As the lead engineer in an automotive company, you need to make a critical decision: whether to “outsource” the design and maintenance of your powertrain or to keep that responsibility “in-house”. While making that decision, there is uncertainty associated with how often the powertrains will fail: either “rare” or “often”. • If you decide to outsource the design and maintenance, you pay a fixed contract rate of $20M to an external company, which delivers the design and takes the responsibility of the maintenance service under a warranty regardless of how often the vehicle powertrain fails. • If you decide to keep the design and maintenance “in-house”, your company must decide whether to use the “existing design” with minimal changes or to invest on a “new design”. o The existing design is difficult to maintain and cheap to develop. If the failures occur often, it will cost $25M in the long run for the design and maintenance, and if the failures are rare, it will cost $15M. The new design will be easier to maintain but costly to develop. If the failures are often, it will cost $23M in the long run; and if the failures are rare, it will cost $16M. Based on your rough estimates, the failures will be often with a probability of 0.4, and it will be rare with a probability of 0.6. a) Create a decision tree diagram based on the information above. Show decision nodes, chance nodes, probabilities and the payoffs (costs). b) Find the expected payoffs of each decision and determine the most rational decision out these two options (outsource or in-house). If you decide to keep it in- house, specify whether to use the existing design or the new design. Show your work. c) Find the maximum amount you should pay to obtain perfect forecasts about the failure rates in the future, i.e., find the expected value of perfect information.

As the lead engineer in an automotive company, you need to make a critical
decision: whether to “outsource” the design and maintenance of your powertrain or to
keep that responsibility “in-house”. While making that decision, there is uncertainty
associated with how often the powertrains will fail: either “rare” or “often”.
• If you decide to outsource the design and maintenance, you pay a fixed contract
rate of $20M to an external company, which delivers the design and takes the
responsibility of the maintenance service under a warranty regardless of how
often the vehicle powertrain fails.
• If you decide to keep the design and maintenance “in-house”, your company must
decide whether to use the “existing design” with minimal changes or to invest on a
“new design”.
o The existing design is difficult to maintain and cheap to develop. If the
failures occur often, it will cost $25M in the long run for the design and
maintenance, and if the failures are rare, it will cost $15M. The new design
will be easier to maintain but costly to develop. If the failures are often, it
will cost $23M in the long run; and if the failures are rare, it will cost $16M.

Based on your rough estimates, the failures will be often with a probability of 0.4, and it
will be rare with a probability of 0.6.

a) Create a decision tree diagram based on the information above. Show
decision nodes, chance nodes, probabilities and the payoffs (costs).

b) Find the expected payoffs of each decision and determine the most rational
decision out these two options (outsource or in-house). If you decide to keep it in-
house, specify whether to use the existing design or the new design. Show your
work.

c) Find the maximum amount you should pay to obtain perfect forecasts about
the failure rates in the future, i.e., find the expected value of perfect information.