Question

1-ArmaCo must determine whether or not to drill for oil at the Northern part of Jubail. It costs $100,000 to drill, and if oil is found, the value is estimated to be $600,000. At present, ArmaCo believes there is a 45% chance that the field contains oil with the profit payoffs give in the table below. Alternatives State of Nature Oil Dry Drill 500 –100 No Drill 0 0 a. [0.5 Mark] Show the decision tree for the situation. b. Which alternative should the Armaco choose using: i. [1 Mark] the optimistic approach ii. [1 Mark] the conservative approach iii. [1 Mark] the minimax regret approach. c. [1 Mark] Determine which alternative should be chosen based on expected value. d. [1 Mark] Determine the expected value with perfect information. e. [1 Mark] Determine the expected value of the perfect information.

2-Before drilling, ArmaCo can hire (for $10,000) a geologist to obtain more information about the likelihood that the field will contain oil. There is a 50% chance that the geologist will issue a favorable report and a 50% chance of an unfavorable report. Given a favorable report, there is an 80% chance that the field contains oil. Given an unfavorable report, there is a 10% chance that the field contains oil. f. [1 Mark] Show the decision tree for the situation. g. [1 Mark] Determine ArmaCo’s optimal course of action. h. [0.5 Mark] How much is the expected profit? i. [1 Mark] Determine the Expected Value of Sample Information.

Answer 1

Q1.

a) Decision tree is as follows:

Payoffs are in $ 1000

Expected Value of Drill = 500*0.45+(-100)*0.55 = 170

Expected Value of No Drill = 0

Expected Value of Drill is higher. Therefore, best decision is Drill

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b)

i) Using optimistic approach, alternative whose maximum payoff is the maximum, is preferred.

Maximum payoff of Drill is the maximum.

Therefore, best decision is Drill

ii) Using conservative approach, alternative minimum payoff is the maximum, is preferred.

Minimum payoff of Drill -100 and Minimum payoff of No Drill is 0 .

Minimum payoff of No Drill is the maximum.

Therefore, best decision is No Drill

iii) Using minimax regret approach, decision whose Maximum regret is the minimum, is preferred.

Regret for each decision for each state of nature = MAX payoff for that state of nature - Payoff for given decision for that state of nature

Resulting regret table is following:

Maximum regret for Drill = 100

Maximum regret for No Drill = 500

Minimum of the above is 100, pertaining to Drill.

Therefore, best decision is Drill

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c)

Expected Value of Drill = 500*0.45+(-100)*0.55 = 170

Expected Value of No Drill = 0

Expected Value of Drill is higher. Therefore, using Expected Value approach, best decision is Drill

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d)

Expected Value with Perfect Information, EVwPI = MAX(500,100)*0.45+MAX(-100,0)*0.55

= 225

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e)

Expected Value without Perfect Information, EVw/oPI = Maximum EV

= 170 (as computed in part a and c)

Expected Value of Perfect Information, EVPI = EVwPI - EVw/oPI

= 225 - 170

= 55