MRSQ1153-DECISION ANALYSIS FOR
PROFESSIONALS
LECTURER: DR. RUZANA BINTI ISHAK
FTIR, UTMKL
EMAIL: ruzana.kl@utm.my
Contact: 0122982650
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Module 3
DECISION ANALYSIS –
MULTISTAGE DECISION
PROBLEMS
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Multi-stage Decision Problems
◆ Many problems involve a series of decisions
◆ Example
• - Should you go out to dinner tonight?
• - If so,
•
How much will you spend?
•
Where will you go?
•
How will you get there?
◆ Multi-stage decisions can be analyzed using
decision trees
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Multi-Stage Decision Example: COM-TECH
◆ Steve Hinton, owner of COM-TECH, is
considering whether or not to apply for a
$85,000 OSHA research grant for using
wireless communications technology to
enhance safety in the coal industry.
◆ Steve would spend approximately $5,000
preparing the grant proposal and estimates a
50-50 chance of actually receiving the grant.
◆ If awarded the grant, Steve would then need
to decide whether to use microwave, cellular,
or infrared communications technology.
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COM-TECH (continued
•Steve would need to acquire some new
equipment depending on which technology is
used. The cost of the equipment is
summarized as:
•Steve knows he will also spend money in
R&D, but he doesn't know exactly what the
R&D costs will be.
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COM-TECH (continued
•Steve estimates the following best case and
worst case R&D costs and probabilities,
based on his expertise in each area.
•◆ Steve needs to synthesize all the factors in
this problem to decide whether or not to
submit a grant proposal to OSHA.
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COM-TECH (continued
•The immediate decision in this example
problem is whether or not to submit a grant
proposal.
•To make this decision, Steve must also
consider the technology selection decision
that he will face if he receives the grant.
•So, this is a multistage decision problem.
Figure 3-1 shows the decision tree
representation of this problem
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Figure 3-1
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• According to this decision tree, Steve should submit a
proposal because the expected value of this decision is
$13,500 and the expected value of not submitting a proposal
is $0.
• The decision tree also indicates that if Steve receives the
grant, he should pursue the infrared communications
technology because the expected value of this decision
($32,000) is larger than the expected values for the other
technologies.
• In Figure 3-1, note that the probabilities on the branches at
any event node must always sum to 1 because these branches
represent all the events that could occur.
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• The R&D costs that would actually occur using a given
technology could assume an infinite number of values.
• Some might argue that these costs could be modeled more
accurately by some continuous random variable.
• However, our aim is to estimate the expected value of this
random variable.
• Most decision makers probably would find it easier to assign
subjective probabilities to a small, discrete set of
representative outcomes for a variable such as R&D costs
rather than try to identify an appropriate probability
distribution for this variable.
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Analyzing Risk in a Decision Tree
◆ How sensitive is the decision in the COMTECH problem to changes in the probability
estimates?
◆We can use Solver to determine the smallest
probability of receiving the grant for which
Steve should still be willing to submit the
proposal.
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Risk Profiles
• A risk profile summarizes the make-up of an EMV.
• The $13,500 EMV for COM-TECH was created as follows:
• This can also be summarized in a decision tree.
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A risk profile for the alternatives of
submitting or not submitting the proposal
Figure 3-1
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