For MichaelsSolutions Only

These two problems cover the material in Evans Chapter 11 and will require TreePlan/Decision tree. Remember this is a free trial of commercial software that is 30 days long. You can download it here: http://treeplan.com/trial/

#1 A data science company is bidding on a predictive modeling project that, of course, involves uncertainty. Based on past experience, the company developed the following table:

Problems experienced	Minimum	Typical	Worse Case
Project Cost	$1,250,000	$1,450,000	$1,790,000
Associated Probability	0.12	0.69	0.19

Assume that the firm is bidding competitively, and the expectation of successfully gaining the job at a bid of $2.25 million is 0%, at $2.15 million is 10%, at $2.05 million is 20%, at $1.95 million is 030%, at $1.85 million is 50%at $1.75 million is 80%, and at $1.65 million is practically certain.

a. Calculate the expected monetary value for the given bids.

b. What is the best bidding decision?

c. What is the expected value of perfect information?

2# Drilling decisions by oil and gas operators involve intensive capital expenditures made in an environment characterized by limited information and high risk. A well site is dry, wet, or gushing. Historically, 45% of all wells have been dry, 32.5% wet, and 22.5% gushing. The value (net of drilling costs) for each type of well is as follows:

Dry	−$75.000
Wet	$115,000
Gushing	$205,000

Wildcat operators often investigate oil prospects in areas where deposits are thought to exist by making geological and geophysical examinations of the area before obtaining a lease and drilling permit. This often includes recording shock waves from detonations by a seismograph and using a magnetometer to measure the intensity of the Earth’s magnetic effect to detect rock formations below the surface. The cost of doing such studies is approximately $18,000. Of course, one may choose to drill in a location based on “gut feel” and avoid the cost of the study. The geological and geophysical examination classify an area into one of three categories: no structure (NS), which is a bad sign; open structure (OS), which is an “OK” sign; and closed structure (CS), which is hopeful. Historically, 42% of the tests have resulted in NS, 34% resulted in OS, and 24% resulted in CS readings. After the result of the test is known, the company may decide not to drill. The following table shows probabilities that the well will actually be dry, wet, or gushing based on the classification provided by the examination (in essence, the examination cannot accurately predict the actual event):

	Dry	Wet	Gushing
NS	0.716	0.204	0.080
OS	0.445	0.379	0.176
CS	0.234	0.370	0.396

a. Construct a decision tree of this problem that includes the decision of whether or not to perform the geological tests.

b. What is the optimal decision under expected value when no experimentation is conducted?

c. Find the overall optimal strategy by rolling back the tree.