Decision Models. An oil company has some land that is reported to possibly conta
ID: 379114 • Letter: D
Question
Decision Models. An oil company has some land that is reported to possibly contain oil. The company classifies such land into four categories by the total number of barrels that are expected to be obtained from the well, i.e. a 500,000 – barrel well, 200,000 – barrel well, 50,000 – barrel well, and a dry well. The company is faced with deciding whether to drill for oil, to unconditionally lease the land or to conditionally lease the land at a rate depending upon oil strike. With considerations of the cost of drilling the well and the (un)conditional lease agreement, the pay-off table is given below:
In case of making decisions under risk, the probability for striking a 500,000 – barrel well is 0.2, probability for striking a 200,000 – barrel well is 0.3, probability for striking a 50,000 – barrel well is 0.1, and probability for a dry well is 0.4.
Payoff Table
States of Nature
Probability
0.2
0.3
0.1
0.4
Decision
500K Barrel Well
200K Barrel Well
50K Barrel Well
Dry Well
1. Drilling
-100
-50
20
-40
2. Unconditional Lease
-70
10
-10
0
3. Conditional Lease
-20
-200
10
100
(a) Determine the optimal action based on the Maximin criterion. (3 pts)
(b) Compute the expected monetary value (EMV) for each decision. (3 pts)
(c) Compute the expected value of perfect information (EVPI) and explain the meaning of it in this problem. (4 pts)
States of Nature
Probability
0.2
0.3
0.1
0.4
Decision
500K Barrel Well
200K Barrel Well
50K Barrel Well
Dry Well
1. Drilling
-100
-50
20
-40
2. Unconditional Lease
-70
10
-10
0
3. Conditional Lease
-20
-200
10
100
Explanation / Answer
a. We shall try to understand the maximin criterion as required in the problem. As per this decision making criteria, we need to maximize the mininimum pay-off for each of the alternatives available among the states of nature.
For example, for the alternative, drilling pay-off in different states of nature is given as -100, -50, 20 and -40. So, the minimum among these is -100 which occurs in the first state of nature, i.e.500K barrel well. We shall put these details in a column next to the provided column and call it the 'Min pay-off' for the alternative as shown in the table below.
We repeat this for each of the decision alternative available and write in the last column as shown in bold below.
States of Nature
Probability
0.2
0.3
0.1
0.4
Decision
500K Barrel Well
200K Barrel Well
50K Barrel Well
Dry Well
1. Drilling
-100
-50
20
-40
2. Unconditional Lease
-70
10
-10
0
3. Conditional Lease
-20
-200
10
100
Among the last column, i.e. the minimum pay-off for each of the alternatives, i.e. -100, -70 and -200 the maximum is -70 which occurs in the alternative Unconditional Lease.
Thus by the Maximin criterion, the optimal action is to conditionally lease the land.
b. Expected Monetary Value (EMV) for each decision is the weighted average of pay-offs for each alternative for different states of nature. The weights are the probabilities for each of the state of nature.
So, from the table, let us compute the EMV for each of the decisions
EMV for Drilling = (-100) x (0.2) + (-50) x (0.3) + (20) x (0.1) + (-40) x (0.4) = -49
EMV for unconditional lease = (-70) x (0.2) + (10) x (0.3) + (-10) x (0.1) + (0) x (0.4) = -12
EMV for conditional lease = (-20) x (0.2) + (-200) x (0.3) + (10) x (0.1) + (100) x (0.4) = -23
So, among the EMVs computed, the maximum is -12, so the decision should be to go for unconditional lease.
c. We shall now compute the Expected value of perfect information (EVPI)
EVPI is the maximum amount the decision maker is willing to pay for a perfect information about the states of nature before making the decision to choose the alternative.
EVPI = Expected value if perfect information is available - Expected value without perfect information
also can be written as EVPI = EVwPI - EVwoPI
Expected pay-off without perfect information is the maximum EMV among the EMVs we had computed in earlier problem 'b'.
So EVwoPI = -12.
Let us now compute Expected value with perfect information, i.e. EVwPI
If we have perfect information, we shall choose the best pay-off for each state of nature under different alternatives and multiply with the probability of the particular state of nature.
So, for the 500K barrel well state of nature, max pay-off is -20 (conditional lease)
Similarly, for 200K barrel well state of nature, max pay-off is 10 (unconditional lease)
for 50K barrel well, max pay-off is 20 (drilling) and dry well the max pay-off is 100 (conditional lease)
we shall multiply these maximum pay-offs for different states of nature with their respective probabilities.
So, EVwPI = (-20) x (0.2) + (10) x (0.3) + (20) x (0.1) + (100) x (0.4) = 41
Thus EVPI = EVwPI - EVwoPI = 41 - (-12) = 41 + 12 = 53
Let us understand EVPI in the context of this problem.
EVPI as we defined earlier, is the amount one willing be pay to gain access to perfect information on the states of nature.
So, if anyone is willing to sell the exact probabilities of occurance for the four states of nature to the oil company for an amount less than 53, the company shall pay the quoted price to obtain the information. Here the company will make profit. Suppose the information is available for say 45, then the company can purchase the information and still make an profit of 53 - 45 = 8
However, if the information on probabilities is available for more than 53, the oil company should not take the same as the company will make loss after taking the same information. Suppose, if the data is available for 55, if the company takes the information, the net profit the company is expected to make is 53 - 55 = -2, i.e. the oil company will make loss.
In other case, if the information is available for exactly 53, then the oil company is indifferent of taking the exact information on probabilities or not.
States of Nature
Probability
0.2
0.3
0.1
0.4
Min Pay-offDecision
500K Barrel Well
200K Barrel Well
50K Barrel Well
Dry Well
1. Drilling
-100
-50
20
-40
-1002. Unconditional Lease
-70
10
-10
0
-703. Conditional Lease
-20
-200
10
100
-200Related Questions
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