Critical Path Analysis

Force Field Analysis

Decision Theory and Decision Trees

How to Draw a Decision Tree

At the end of each solution line, consider the results. If the result of taking that decision is uncertain, draw a small circle. If the result is another decision that needs to be made, draw another square. Squares represent decisions, circles represent uncertainty or random factors. Write the decision or factor to be considered above the square or circle. If you have completed the solution at the end of the line, just leave it blank.

Starting from the new decision squares on your diagram, draw out lines representing the options thatcould be taken. From the circles draw out lines representing possible outcomes. Again mark a brief note on the line saying what it means. Keep on doing this until you have drawn down as many of thepossible outcomes and decisions as you can see leading on from your original decision.

An example of the sort of thing you will end up with is shown below:

Once you have done this, review your tree diagram. Challenge each square and circle to see if there areany solutions or outcomes you have not considered. If there are, draw them in. If necessary, redraft your tree if parts of it are too congested or untidy.

You should now have a good understanding of the range of possible outcomes.

Starting to Evaluate Your Decision Tree

Next look at each circle (representing an uncertainty point) and estimate the probability of each outcome. If you use percentages, the total must come to 100% at each circle. If you use fractions, these must add up to 1. If you have data on past events you may be able to make rigorous estimates of the probabilities. Otherwise write down your best guess.

This will give you a tree like the one below:

Note that the tree looks less confused when different colours are used for numbers than for the structure of the tree.

Calculating Tree Values

We start on the right hand side of the decision tree, and work back towards the left. As we complete a set of calculations on a node (decision square or uncertainty circle), all we need to do is to record the result. All the calculations that lead to that result can be ignored from now on - effectively that branch of the tree can be discarded. This is called 'pruning the tree'.

Calculating The Value of Uncertain Outcome Nodes

In the example above, the value for 'new product, thorough development' is:

0.4 (probability good outcome) x $500,000 (value)           $200,000
0.4 (probability moderate outcome) x $25,000 (value)     $10,000
0.2 (probability poor outcome) x $1,000 (value)                $200
-------------------------------------------------------------------------------------------
                                                                                                 $210,200

This is shown across our example tree in the diagram below:

Note that the values calculated for each node are shown in the boxes.

Calculating The Value of Decision Nodes

Sunk costs, amounts already spent, do not count for this analysis.

When you have calculated the benefit of each decision, select the decision which has the largest benefit, and take that as the decision made and the value of that node.

Calculation of decision nodes in our example is shown below:

In this example, the benefit we previously calculated for 'new product, thorough development' was $210,000. This example shows that we calculate the cost of this approach as $75,000. This gives a net benefit of $135,000. The benefit of 'new product, rapid development' was $15,700. On this branch we therefore choose the most valuable option, 'new product, thorough development', and allocate this value to the decision node.

Result

Summary

• clearly lay out the problem so that all choices can be viewed, discussed and challenged
• provide a framework to quantify of the values of outcomes and the probabilities of achieving them
• help us to make the best decisions on the basis of our existing information and best guesses.