Question : Decision Analysis

Alisha is a second-year master's student who is very concerned with the environment. She decided to lease a hybrid car for 3 years. The car she wants is available from only one dealer in Wollongong, but that dealer can offer three leasing options to match with different driving habits. All three leasing options require no money at the time of signing the lease. Alisha has estimated that the average total mileage could be 20,000 or 30,000 miles per year. Leasing option 1 has a monthly cost of $950 if Alisha drives about 20,000 km per year, and $1,050 if she drives 30,000 km per year. Leasing option 2 has a monthly cost of $850 if Alisha drives about 20,000 km per year, and $1,100 if she drives 30,000 km per year. Finally, leasing option 3 has a monthly cost of $700 if Alisha drives about 20,000 km per year, and $1,000 if she drives 30,000 km per year. Alisha estimates that the probability that she drives about 20,000 km is 30% and that the probability that she drives 30,000 km is 70%.

1. Develop a payoff (cost) table (decision table) for Alisha's situation.

2. What decision would Alisha make if she were optimistic?

3. What decision would Alisha make if she were pessimistic?

4. What decision would Alisha make if she wanted to minimise her expected cost (monetary value)?

5. Calculate the expected value of perfect information for Alisha's problem.