ISE 562; Dr. Smith
Decision Theory
Decision Theory
Car Part Replacement Case
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ISE 562; Dr. my future son-in-law was faced with the following problem:
Check engine light came on in car (Jetta). It appeared after some checking to be a sensor called the MAF sensor. He asked me, “Should I buy a new one ($400) or take a chance on a used one from a salvage yard that came off another jetta with 18,000 miles on it that cost $100? (He is worried that a salvage part won’t be as reliable as new part.)
Can a decision tree help here?
9/11/2022 2
ISE 562; Dr. are the choices (the actions)?
Buy used part
Buy new part
What are the states of nature (the uncertain outcomes)?
9/11/2022 3
ISE 562; Dr. are the states of nature (the uncertain outcomes)?
Buy used part
Buy new part
Part works
Part does not work
Part works
What are the probabilities of the uncertain outcomes?
9/11/2022 4
ISE 562; Dr. are the probabilities of the uncertain outcomes?
Buy used part
Buy new part
Part works
not work 1-P=.10
Part works
What are the payoffs?
9/11/2022 5
ISE 562; Dr. are the payoffs?
Buy used part
Buy new part
-$100 P=.90
Part does -$100-400=-$500 not work 1-P=.10
Part works
Part works P=1.0
What is the choice that minimizes the cost? Roll
back the expected values…
9/11/2022 6
ISE 562; Dr. are the payoffs?
-100(.90)+-500(.10)= -$140
Buy used part
Buy new part
-400(1.0)= -$400
-$100 P=.90
Part does -$100-400= -$500 not work 1-P=.10
Part works
Part works P=1.0
Buy the used part! Its cheaper.
9/11/2022 7
ISE 562; Dr. what if the probability part works is lower than 0.90?
Part works -$100 -100(.10)+-500(0.90)= -$460
Buy used part
Buy new part
-400(1.0)= -$400
Part does not work
-$500 1-P=.90, .80, .70
P=.10, .20, .30
-100(.20)+-500(0.80)= -$420 -100(.30)+-500(0.70)= -$380
P= break even: -100(P)+-500(1-P)= -$400 P=0.25
Part works P=1.0
What would you do?
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