An oil company must decide whether or not to drill an oil well in a particular area that they already own. The decision maker (DM) believes that the area could be dry , reasonably good or a bonanza. See data in the table which shows the gross revenues for the oil well that is found.
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Decision
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Dry (D)
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Reasonably Good(G)
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Bonanza(B)
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Drill
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$0
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$85
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$200m
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Abandon
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$0
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$0
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$0
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Probability
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0.3
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0.3
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0.4
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Drilling costs 40M. The company can take a series of seismic soundings ( at a cost of 12M) to determine the underlying geological structure. The results will be either "no structure", "open structure or "closed structure". The reliability of the testing company is as follows that is, this reflects their historical performance .
otherwise (for the other results) it can abandon the drilling idea at no benefit to itself.
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Conditional Probability for a given state of nature
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|
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Seismic Results
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Dry (d)
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Reasonably good (g)
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Bonanza (b)
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No structure (N)
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0.7
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0.3
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0.1
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Open (O)
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0.2
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0.3
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0.4
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Closed (C)
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0.1
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0.4
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0.5
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That is P (N/D) =0.7; P (O/G) =0.3, P(C/B) =0.5
After you have computed the revised probabilities round to two decimal places
a) Construct the appropriate decision tree to help the oil company make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs. It also includes the revised probabilities
b) Fold back the decision tree to determine the best strategy for the company;
you must state this strategy. What is the final expected profit?
c) What is the expected value of sample information(EVSI)- the most that should be paid to seismic testing firm for the test?
d) Calculate the expected value of perfect information (EVPI)- the most that should be paid to an expert for perfect prediction of the uncertain outcomes.
e) What is the efficiency of sample information?
The revised outcome(probabilities) from the drilling branch are (d/n),g/n.b/n), (d/o,g/o,b/o) and (d/c,g/c,b/c).