2.4.1 Construct a new decision tree

Begin the revised decision tree at the left and through the first chance event nodes as in the prior version. The results for the motion detector and no project remain unchanged.

The chance node for the successful development of the smoke and fire detector can now lead to a new decision node; represent this new decision node with a small square. The decision at this node is whether to submit an application for the UL safety certification. There are only two choices possible: submit an application, at an investment of $5,000, or do not submit an application. You may guess that failure to submit the application after successful project development does not make good sense, and that is correct. The decision tree shows that your guess is correct. You “resolve” decision nodes in terms of the branch with the highest EV. Therefore a “failure to submit application” branch does not play a role in the value of its decision node.

The “submit application” path leads to one of three possible outcomes: commercial grade, residential grade, or no certification. The probability of each outcome is 0.3, 0.6, and 0.1 respectively. Write these probabilities on their respective branches.

The commercial grade outcome terminates with a payoff calculated as follows:
revenue + development cost + application cost =
$1,000,000 + (-$100,000) + (-$5,000) = $895,000.

In a similar way, the residential grade outcome terminates with this payoff:
$800,000 + (-$100,000) + (-$5,000) = $695,000.

If the device does not earn a certification it cannot be sold with a UL certification. This situation dooms its marketing prospects to no revenue and a loss of the investments. In that case:
$0 + (-$100,000) + (-$5,000) = (-$105,000), a loss.

Write each payoff near the matching endpont as you calculate its value, as shown in figure 2.4.1.

Fig 2.4.1

2_4_1



This is an example of a sequential decision. The original root decision leads to at least one other decision on some branch path. The second decision leads to further chance events. Add decision nodes representing how they must occur in time on a branch path. A decision tree can help you keep track of many such sequential decisions.

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