Activity 8.1
Thursday, September 29, 2022
10:32 AM
The company has three options:
1) License their designs to chip manufacturers (I will refer to this by 'Licensing')
2) Manufacture and sell chips based on their design (I will refer to this by 'Manufacturing')
3) Do nothing
So, we can build already part of the tree.
There is also one distinction: the yield of the manufacturing facility. This may be:
1) Low
2) Moderate
3) High
This can be represented as follows:
Now, let's figure out how this distinction relates to the decision. Yield is relevant to manufacturing.
Therefore, such a distinction will only materialize in the context of the Manufacturing alternative. It will
not be relevant if the company decides to license their designs or to do nothing. The decision tree looks
then like this:
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Once I have the tree structure in place, I start to characterize its branches. I start by the elements that
contribute to the outcomes that are associated with the fundamental value to the decision maker. While
the objective is not specified in the problem statement, I am going to assume that it is profit, given that
this is a private company.
There are two elements contributing to profit in the problem statement: investment costs and revenue.
I use the figures in the problem statement to characterize each branch. The tree results as follows:
The only other thing that I need to evaluate the expected value of each alternative is to characterize the
likelihood of each possibility of the yield distinction. These numbers are directly given in the problem
statement. The tree looks then like this:
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Note that I have not calculated the final outcome of each decision path. This is because it is unnecessary
if we are using expected value to inform the decision. I calculate now the e -value (expected value) of
each alternative:
Therefore, licensing is the best option. These values can be added to the tree and the two paths not
selected are crossed off the tree:
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Activity 8.2
Thursday, September 29, 2022
10:51 AM
I will take a more direct approach to solve this problem, focusing on the things that may be confusing.
The problem presents a decision with three alternatives:
1) Build a 3 m high cofferdam.
2) Build a 4.5 m high cofferdam.
3) Do not build any cofferdam.
There is one distinction defined in the problem: whether a flooding will occur or not. Is this distinction
relevant to the decision? Yes, because Mary wants to minimize cost and flooding results in cost. Is this
distinction relevant to each alternative? Yes, because the likelihood of flooding depends on the height of
the cofferdam.
The key issue here is to recognize that the relationship between height, river's flow, and flooding can be
modeled as a single decision and a single distinction. This is because there is (in the problem statement)
a deterministic relationship between river's flow and flooding. That is, in the first case, if flow exceeds
200 m3/s, then there is flooding. So both events can be considered as the same event:
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And, because flow does not "really" matter, but it is flooding which has the impact on cost, the
distinction can be just formulated on the basis of flooding.
The structure of the decision tree would look as follows:
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Because Mary cares about cost, from the problem statement I can characterize the impact on cost that
each alternative has, as well as each possibility in the flooding distinction:
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And, finally, we incorporate the likelihood of each possibility. These are given directly in the statement,
as Mary is frequentist. Furthermore, per the numbers, it is clear that there is relevance between
cofferdam height and flooding. However, the problem does not provide any information about the
likelihood of flooding for no cofferdam. Let's assign a value of x to the probability of flooding if there is
no cofferdam. The tree would look like this:
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And let's compute the expected value of each alternative:
Most people solving this problem would not identify the alternative to not build any cofferdam. Most
engineers always have the urge to do something! If that is the case, then the 4.5 m high cofferdam is the
best alternative because it has the highest expected value.
However, how do we evaluate the option to not build a dam at all if we do not have information about
the likelihood of flooding for such a case? We can do some sensitivity analysis. See how, assuming a
worst case scenario in which a flooding is guaranteed in the case of not building a cofferdam, x =1 and
the worst-case expected value of such an alternative is -$30K… which is better than the other two
alternatives!
Hence, the correct recommendation in this case is to not build a cofferdam:
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Activity 8.3
Thursday, September 29, 2022
11:16 AM
This problem does not really have any special complication with respect to previous problems, other
than the size of the tree. The solution is directly represented below:
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(Note: I have drawn this with a computer tool that we will be using in class right after the mid-term
exam.)
Using the tree, let me point to a few aspects that are important:
1) Note that the distinction in the top of the tree could have been not represented, since the
outcome is deterministic. Instead, the value of the success of the crop could have been added to
the path.
2) The alternatives can be represented as three decision points with different alternatives, or
condense them as one decision point with 9 alternatives. In such a case, each alternative is
characterize by the sum of the impact of each element in the alternative. This is shown below,
including the removal of the distinction for one of them.
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