Analyze Example 15-9 based on the most probable criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example?

Example 15-9

In this example, the basic decision task is extended to several decisions. The decision tree is shown in Fig. 15-26. The first decision is whether to develop a new product or contract with a supplier. This is indicated by the box labeled Develop?If a new product is developed, it may be unique, but it may be more typical of what is currently available on the market. This is indicated by the circle labeled Unique? For either a new product or a contracted one, the price needs to be set. Here the decision is indicated by Price?boxes. The choices are either high or low. Finally, the market conditions when the product is available may be favorable or unfavorable to sales as indicated by the circle labeled Sales. Favorable and unfavorable markets are indicated by the arcs labeled + and –, respectively.
The probability of an arc is denoted by the number below it. For example, the probability that a unique product is developed is 0.7. Similarly, the probabilities of favorable or unfavorable markets are shown with the corresponding probabilities. Note that a lower price decision leads to the higher probability of a favorable market. Furthermore, the dollar amount shown in the figure indicates the profit to the corporation for the corresponding path through the decision tree. As mentioned previously, one might base a decision on profits (more generally, gains) rather than costs. In such a case, the objective is to maximize profits.

We can extend the procedure for a single decision node as follows. Start with the dollar amounts at the terminal nodes and work backward through the tree to evaluate a decision based on one of the criteria. Because we work with profits in this example, the pessimistic approach is to select the decision to maximize the minimum profit. For example, suppose that a new product is developed, the result is unique, and the price is set high. The two possible dollar values are $6M and $2M. The pessimistic approach is to value the decision to set the price high in this path as $2M. Similarly, the decision to set the price low is valued at $3M. Consequently, the decision along this path is to set the price low with a worst-case profit of $3M.

Similarly, suppose that a new product is developed, the result is not unique, and the price is set high. The two possible dollar values are $3M and $1M. The pessimistic approach is to value the decision to set the price high in this path as $1M. The decision to set the price low is pessimistically valued at $2M. Consequently, the decision to develop a new product can result in a unique product (which is pessimistically evaluated as $2M with probability 0.7) or a nonunique product (which is pes-simistically evaluated at $1M). The pessimistic view is that the decision to develop a new product generates a profit of $1M.

Furthermore, suppose that the product is not developed (but contracted) and the price is set high with the pessimistic profit of $1M. If the price is set low, the pessimistic profit is $1.5M. Consequently, the price decision based on this criterion is to set the price low with a pessimistic profit of $1.5M. Finally, the pessimistic profit from the decision to develop or not develop a new product is $1M and $1.5M, respectively. Therefore, based on this criterion, a new product is not developed.

Note that the probabilities do not enter into this decision. This was mentioned previously as one of the disadvantages of the pessimistic criterion. Alternative criteria are left as exercises.