Decision Tree Analysis Example
Now first, whenever you use decision tree analysis there are three things you need upfront.
Of course, you need the diagram and as you can see this is simply showing branches, hence the analogy of trees, but what you need to generate either by speaking to sales and marketing, or engineering, is some form of metrics.
You need to know what the option benefits are, you need to know what the option probabilities are, and you need to know what the option costs are.
So, the first thing you need to do is to draw the diagram itself and for that you start over at the left-hand side at this square box and you develop the branches from left to right.
In this case let’s imagine that sales and marketing are considering the options of whether we should launch a new product in a product range, or to consolidate what we’ve already got.
Drawing a Decision Tree Diagram for Analysis
Those are the two broad options they’ve come up with.
If you’ve ever considered buying a car, you’ll know that each year, manufacturers often bring out new models but sometimes they merely enhance existing models – by the same token, you’ll sometimes find a manufacturer brings out a brand-new model and that’s what we’re suggesting here…
Not necessarily for the car industry but for some invented company that has a range of products.
So, the option is either to have a new product, or to consolidate an existing one.
But there are sub-branches of that, so these branches must be drawn first.
After discussion with engineering it’s become evident that you could either do a standard detailed development, or you could do what’s known as a quick and dirty rapid development.
So, referring to this new product branch alone, we needed to get engineering to tell us what the estimated costs are to do each of these.
Well the detailed development will cost one hundred and twenty-five thousand pounds, whereas the rapid development can be done for only forty thousand pounds.
Follow your eyes over top right here. So, assuming we’re on the detailed development branch you may just have one single number here.
On the other hand, you may have something such as best case, worst case and most likely case – or simply calling it best average and poor.
What marketing would need to do in this example would be to come up with, let’s imagine these are the core sales figures, or it might be quarterly profits, or it might be quarterly revenue streams…
Whichever, if you keep them consistent throughout the entire model.
So, in the case of the detailed development, sales and marketing estimate that the best case will make half a million pounds revenue per quarter.
If it doesn’t pan out as well as that they think, then on average we would really make at least twenty-five thousand a quarter. If sales are poor in a worst-case situation, we may only make a thousand pounds a quarter.
Now these are invented figures, you’d have to put your own in, and in this case, I’m using best, average and poor.
But just to make the point, you may just have a best case and a worse case.
It’s your choice on how it must be done based on the logical options that you can either see or calculate.
The other thing you’ll need to know, again from sales and marketing, is that for each of these, what is the probability of achieving that, and the probabilities must always add up to one hundred percent or decimal one.
If you’re using decimal fractions as I have, and I’ve added these figures for each of these, they’re slightly different than each case as would happen in the real world.
So, what we’ve done now, by perhaps talking with sales, marketing, engineering and drawing the diagram itself, is we’ve got a raw decision tree waiting for us to do the calculations.
So, let’s do that next…
They’re fairly obvious and straightforward.
Whereas you would develop the decision tree from left to right as I’ve talked you through, when you do the calculations, you work backwards.
Starting top right in my diagram, there’s a 40 % chance of best case of getting half a million let’s say it’s revenue per quarter, in which case that’s point four of that, which is 200 thousand pounds.
And we do that for each of these – let me just plug those in I think you will understand exactly what’s going on here…
All right, so in this case, we’ve got these three options now.
Coming on to rapid development, again best average and poor, and using the probability split summing to 40 % we get these figures.
Notice that since this top branch is related to a new product, these figures will be the same, despite the fact we’re taking two different routes to get there.
But when we come down to consolidate, there needs to be a new set of figures, as you might imagine, merely increasing the functionality of an existing model, will certainly sell more but maybe not as much as having a new product.
And consolidating in terms of doing a cosmetic upgrade, again you’d have different expectations of revenue (or indeed risk) from such a choice, and I’ve added these numbers in here.
You’ll see they’re different to the top two.
Yet again, we just calculate by multiplying the benefit (or it may be the risk if that’s the way you’re using decision trees), against in this case % probability.
Let’s do the same for the cosmetic option, there’s those two numbers now.
Because we’re moving backwards, we now need with each of these to sum them up because they’re all independent approaches and in terms of the detailed development these sum to two hundred and ten point two thousand pounds.
When it comes to rapid development, these sums are fifty-five point seven et cetera – you’ve got the idea…
Now we’re almost done.
Again, starting at the top, so looking at these outcomes, we’ve got two hundred and ten point two thousand, but from that we need to subtract the detailed development cost which gives us eighty-five point two thousand pounds for this option.
What about rapid development?
Again, deducting the cost of development, we get fifteen point seven, subtracting we get forty-nine point nine and down below you can do similar.
We can now make a decision.
What we’re looking for in this case is the biggest number, and that clearly is the top one, so this would be the most valuable option.
Now I’ve looked at the probabilities using revenue streams, these numbers in the green boxes could be replaced with risk costs, and in which case we’d be looking for the lowest risk approach.
Okay so that’s Decision Tree Analysis – not so hard was it?
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