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the contingency the project "Buffer." For 95 percent, the buffer is equal to 1.645 * the standard deviation, or 3.26, and the total project duration is the buffer plus the mean project duration, or 21.83 + 3.26 or 25.03.

Decision Trees and Uncertainty

Another tool we will be using in managing new product development is decision tree analysis. This tool is used when you have choices to make in a new product project, e.g., whether to test a new product early in the project despite the possibility that new external product safety regulations might be enacted that would change a key test standard, versus waiting to test the new product later after new regulations are in place but losing valuable time.

We will begin by evaluating a sample problem that is typical of the type of decision we would use a decision tree to evaluate. Consider that following problem.

Decision tree example

Pat is a project manager with a local contractor that has submitted a proposal to install telephone trunk line between Macon central station and Kathlyne, GA. Pat has just received an option on 1,000 acres of right-of-way property at \$100/acre. If Pat purchases the options and the project is not selected, there is a 60 percent chance that Pat can sell the property at what she paid for it; otherwise, she believes there is a 40 percent chance she can sell it at \$90/acre. Pat has another option to wait until the project is awarded to purchase the property. However, there is a 20 percent chance that the property will increase to \$120/acre. Pat feels that there is a 60 percent chance that the company will be awarded that project. The original proposal, based on the \$100/acre netted the company a profit of \$100,000.

Figure 3-8 Decision component.

Decision tree theory

There are only two components to the decision tree—a decision and an uncertainty. The decision is shown as a box with one arrow for each option available in the decision (see Figure 3-8). The uncertainty is represented by a circle and an arrow for each state of the uncertainty (see Figure 3-9). The arrows for the uncertainty must contain the outcome if that state occurs and the probability of it occurring.

Note that the sum of all probabilities around the uncertainty circle must add to 1.0. Therefore, the states must represent all possible conditions. These components are strung together to give a picture of the decision to be made. With the addition of a method for making a decision using the decision tree called the expected value, we can make our decision and have a method for presenting the results in a consistent manner.

Expected value

Given the uncertainty in the previous section, and a given outcome for each state, we can make the following observations. If the uncertainty was run as an experiment, using the probabilities given on the tree, we can assume that if we performed the experiment numerous times, the results would occur at the probabilities given. Therefore, on average, the result for the uncertainty would approach the weighted average of each outcome at its given probability. For the whole uncertainty this is called the expected value or mean result. Remember this: the expected value is the mean!!!

E(v) = Outcome1(P1) + Outcome2(P2) + . . . + OutcomeN(PN) Consider the uncertainty shown in Figure 3-10.

Figure 3-9 Uncertainty component.