Sum Of The Probabilities Must Equal

FIGURE 17-3. Decision tree. FIGURE 17-4. Expanded tree diagram.

For more sophisticated problems, the process of constructing a decision tree can be complicated. Decision trees contain decision points, usually represented by a box or square, where the decision-maker must select one of several available alternatives. Chance points, designated by a circle, indicate that a chance event is expected at this point.

The following three steps are needed to construct a tree diagram:

• Build a logic tree, usually from left to right, including all decision points and chance points.

• Put the probabilities of the states of nature on the branches, thus forming a probability tree.

• Finally, add the conditional payoffs, thus completing the decision tree.

Consider the following problem. You have the chance to make or buy certain widgets for resale. If you make the widgets yourself, you must purchase a new machine for \$35,000. If demand is good, which is expected 70 percent of the time, an \$80,000 profit will occur on the sale of the widgets. With poor market conditions, \$30,000 in profits will occur, not including the cost of the machine. If we subcontract out the work, our contract administration costs will be \$5,000. If the market is good, profits will be \$50,000; for a poor market, profits will be \$15,000. Figure 17-4 shows the tree diagram for this problem. In this case, the expected value of the strategy that subcontracts the widgets is both positive and \$4,500 greater than the strategy that manufactures the widgets. Hence, here we should select the strategy that subcontracts the widgets. 