Decision Analysis Lecture 9

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Decision Analysis - Lecture 9

• Gilbert Gilbert
• Value of information
• EVPI
• EVSI
• Efficiency of sample information
• Dominance, utility and risk

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EVPI

• What if you knew that you would have perfect
  information about a state of nature before you
  had to make a decision?
• Then you would have a new tree with a state of
  nature node before the decision nodes.

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EVPI

• The EMV of this new tree is called the Expected
  profit with perfect prediction
• The difference between the expected profit with
  perfect prediction and the EMV of the old tree is
  called the Expected Value of Perfect Information
  (EVPI)

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Stocking Example EVPI
545
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Stocking Example EVPI

• Expected profit with perfect prediction
• Old EMV
• EVPI
• What does this mean?

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EVSI

• What if you knew you could get some sample
  information (for example a market research
  study) about the state of nature before you had
  to make a decision?
• Then your new tree would have a new state of
  nature node at the beginning in front of the
  decision node in addition to the current state of
  nature nodes.

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EVSI

• Also the probabilities on the old state of nature
  nodes are changed and are dependent on the sample
  information.
• The difference between the EMV of the new tree
  and the old EMV is the Expected Value of Sample
  Information (EVSI)

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Stocking Example EVSI

• Suppose that the demand probabilities are
  dependent on last periods demand

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Stocking Example EVSI
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Stocking Example detail
500
500
473
424
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Stocking Example EVSI
500
520.8
528
541.33
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Stocking Example EVSI

• Expected profit with sample information
• Old EMV
• EVSI
• What does this mean?

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EVSI

• The sample information captures part of the extra
  profits that were possible with perfect
  information.
• The better the sample information (I.e. the more
  precisely the sample information is able to
  predict the state of nature) the closer the EVSI
  will be to the EVPI.

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How good is the sample info?

• A quick measure is EVSI / EVPI
• This is called the efficiency of the sample
  information.
• In our stocking example, the efficiency of last
  periods information is .
• So about of all the possible value of
  information is being captured by the sample
  information

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Trains

• A company that operates metro trains must decide
  whether to extend one of their lines.
• They estimate that customer demand has a 0.4
  chance of being high, 0.5 of being moderate and
  0.1 of being low.
• The cost of extending the line is 3.5 million to
  the company (part of the costs will be borne by
  the state government)

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Trains

• The estimated present value of revenues if
  customer demand is high is 5 million, if demand
  is moderate then 3 million and if low then 2
  million.
• Should the company extend the line? What is the
  EMV? What is the EVPI for demand information?

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Trains

• Suppose a market research company is approached
  about undertaking a study to determine likely
  customer demand.
• The company indicates that their research is
  usually right about 80 of the time.
• Assume, if theyre wrong, probabilities are
  equally distributed between the other two options.

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Trains

• Before the study is done, the best estimate there
  is of what the research will predict is that
  there is a 0.4 chance that it will predict high
  demand, 0.5 chance that it will predict moderate
  demand and 0.1 chance that it will predict low
  demand.

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Trains

• What is the EVSI?
• The company would charge 250,000 to carry out
  the study.
• Is it worth commissioning the market research
  study?
• What is the efficiency of the market research
  information?

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Dominance

• Outcome dominance
• Event dominance
• Probabilistic dominance

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Outcome Dominance

• If a decision options worst outcome is as good
  as the best outcome for any other decision, the
  option is outcome dominant

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Event Dominance

• If a decision option has outcomes that are each
  as good as the outcomes for the same states of
  nature of any other decision, the option is event
  dominant.

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Probabilistic Dominance

• For probabilistic dominance, all outcomes are
  ordered from lowest to highest. For each option
  the probability of achieving at least each
  outcome is determined. If a decision always has a
  higher (cumulative) probability of achieving
  every outcome then it is probabilistically
  dominant.

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Dominance

• Why use ideas of dominance?
• Quick way to find best options
• Way of narrowing down decisions by eliminating
  worst options
• Leads to idea of risk profile

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Risk Profiles

• Can draw a graph of cumulative probabilities
  (same ones that are in the table for
  probabilistic dominance) for different decision
  options.
• These are commonly called risk profiles.

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Utility

• What is Utility?

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Which would you rather have?

• 200 for sure or 50 chance of 1000 and 50
  chance of nothing?
• 400 for sure or 50 chance of 1000 and 50
  chance of nothing?
• 500 for sure or 50 chance of 1000 and 50
  chance of nothing?
• 600 for sure or 50 chance of 1000 and 50
  chance of nothing?

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Utility

• Answering these questions helps to determine your
  personal utility for money
• You can now draw your own utility curve

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Risk preferences

• When might you be risk averse?
• When might you be risk seeking?
• What does utility have to do with risk
  preferences?
• How can you use utility in decision trees?

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Next lecture

• Read texts
• Read and prepare St Swithins
• Remember syndicate projects are due next week
  please email them to me before class