## Info

Figure 3-10 Uncertainty.

The expected value of 1450 is calculated as follows:

E(Uncertainty) = 1000(0.10) + 2000(0.60) + 500(0.30) = 1450

So, on average, we will get an answer of 1450 if we were to perform the experiment numerous times. How can we use that to get an answer to our decision problem? If we assume that the answers are the actual results of our analysis, and continue to chain such uncertainties together and attach the results to our decision node, we can see that we would want to choose the alternative that "on average" gave us the highest average PW results.

Pat's decision example using decision trees

In building the decision tree for this problem we need to establish what decisions should be made. In this case, the decision is to either buy now or buy later. We then need to establish what the uncertainties are in the problem. In this problem there are two uncertainties. The first is the same no matter which option we choose. That is, whether we win the contract. There is a 60 percent chance that we will when the contract. Therefore, there is a 40 percent chance we will not. The second uncertainty is different depending upon the option being evaluated. That is, if we buy now and lose the contract, there is an uncertainty as to the price we can sell the land for to recoup our expenses. If we do not buy the land and win the contract, then we have to purchase the land. There is an uncertainty as to the price for which we can buy the land at this point. The answer is calculated in the same manner above using expected value. When you have uncertainties that are chained together, the expected value starts at the right side and works to the left. You calculate the expected value around each uncertainty. The resulting expected value replaces the entire uncertainty in the next uncertainty. The result decision tree of Pat's decision is shown as follows.

Using the decision tree we start with the upper decision alternative of Buy Later. At the left side we see that the expected value of the purchase price of land is 100,000(0.8) + 80,000(0.2) or \$96,000. The entire uncertainty can be replaced by the \$96,000. The next uncertainty expected value can be determined as 96,000(0.60) + 0(.4) or \$57,600. Following the same procedure, we can calculate

Figure 3-10 Uncertainty.

J Pat's Decision I

j^uyLate^-

False

Decision 58400

True

False