Nasa has to decide between 3 choice
- Have 0 backup systems
- Fail with probability 0.01 and incur $8,000,000 additional cost
(in addition to production cost)
- success with probability 0.99 and incur $0 additional cost (in
addition to production cost)
- Have 1 backup systems
- Original Fail with probability 0.01
- Backup fails with probability 0.01 and incur $8,000,000+70,000
additional cost (in addition to production cost)
- Backup succeeds with probability 0.99 and incur $70,000
additional cost (in addition to production cost)
- success with probability 0.99 and incur $70,000 additional cost
(in addition to production cost)
- Have 2 backup systems (Cost of 2 backup systems $140,000)
- Original Fail with probability 0.01
- Backup fails with probability 0.01
- The second backup fails with probability 0.01 and incur
$8,000,000+140,000 additional cost (in addition to production
cost)
- The second backup succeeds with probability 0.99 and incur
$140,000 additional cost (in addition to production cost)
- Backup succeeds with probability 0.99 and incur $140,000
additional cost (in addition to production cost)
- success with probability 0.99 and incur $140,000 additional
cost (in addition to production cost)
The decision tree is below
![Original fail with p(f)-0.01 EV-$80,000 Additional Cost-$8,000,000 0 backu systems 2 Original Succeed with probabili P(s) 0.9](//img.homeworklib.com/images/dee471ff-f614-43ca-8e3a-9172382ce980.png?x-oss-process=image/resize,w_560)
Moving from the right to the left
Chance node 7: 2 backup systems
The expected cost is
![EV (7) Probability of failure of 2nd backup × Cost of failure + Probability of success of 2nd backup = 0.01 × 8140000+0.99 ×](//img.homeworklib.com/images/5af3e285-e988-4d73-ac32-aec7a4807290.99%5Ctimes%20140000%5C%5C%20%26%3D%5C%24220%2C000%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
chance node: 6: 2 backup systems
The expected cost is
![Probability of failure of 1st backup × expected cost of failure of 1st backup + Probability of success of 1st backup × Cost o](//img.homeworklib.com/images/12b19900-9bf5-4337-a161-47dc2fa0b690.99%5Ctimes%20140000%5C%5C%20%26%3D%5C%24140%2C800%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
chance node 5: 1 backup system
The expected cost is
![EV(5) Probability of failure of 1st backup x Cost of failure of 1st backup + Probability of success of 1st backup x Cost of s](//img.homeworklib.com/images/03f07813-aad1-403d-812d-d115fcde2f57.99%5Ctimes%2070000%5C%5C%20%26%3D%5C%24150%2C000%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
chance node 2: 0 backups
The expected cost is
![EV 2 Probability of failure of original × Cost of failụre of original + Probability of success of original x Cost of success](//img.homeworklib.com/images/970319f5-864b-4e2c-9398-29eab3b4dc8c.99%5Ctimes%200%5C%5C%20%26%3D%5C%2480%2C000%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
chance node 3: 1 backup
The expected cost is
![EN 3 Probability of failure of original × expected Cost of failure of original Probability of success of original x Cost of s](//img.homeworklib.com/images/9f027c3f-300a-4ecd-bb31-5aa5eb9d7136.99%5Ctimes%2070000%5C%5C%20%26%3D%5C%2470%2C800%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
chance node 4:
The expected cost is
![EN 4 Probability of failure of original × expected Cost of failure of original Probability of success of original x Cost of s](//img.homeworklib.com/images/3470fed0-c959-48cb-8350-66b3bdb1c318.99%5Ctimes%20140000%5C%5C%20%26%3D%5C%24140%2C008%20%5Cend%7Balign*%7D?x-oss-process=image/resize,w_560)
At the decision node 1 NASA has 3 options
- 0 backup systems at an expected total cost of $80,000+Product
cost
- 1 backup system at an expected total cost of $70,800+Product
cost
- 2 backup system sat an expected total cost of $140,008+Product
cost
The lowest expected total cost is when NASA goes for 1 backup
systems
ans: The strategy that minimizes NASA's expected total cost is
to go for 1 backup system.
Original fail with p(f)-0.01 EV-$80,000 Additional Cost-$8,000,000 0 backu systems 2 Original Succeed with probabili P(s) 0.99 First backup fail Additional Cost-$8,070,000 Additional Costcost-$o p(f)-0.01 Original fail with EV-$150,000 p(f) 0.01 First backup succeed with probability p(s)-0.99 1 backup system EV-$70,800 Additional Costcost $70,000 Original Succeed with probability Additional Costcost $70,000 second backup fail Original Succeed with probability p SF0.99 Additional Costcost $140,000 First backup fail p(f) 0.01 Additional Costcost-$8,140,000 p(f)-0.01 EV-$140,008 2 backup EV-$220,000 4 7 second backup succeed with probability P(s)-0.99 Original fail with probability p(f)-0.01 Additional Costcost $140,000 EV $140,800 First backup succeed with probability p(s)-0.99 6 Additional Costcost-$140,000
EV (7) Probability of failure of 2nd backup × Cost of failure + Probability of success of 2nd backup = 0.01 × 8140000+0.99 × 140000 = $220,000 Cost of success
Probability of failure of 1st backup × expected cost of failure of 1st backup + Probability of success of 1st backup × Cost of success = 0.01 × 220000+0.99× 140000 = $140,800 EV 6
EV(5) Probability of failure of 1st backup x Cost of failure of 1st backup + Probability of success of 1st backup x Cost of success = 0.01 × 8070000 + 0.99 × 70000 $150, 000
EV 2 Probability of failure of original × Cost of failụre of original + Probability of success of original x Cost of success 0.01 × 8000000 + 0.99 × 0 = $80、000
EN 3 Probability of failure of original × expected Cost of failure of original Probability of success of original x Cost of success = 0.01 × 150000+0.99 × 70000 $70,800
EN 4 Probability of failure of original × expected Cost of failure of original Probability of success of original x Cost of success = 0.01 × 140800+0.99 × 140000 $140, 008