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How to construct a decision tree

How to construct a decision tree. List each decision nodes & its alternatives. List each chances nodes& its alternatives. Draw the nodes and links. Add costs & probabilities along links Calculate utilities for utility (leftmost) nodes Calculate expected utilities. Example.

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How to construct a decision tree

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  1. How to construct a decision tree • List each decision nodes & its alternatives. • List each chances nodes& its alternatives. • Draw the nodes and links. • Add costs & probabilities along links • Calculate utilities for utility (leftmost) nodes • Calculate expected utilities

  2. Example • You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do?

  3. 1. List each decision nodes & its alternatives. • Which project? • Fancy • Mundane You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do?

  4. 2. List each chance nodes & its alternatives. • Outcome? • Success • Failure You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do?

  5. 3. Draw nodes as tree You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? Success Outcome? Outcome? Failure Fancy Project? Mundane Success Utility nodes are like diamonds Decision nodes are square Failure Chance nodes are oval

  6. 4. Add costs and probabilities to links You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? Successp=0.1 Outcome? Outcome? Failurep= 0.9 Fancycost 1M$ Project? Mundanecost 0.5M$ Success p=0.8 Failurep=0.2

  7. 5. Calculate utility values for utility nodes You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? Benefit: 11M$ Cost: 1M$ Successp=0.1 -0.5M$ -1M$ 10M$ 1M$ Outcome? Outcome? Failurep= 0.9 Fancycost 1M$ Project? Mundanecost 0.5M$ Success p=0.8 Benefit: 0 Cost: 0.5M$ Failurep=0.2

  8. 6. Calculate expected utilities, moving leftward You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? EU = 0.1*10=1.0 Successp=0.1 -0.5M$ -1M$ 10M$ 1M$ EU = 0.9*(-1)=-0.9 Outcome? Outcome? Failurep= 0.9 Fancycost 1M$ Project? EU = 0.8*1=0.8 Mundanecost 0.5M$ Success p=0.8 EU = 0.2*(-0.5)=-0.1 Failurep=0.2

  9. 6. Calculate expected utilities moving leftward You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? EU = 0.1*10=1.0 EU = 1.0-0.9= 0.1 Successp=0.1 -0.5M$ -1M$ 10M$ 1M$ EU = 0.9*(-1)=-0.9 Outcome? Outcome? Failurep= 0.9 Fancycost 1M$ Project? EU = 0.8*1=0.8 EU = 0.8-0.1=0.7 Mundanecost 0.5M$ Success p=0.8 EU = 0.2*(-0.5)=-0.1 Failurep=0.2

  10. 6. Calculate expected utilities moving leftward You need to decide whether to do a fancy project or a mundane project. Either project can succeed or fail. There is a 10% chance of success for the fancy project, and 80% chance of success for the mundane project. The fancy project costs 1M$ to execute, and if it succeeds, you get 11M$. If you lose, you get nothing. The mundane project costs 0.5M$ to execute, and you get 1.5M$ if it succeeds. If it fails, you get nothing. Which project should you do? EU = 0.1*10=1.0 EU = 1.0-0.9= 0.1 Successp=0.1 -0.5M$ -1M$ 10M$ 1M$ EU = 0.9*(-1)=-0.9 Outcome? Outcome? Failurep= 0.9 Fancycost 1M$ Project? EU = 0.8*1=0.8 EU = 0.8-0.1=0.7 Mundanecost 0.5M$ Success p=0.8 EU = 0.2*(-0.5)=-0.1 Best choice Failurep=0.2

  11. A more complex example • Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do?

  12. 1. List each decision nodes & its alternatives. • Which treatment? • surgery • chemo • Nothing • After chemo fails, which treatment? • surgery • nothing Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do?

  13. 2. List each chance nodes & its alternatives. • Outcome? • Cancer cured • Died due to surgery (only for surgery node) • Cancer not cured Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do?

  14. 3. Draw nodes • Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do? Cured Die uncured Live Die? Outcome? Die? Outcome? Outcome? Outcome? Surgery Surgery kills Treatment? chemo Cured ? Surgery Nothingcost 0$ Uncured Treatment? Die Die Nothing Live Live

  15. 4. Add costs & probabilities • Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do? Curedp=0.4 Diep=0.9 uncuredp=0.5 Livep=0.1 Die? Outcome? Die? Outcome? Outcome? Outcome? Surgerycost 10K$ Surgery killsp= 0.1 Treatment? chemocost 4K$ Cured p=0.2 Surgerycost 10K$ Nothingcost 0$ Uncuredp=0.8 Treatment? Diep=0.9 Diep=0.9 Nothing Livep=0.1 Livep=0.1

  16. 5. Calculate utility values for utility nodes • Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do? Curedp=0.4 Diep=0.9 896K$ -10K$ -10K$ 890K$ 896K$ 0$ 900K$ -4K$ 890K$ uncuredp=0.5 Livep=0.1 Outcome? Outcome? Outcome? Die? Die? Outcome? Surgerycost 10K$ Surgery killsp= 0.1 Treatment? chemocost 4K$ Cured p=0.2 Surgerycost 10K$ Nothingcost 0$ Uncuredp=0.8 Treatment? Diep=0.9 Diep=0.9 Nothing Livep=0.1 Livep=0.1

  17. 6. Calculate expected utilities • Your show dog has cancer. If you do nothing, there is a 90% chance she will die. If she has surgery, there is a 40% chance of curing the cancer, 10% chance of dying from the surgery, and a 50% chance that the cancer will survive, in which case, she has the usual 90% chance of dying. If she gets chemo, there is a 20% chance of curing the cancer, and an 80% that the cancer will remain, in which surgery can be performed, with the same risks and outcomes as mentioned above. Chemo cannot be done after surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if she is dead. Surgery costs $10K and chemo costs 4K$. What should you do? Curedp=0.4 EU=365 Diep=0.9EU= -9 896K$ -10K$ -10K$ 890K$ 896K$ 0$ 900K$ -4K$ 890K$ uncuredp=0.5 EU=80 Livep=0.1 EU=89 Outcome? Outcome? Outcome? Die? Die? Outcome? Surgerycost 10K$ EU=444 Surgery killsp= 0.1EU=-1 Cured p=0.2 EU=179.2 Treatment? chemocost 4K$EU=619.2 Surgerycost 10K$EU=440 Nothingcost 0$EU=90 Treatment? Uncuredp=0.8EU=440 Diep=0.9 EU=0 Diep=0.9 EU=-3.6 NothingEU=86 Livep=0.1 EU=90 Livep=0.1EU=89.6

  18. EU = 0.03*(-240)+0.97*(-40) = -46 My disk drive is flakey. Tech says that there is a 10% chance it will crash in the next week, and replacing the disk and data will cost me $200. If I replace the disk, it will cost me $70 and it will not crash. If I save its contents to DVD, reformat and restore it, then it costs me 4 hours (equivalent to $40) but reduces the chance of crashing to 3%. Yes p=0.03 -240 0 -200 -40 -70 Nop= 0.97 Yes Save, reformat, restore? Crash? Crash? Yes p=0.1 No No Replace disk? Yes Nop=0.9 EU = 0.10*(-200)+0.90*(0) = -20 EU = -70

  19. Quiz question • You will be drilling a water well in your backyard, and you have to decide where to dig it. If you just dig where you think it is best, there is a 40% chance you’ll hit water. If you hire a seismologist, the chances increase to 60% but it costs you 10K$. If you hire a water witch, the chance of hitting water is 50% and the cost is 1K$. If you get 50K$ for hitting water, what should you do • Draw the decision tree • Evaluate alternatives • Indicate best choice • Put your name on the paper and hand it in.

  20. You will be drilling a water well in your backyard, and you have to decide where to dig it. If you just dig where you think it is best, there is a 40% chance you’ll hit water. If you hire a seismologist, the chances increase to 60% but it costs you 10K$. If you hire a water witch, the chance of hitting water is 50% and the cost is 1K$. If you get 50K$ for hitting water, what should you do? Yes p=0.5 EU=24.5 50K$ • -1K$ 40K$ 49K$ 0 -10K$ Nop= 0.5 EU=-0.5 Water witchcost 1K$EU=24 Water? Water? Water? Yes p=0.6EU=24 Seismologist Cost 10K EU=20 Detector? Nop=0.4 EU=-4 Yes p=0.4 EU=20 Nothing Cost 0$ EU=20 Nop= 0.6 EU=0

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