Question

The senior executives of an oil company are trying to decide whether or not to drill for oil in a particular field in the Gulf of Mexico. It costs the company $1,000,000 to drill in the selected field. Company executives believe that if oil is found in this field its estimated value will be $4,000,000. At present, this oil company believes there is a 45% chance that the selected field actually contains oil. Before drilling, the company can hire a geologist at a cost of $60,000 to prepare a report that contains a recommendation regarding drillin in the selected field. In many similar situations in the past where this geologist has been hired, the geologist has predicted oil on 75% of all fields that have contained oil, and has predicted no oil on 85% of all fields that have not contained oil.

B. First consider the case when hiring the geologist is not an option. Should the company drill for oil?

1. Construct a decision table to represent this problem. Also, construct the regret table.

2. Using an EXCEL spread sheet determine:

a. What should the company do if senior management:

i. is risk prone (optimistic)?

ii. is risk averse (pessimistic)?

iii. wants to maximize his average amount of money it makes?

b. What is the expected value of perfect information (of whether or not oil is really there)?

C. Now consider the case when hiring the geologist is an option. What should the company do?

2. Draw the decision tree for this problem. Include all of the final payoffs.

3. Compute the probabilities needed to solve the decision tree? (Hint – there are prior, test and posterior probabilities.)

4. Solve the tree for the decision strategy that maximizes the average profit for the company. Clearly indicate what action he should take at each decision point.

Answer 1

PART B. when hiring geologist is not an option

1) Decision table and regret table are following

2) (i) Under optimistic approach, the management should Drill, because its maximum payoff is 3 (=4 - 1) , which is the maximum payoff of both the alternatives (Drill, Don't drill)

(ii) Under pessimistic approach, the management should Not Drill, because its minimum payoff is 0, which is the higher of the minimum payoff of both alternatives. (minimum payoff of Drill is -1)

(iii) Average payoff of Drill = (3+(-1))/2 = 1

Average payoff of Do not drill = 0

Average payoff of Drill is higher. Therefore, management should Drill

b) Under perfect information, management should Drill, if there is information of presence of oil, otherwise should not drill. Therefore, Expected Value with perfect information (EVwPI)= 0.45*3 + 0.55*0 = 1.35

Expected Value without Perfect Information EV(w/o)PI = 0.45*3 + 0.55*(-1) = 0.80

Expected Value of Perfect Information (EVPI) = EVwPI - EV(w/o)PI = 1.35 - 0.80 = $ 0.55 m

PART C. when hiring geologist is an option

3) Calculate posterior probabilities

2) Decision tree is constructed using the posterior probabilities as under

4) Expected Value (EV) of node 2 = 0.45*4 + 0.55*0 - 1 = 0.8

Expected Value (EV) of node 6 = 0.8036*4 + 0.1964*0 - 1 = 2.214

Expected Value (EV) of node 7 = 0.1940*4 + 0.8060*0 - 1 = -0.224

Expected Value (EV) of node 4 = MAX(2.214, 0) = 2.214

Expected Value (EV) of node 5 = MAX(-0.224, 0) = 0

Expected Value (EV) of node 3 = 0.42*2.214 + 0.58*0 - 0.06 = 0.87

Expected Value (EV) of node 1 = MAX(0.8, 0.87) = 0.87

Recommendation action: EV of hire geologist is higher. Therefore management should hire the geologist and if there is prediction of oil, then they should Drill, otherwise not.

Expected payoff of this strategy = $ 0.87 m