Probabilistic Evaluation: Building and Pruning the Tree
Even after deterministic sensitivity analysis, it is often difficult to limit the
tree to a reasonable size. If there are, for instance, n nodes in a tree and each
node has three branches, a symmetric tree will have 3n paths. For example,
for seven nodes, we would have 2,187 paths. If the model takes 1 second to
calculate an answer (not untypical of a large spreadsheet model on a personal
computer), the evaluation command will take a little over half an hour to
execute. If we add several more nodes, change a node from three to four
branches, or construct a more elaborate model, we will have a tree that is
impractical to evaluate on a personal computer.
How large a tree is reasonable? This depends greatly on the type of
problem (and on the opinion of the facilitator). However, we feel that for most
problems, 50 to 200 paths per alternative is sufficient. This number of paths
allows us to include the three generic uncertainties that often affect an
alternative: uncertainty about the growth of the market, uncertainty in
competitive action or reaction, and uncertainty in how well we will fare. At
three branches a node, we have 27 paths per alternative, leaving room for
several other nodes if called for. After the full-scale analysis is complete, we
will probably find that around 20 paths per alternative are enough to draw
all the conclusions. Reducing the tree to this size is often important for
clarifying the results and drawing the tree for the final presentation to the
decision-maker.
How can you make your tree small enough to evaluate? By reducing the
number of branches at each node, by reducing the number of nodes, and by
creating asymmetric trees. Simplifying the model can also help by reducing