1 / 66

INFO 631 Prof. Glenn Booker

INFO 631 Prof. Glenn Booker. Week 9 – Chapters 24-26. Decisions Under Risk. Ch. 24. Decisions Under Risk Outline. Introducing decisions under risk Different techniques Expected value decision making Expectation variance Monte Carlo analysis Decision trees

wilbur
Télécharger la présentation

INFO 631 Prof. Glenn Booker

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. INFO 631Prof. Glenn Booker Week 9 – Chapters 24-26 INFO631 Week 9

  2. Decisions Under Risk Ch. 24 INFO631 Week 9

  3. Decisions Under RiskOutline • Introducing decisions under risk • Different techniques • Expected value decision making • Expectation variance • Monte Carlo analysis • Decision trees • Expected value of perfect information INFO631 Week 9

  4. Decisions Under Risk • When you know the probabilities of the different outcomes and will incorporate them • Expected value decision making • Expectation variance • Monte Carlo analysis • Decision trees • Expected value of perfect information INFO631 Week 9

  5. Expected Value Decision Making • The value of an alternative with multiple outcomes can be thought of as the average of the random individual outcomes that would occur if that alternative were repeated a large number of times • Can use PW(i), FW(i), or AE(i) INFO631 Week 9

  6. Expected Value of a Single Alternative • Denali project at Mountain Systems • Imagine 1000 parallel universes where the Denali project could be run at the same time • Should expect most favorable outcome would happen in 15% or 150 of those universes • Fair outcome would happen in 650 • Least favorable outcome would happen in 200 Least Most favorable Fair favorable PW(MARR) -$1234 $5678 $9012 Probability 0.20 0.65 0.15 INFO631 Week 9

  7. Expected Value of a Single Alternative • Total PW(i) income generated • Average PW(i) income in each universe • Notice 200 * -$1234 = -246,800 650 * $5678 = $3,690,700 150 * $9012 = $1,351,800 $4,795,700 $4,795,700 / 1000 = $4795.70 (0.20 * -$1234) + (0.65 * $5678) + (0.15 * $9012) = $4795.70 INFO631 Week 9

  8. Expected Value of a Single Alternative • General formula • Can be used to help decide between multiple alternatives INFO631 Week 9

  9. Expected Value of Multiple Alternatives • Same probability • Several projects at Mountain Systems • Expected values • Choose Shasta, it has the highest expected value Least Most favorable Fair favorable Alternative 20% 65% 15% Denali -$1234 $5678 $9012 Shasta -2101 6601 9282 Washington -3724 4104 9804 Denali (0.20 * -$1234) + (0.65 * $5678) + (0.15 * $9012) = $4795.70 Shasta (0.20 * -$1201) + (0.65 * $6601) + (0.15 * $9282) = $5262.75 Washington (0.20 * -$3724) + (0.65 * $4104) + (0.15 * $9804) = $3393.40 INFO631 Week 9

  10. Expectation Variance • What if probabilities were different for each alternative? • Comparing projects • Lassen has higher expected value but win big-lose big • Moana Loa has lower expected value but more probability of profit Lassen Moana Loa Outcome Probability AE(i) Least favorable 10% -$200 Low nominal 20% 108 High nominal 30% 378 Most favorable 40% 877 Expected value = $466 Outcome Probability AE(i) Least favorable 45% -$3494 Nominal 10% 728 Most favorable 45% 4811 Expected value = $665 INFO631 Week 9

  11. Monte Carlo Analysis • Randomly generate combinations of input values and look at distribution of outcomes • Named after gambling resort in Monaco • Use [a variant of] Zymurgenics project (different data) Least favorable Fair Most favorable estimate estimate estimate Initial investment $500,000 $400,000 $360,000 Operating & maintenance $1500 $1000 $800 Development staff cost / month $49,000 $35,000 $24,500 Development project duration 15 months 10 months 7 months Income / month $24,000 $40,000 $56,000 INFO631 Week 9

  12. Monte Carlo Analysis • Simulation run results Income range Number of occurrences -$75,000 to -$50,001 3 -$50,000 to -$25,001 32 -$25,000 to -$1 76 $0 to $24,999 258 $25,000 to $49,999 655 $50,000 to $74,999 921 $75,000 to $99,999 1044 $100,000 to $124,999 865 $125,000 to $149,999 586 $150,000 to $174,999 329 $175,000 to $199,999 159 $200,000 to $224,999 53 $225,000 to $249,999 17 $250,000 to $274,999 5 INFO631 Week 9

  13. Monte Carlo Analysis INFO631 Week 9

  14. Decision Trees • Maps out possible results when there are sequences of decisions and future random events • Useful when decisions can be made in stages • Basic Elements • Decision nodes – points in time where a decision maker makes a decision (square) • Chance nodes – points in time where the outcome is outside the control of the decision maker (circles) • Node sequencing INFO631 Week 9

  15. Sample Decision Tree INFO631 Week 9

  16. Decision Tree Analysis, Part 1 • Add the financial consequences for each arc (PW(i), FW(i), or AE(i)) • Properly adjust for time periods as required • Sum financial consequences from the root node to all leaf nodes INFO631 Week 9

  17. Sample Decision Tree INFO631 Week 9

  18. Decision Tree Analysis, Part 2 • Write probabilities for each arc out of each chance node • Probabilities out of a chance node must = 1.0 • Roll back values from leaf nodes to root • If node is chance node, calculate expected value at that node based on values on all nodes to its right • If node is decision node, select the maximum profit (or minimum cost) from nodes to its right INFO631 Week 9

  19. Sample Decision Tree INFO631 Week 9

  20. Expected Value of Perfect Information • Value at root node is expected value of decision tree based on current information • Current information is known to be imperfect • Reasonable follow-on question • Research, experimentation, prototyping, … • Might even be able to eliminate one or more paths through the tree because you may discover them to be impossible • Analyzed decision tree provides information that will help answer that question “Would there be any value in taking actions that would reduce the probability of ending up in an undesirable future state?” INFO631 Week 9

  21. Expected Value of Perfect Information • If we had a crystal ball and knew outcomes for chance nodes, we could find which path would be best • Finding best path can be repeated for all possible combinations of random variables • Probabilities for random variables are known • Can calculate probability for each combination of outcomes • For each combination of outcomes, multiply its best value by probability of that combination • Sum the results of (value * probability) for all combinations of outcomes • Sum is expected value given perfect information • Difference between sum and expected value given current information is expected value of perfect information INFO631 Week 9

  22. Expected Value of Perfect Information • EVPI is upper limit on how much to spend to gain further knowledge • Probably impossible to actually get perfect information, organization should plan on spending less INFO631 Week 9

  23. Key Points • Value of an alternative with multiple outcomes is the average of the random individual outcomes that would occur if that alternative were repeated a large number of times (expected value) • The alternative with the highest expected value is best • With expectation variance, differing probabilities could influence the decision • Alternative with lower expected value might be a better choice if it also has a much lower probability of a negative outcome • Monte Carlo analysis generates random combinations of the input variables and calculates results under those conditions • Repeated many times and statistical distribution of outcomes is analyzed • Decision trees map out possible results when there are sequences of decisions together with a set of future random events that have known probabilities • Useful with many possible future states and decisions can be made in stages • The Expected value of perfect information provides answer to, “Would there be any value in taking actions that would reduce the probability of ending up in an undesirable future state?” INFO631 Week 9

  24. Decisions Under Uncertainty Ch. 25 Slides adapted from Steve Tockey – Return on Software INFO631 Week 9

  25. Decisions Under UncertaintyOutline • Introducing decisions under uncertainty • Different Techniques • Payoff matrix • Laplace Rule • Maximin Rule • Maximax Rule • Hurwicz Rule • Minimax Regret Rule INFO631 Week 9

  26. Decisions Under Uncertainty • Used when impossible to assign probabilities to outcomes • Can also be used when you don’t want to put probabilities on outcomes, e.g., safety-critical software system where a failure could threaten human life • People may not react well to an assigned probability of fatality • If probabilities can be assigned, Decision Making under Risk should be used INFO631 Week 9

  27. Payoff Matrix • Shows all possible outcomes to consider • One axis lists mutually exclusive alternatives • Other axis lists different states of nature • Each state of nature is a future outcome the decision maker doesn’t have control over • Cells have PW(i), FW(i), AE(i), … Alternative State1 State2 State3 A1 -4010 1002 2001 A2 948 1101 4021 A3 -2005 1516 6004 A4 0 2020 5104 A5 1005 3014 2008 INFO631 Week 9

  28. Reduced Payoff Matrix • One alternative may be “dominated” by another • Another alternative has equal or better payoff under every state of nature • Reduced payoff matrix has no dominated alternatives • Less work if dominated alternatives are removed Alternative State1 State2 State3 A1 -4010 1002 2001 A2 948 1101 4021 A3 -2005 1516 6004 A4 0 2020 5104 A5 1005 3014 2008 INFO631 Week 9

  29. Laplace Rule • Assumes each state of nature is equally likely • Sometimes called “principle of insufficient reason” • Calculate average payoff for each alternative across all states of nature • Same as expected value analysis for multiple alternatives with equal probabilities INFO631 Week 9

  30. Laplace Rule • Example • Alternative A4 is chosen; the highest payoff always wins! Alternative State1 State2 State3 Average payoff A2 948 1101 4021 1933 A3 -2005 1516 6004 1838 A4 0 2020 5104 2374 A5 1005 3014 2008 2009 INFO631 Week 9

  31. Maximin Rule • Assumes worst state of nature will happen • Most pessimistic technique • Pick alternative that has best payoff from all worst payoffs • Formula INFO631 Week 9

  32. Maximin Rule • Example • Alternative A5 is chosen Alternative State1 State2 State3 Worst payoff A2 948 1101 4021 948 A3 -2005 1516 6004 -2005 A4 0 2020 5104 0 A5 1005 3014 2008 1005 INFO631 Week 9

  33. Maximax Rule • Assumes best state of nature will happen • Most optimistic technique • Pick alternative that has best payoff from all best payoffs • Formula INFO631 Week 9

  34. Maximax Rule • Example • Alternative A3 is chosen Alternative State1 State2 State3 Best payoff A2 948 1101 4021 4021 A3 -2005 1516 6004 6004 A4 0 2020 5104 5104 A5 1005 3014 2008 3014 INFO631 Week 9

  35. Hurwicz Rule • Assumes that without guidance people will tend to focus on extremes • Blends optimism and pessimism using a selected ratio • Index of optimism, a, between 0 and 1 • a = 0.2 means more pessimism than optimism • a = 0.1 means more pessimism than a = 0.2 • a = 0.85 means lots of optimism but a small amount of pessimism (15%) remains INFO631 Week 9

  36. Hurwicz Rule • Formula • Example • a = 0.2 • Alternative A2 is chosen Alternative State1 State2 State3 Blended payoff A2 948 1101 4021 (0.2 * 4021) + (0.8 * 948) = 1563 A3 -2005 1516 6004 (0.2 * 6004) + (0.8 * -2005) = -403 A4 0 2020 5104 (0.2 * 5104) + (0.8 * 0) = 1021 A5 1005 3014 2008 (0.2 * 3014) + (0.8 * 1005) = 1407 INFO631 Week 9

  37. Hurwicz Rule A3 6000 6000 A4 A2 4000 4000 A5 2000 2000 0 0 0.5 -2000 -2000 .25 INFO631 Week 9

  38. Minimax Regret Rule • Minimize regret you would have if you chose wrong alternative under each state of nature • If you selected A1 and state of nature happened where A1 had the best payoff then you would have no regrets • If you selected A1 and state of nature happened where another alternative was better, you can quantify regret as difference between payoff you chose and best payoff under that state of nature • Regret matrix • Need to calculate • Difference between payoff you chose and best payoff under that state of nature INFO631 Week 9

  39. Minimax Regret Rule – Calculate Regret matrix • Regret matrix • Difference between payoff you chose and best payoff under that state of nature • For State 1 – A2 • 1005 – 948 = 57 • For State 1 – A3 • 1005 – (-2005) = 3010 • Etc. • NOTE: use numbers from original matrix Alternative State1 State2 State3 A2 57 2003 1983 A3 3010 1498 0 A4 1005 994 900 A5 0 0 3966 INFO631 Week 9

  40. Minimax Regret Rule • Choose alternative with smallest maximum regret • Alternative A4 is chosen Alternative State1 State2 State3 Maximum regret A2 57 2003 1983 2003 A3 3010 1498 0 3010 A4 1005 994 900 1005 A5 0 0 3966 3996 INFO631 Week 9

  41. Summary of Uncertainty Rules Decision rule Alternative selected Optimism or pessimism Laplace A4 Neither Maximin A5 Pessimism Maximax A3 Optimism Hurwicz (a=0.2) A2 Blend Minimax regret A4 Pessimism INFO631 Week 9

  42. Key Points • Uncertainty techniques used when impossible, or impractical, to assign probabilities to outcomes • Payoff matrix shows all possible outcomes to consider • Laplace rule assumes each state of nature is equally likely • Essentially expected value with equal probabilities • Maximin rule is most pessimistic • Pick alternative with best payoff from all worst payoffs • Maximax rule is most optimistic • Pick alternative with best payoff from all best payoffs • Hurwicz Rule assumes that without guidance people will tend to focus on the extremes • Blend optimism and pessimism using selected ratio • Minimax Regret rule minimizes regret you would have if you chose the wrong alternative under each state of nature • Choose alternative with smallest maximum regret INFO631 Week 9

  43. Multiple Attribute Decisions Ch. 26 INFO631 Week 9

  44. Multiple Attribute DecisionsOutline • Introducing multiple attribute decisions • Case study: Fly-by-Night Air • Different kinds of “value” • Choosing attributes • Measurement scales • Non-compensatory techniques • Compensatory techniques INFO631 Week 9

  45. IntroducingMultiple Attribute Decisions • Previous chapters explained how to make decisions using a single criterion, money • Alternative with best PW(i), AE(i), incremental IRR, incremental benefit-cost ratio, etc. is selected • Aside from technical feasibility, money is almost always the most important decision criterion • But not the only one • Often, other criteria (“attributes”) must be considered and can’t be cast in terms of money INFO631 Week 9

  46. Case Study: Fly-by-Night (FBN) Airlines • 10-year old regional airline with above average growth • Moving into nationwide market as no-frills carrier • As part of strategic planning, IT department charged with examining airline reservations systems • 10 year planning horizon, effective income tax rate=37%, after-tax MARR=15% • Research has identified five technically-viable alternatives • Keep existing software • Buy Jupiter commercial system • Buy Sword commercial system • Buy Guppy commercial system • Develop new software in-house • Develop new software offshore INFO631 Week 9

  47. Different Kinds of “Value” • Decision process is all about maximizing value • Choose from available alternatives the one that maximizes value • When value is expressed as money, decision process may be complex but is straightforward • Money isn’t the only kind of value • Money is really only a way to quantify value • Two kinds of value • Use-value - the ability to get things done, the properties of the object that cause it to perform • Esteem value - the properties that make it desirable INFO631 Week 9

  48. Choosing Attributes • Decisions should be based on appropriate attributes • Each attribute should capture a unique dimension of decision • Set of attributes should cover important aspects of decision • Differences in attribute values should be meaningful in distinguishing among alternatives • Each attribute should distinguish at least two alternatives • Selection of attributes may be subjective • Too many attributes is unwieldy • Too few attributes gives poor differentiation • Potential for better decisions needs to be balanced with extra effort of more attributes INFO631 Week 9

  49. FBN Air: Decision Attributes • Total cost of ownership • In-service availability • Liffey performance index • From Liffey Consultancy, Ltd in Dublin, Ireland • Alignment with existing business processes INFO631 Week 9

  50. Measurement Scales • Each alternative will be evaluated on each attribute • Many ways to measure things • In fact, different “classes” of measurements • Within a class, some manipulations make sense and others don’t • So it’s important for you to know what the different classes of measurements are, how to recognize them, and what can and can’t be done with them. INFO631 Week 9

More Related