TreePlan Limit of Five Branches per Node

The TreePlan decision tree add-in is limited to a maximum of five branches per node.

If you need to represent a set of alternatives or a set of outcomes with more than five elements, a workaround is to use two sets of branches, one following the other.

The following example shows two ways to represent a set of seven outcomes with the following probability assignment.

seven-outome-probability

One way is to use a first set of branches with five branches: one branch for each of the first four outcomes, and a fifth branch for the event More Than Four.

P(More Than Four) = P(Five) + P(Six) + P(Seven) = 0.10 + 0.06 + 0.04 = 0.20

The second set of three branches following More Than Four uses the probability for each outcome Five, Six, or Seven, conditional on the event More Than Four.

For example, P(Five | More Than Four) = P(Five) / P(More Than Four)

= 0.10 / (0.10 + 0.06 + 0.04) = 0.10 / 0.20 = 0.50

The following tree diagram shows the calculation formulas for each probability.

more-than-four-formulas

The following tree diagram shows how the probabilities are displayed.

more-than-four-display

The path combining the product of the probabilities on the branch More Than Four and the branch Five yields the probability of the original outcome:

P(More Than Four) * P(Five | More Than Four) = 0.20 * 0.50 = 0.10 = P(Five)

 

A second way to represent the same seven outcomes is to use a first set of branches with two outcomes: Even Numbers and Odd Numbers.

The seven outcomes and probabilities may be grouped as shown in the following table.

even-odd-outcome-probability

The following tree diagram shows the calculation formulas for each probability.

even-odd-formulas

The following tree diagram shows how the probabilities are displayed.

even-odd-display