Data analytics/ Decision Analysis

Question 1

1.Clearly dealing with artifacts can be very costly for Reliable Construction. It is known from experience that about 30% of building sites in this area contain special artifacts. Fortunately, they can purchase an insurance policy – a quite expensive insurance policy. The insurance policy costs $500000 ($.5 million), but it covers all fines and penalties for delays in the event that special artifacts are found that require remediation. Effectively, this means that Reliable could expect the same profit they would get without insurance (minus the cost of the policy).

Given the estimated profit without artifacts, the estimated profit with artifacts, the cost of insurance, the 30% likelihood of finding artifacts, create a payoff table and determine what decision Reliable should make. Their decision should use as much information as is available. You should use round the simulated costs to nearest $100,000 and use units of millions of dollars so that, for example, $8,675,309 is 8.7 million dollars.

Provide appropriate evidence for the best decision such as a payoff table or picture of a suitable (small) decision tree.

Question 2

Clearly dealing with artifacts can be very costly for Reliable Construction. It is known from past experience that about 30% of building sites in this area contain special artifacts. Fortunately, they can purchase an insurance policy – a quite expensive insurance policy. The insurance policy costs $500000 ($.5 million), but it covers all fines and penalties for delays in the event that special artifacts are found that require remediation. Effectively, this means that Reliable could expect the same profit they would get without insurance (minus the cost of the policy).

Given the estimated profit without artifacts, the estimated profit with artifacts, the cost of insurance, the 30% likelihood of finding artifacts, create a payoff table and determine what decision Reliable should make. Their decision should use as much information as is available. You should use round the simulated costs to nearest $100,000 and use units of millions of dollars so that, for example, $8,675,309 is 8.7 million dollars.

Provide appropriate evidence for the best decision such as a payoff table or picture of a suitable (small) decision tree.

1.What is the expected payoff?

2.Should Reliable Construction purchase insurance?

Question 3

Posterior Probabilities and Full Decision Tree

Reliable has been contacted by an archeological consulting firm. They assess sites and predict whether special artifacts are present. They have a pretty solid track record of being right when artifacts are present – they get it right about 86% of the time. Their track record is less great when they there are no artifacts. They’re right about 72% of the time.

Find the posterior probabilities for this decision tree, given the this prior information.

1.What is the posterior probability of artifacts, given artifacts were predicted?

2.What is the posterior probability of no artifacts, given no artifacts were predicted?

Question 4: Create a Full Decision Tree

The consulting fee for the site in question is $50,000 ($.05 million).

Construct a decision tree to help Reliable decide if they should hire the consulting firm or not and if they should buy insurance or not. Again, you should round the simulated costs to nearest $100,000 and use units of millions of dollars (e.g., 3.8 million dollars) in your decision tree.

Include a picture of the tree exported from Silver Decisions.

25

Question 5: What is the best course of action for Reliable?

• Don’t hire firm. Buy insurance.
• Don’t hire firm. Don’t by insurance.
• Hire firm. Don’t buy insurance no matter what they predict.
• Hire firm. Buy insurance no matter what they predict.
• Hire firm. Buy insurance if they predict artifacts. Don’t buy insurance if they don’t predict artifacts.

Question 6: What is the expected payoff?

Question 7.

How confident are you in your decision? What could you do to increase your confidence?