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Decision Making with Decision Trees

Every business owner must make decisions in the face of uncertainty, and live with the consequences. But decision-making doesn't have to be done in the dark. Analyzing the outcomes of a few alternative actions before making a decision can help you determine if you've made a decision that produces the most favorable -- or least painful -- consequences.

One way to do this is to analyze the consequences of a decision by using a decision tree. Decision trees, as Sam L. Savage, author of *Decision Making with Insight* (Brooks/Cole, 2003), notes, "can sharpen and formalize the decision-making process ..." They can both aid us in making up our minds and bring into focus future events that should change our minds." Just as handles help us grasp things with our hands, Dr. Savage has coined the term "mindles" for tools like decision trees that help us grasp things with our minds.

Quite simply, a decision tree is a graphical representation of the path taken and the path not taken, and how the decision to go one way over another affects your business. Decisions are typically represented by squares, and uncertain outcomes by circles. To better explain this, we've provided an example from Savage's book and offer a sample decision tree for you to see for yourself how different variables can change the consequence of a decision you make.

#### Example: Experimental Drug Development

Imagine you work for a pharmaceutical manufacturer that has been investigating the cure for Some Horrible Disease (SHD). If a cure could be developed, it would yield a profit of $200 million. Initial research indicates a 25% chance that a particular compound X will be effective against SHD. However, it will require an additional $12 million in research and development to know for sure. Furthermore, even if the resulting compound is proven effective, another $8 million in testing (for a total of $20 million invested) will be required to have it approved by the FDA. There is an estimated 40% chance the testing will reveal serious side effects and approval will be denied. This is reflected in the figure below.

The tree may be interpreted as follows: Starting on the right, a 60% chance of $200 million plus a 40% chance of losing $20 million is .6 x 200 - .4 x 20 = $112 million. Thus if, you pursued development, and the drug actually worked, but the FDA had not yet tested it, your expected profit would be $112 million. Now moving to the left, a 25% chance of $112 million plus a 75% chance of losing $12 million is .25 x 112 - .75 x 12 = $19 million. If you don?t develop the drug you will receive nothing, so development is the correct decision. The path representing drug development is colored green, and the value at the root of the tree is $19 million.

Now of course in reality one may never know the probabilities with any accuracy. But even here, a decision tree can be a useful *mindle*. For example, suppose we have enough experience with the FDA to be confident in the 60% chance of approval, but the efficacy of compound X is more problematic. The chemist who came up with it is the most optimistic and thinks it has a 35% chance, while the CEO is the most pessimistic, and only gives it a 15% chance. By experimenting with this probability the decision tree software can quickly find the "break-even" probability at which we would make the alternative decision. In this case it turns out to be 10%. That is, if the probability that the drug will actually work is 10% or greater, we should pursue development. If it is less, we are better off abandoning the project. Since this threshold is lower than even the most pessimistic estimate by management, it is easy to agree to go ahead with development. This is reflected in the two figures below.

#### Probability greater than 10%

#### Probability less than 10%

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