 * 75% chance), the resulting expected margin of $3,046,875 is depicted in blue on the decision tree.

Walking that backwards to the next decision node of "advertise" or "do nothing": you can see the same number shown in blue because given the option to have a $3,046,875 outcome by advertising vs -$10,062,500 outcome by not advertising, you would always choose to advertise.

Following the tree to conclusion, based on the inputs we provided, the highest expected results comes with the decision to build the large facility.

**One thing to point out here is that you can always decide to do nothing. While I did not depict it as a choice in this example, it would clearly be the path you would choose should the other choices lead you to negative dollar expected outcomes. Should you wish to depict it for completeness, you can do so by adding a third branch to your main decision node with an expected outcome of $0, and tie in the conditional formatting to capture that as one of the cells queried for MAX value.

Now, let's say that you are about to break ground on the large facility when the marketing team come back to you with some unwelcome news: they were going over their notes and realized that the numbers provided earlier were backwards. In fact there is a 60% chance of the low demand numbers, and they expect a 75% chance of a modest response to their advertising efforts. They have placed all blame for the error on their summer intern (who likely has more potential than the rest of them, from your perspective). Either way, you need to reevaluate... FAST.

Good thing you have your decision tree model. 30 seconds of updating the percentages on the chance nodes yields the following:

With the updated percentages around the chance nodes, the highest expected outcome now follows the decision to build the small facility.

You can follow the branches above to see how the new chance node percentages impacted the expected outcomes. Despite the last minute changes, you are able to quickly determine the best course of action is to build the small facility and redirect the engineering team accordingly.

You will save your decision on the fate of the marketing team for another time (and possibly another decision tree)...