Presentation Transcript

1. Chapter 10 - Objectives Structure uncertain decisions – tree format Symmetric Asymmetric Sequential decisions and Information seeking Analyze uncertain decisions Solve a decision tree – Maximize (or Minimize) the expected value Risk Profile Simple tree Sequential decisions Asymmetric tree Sensitivity Analysis – Robustness – easy to do with Precision Tree 02/26/12
2. Analyze uncertain decisions Create Tree Structure Symmetric Tree Asymmetric Tree Input data on probabilities and values Construct mathematical equation of objective function Solve a decision tree – Maximize (or Minimize) the expected value Risk Profile Sensitivity analysis of parameters Excel spreadsheet structure  facilitate sensitivity analysis of key parameters 02/26/12
3. Users of Decision Trees Oil (Energy) – Shell, Chevron, Exxon, Conoco, Texaco, Pharmaceuticals (Medical) – Eli Lilly, Abbot Labs, Merck, Pfizer, Bristol Myers, Baxter Chemical – Monsanto, DuPont Consulting groups – Strategic Decisions, Innovative Decisions Individual companies AT&T GM, Kodak (Decision analysis not a substitute for good product development strategy and implementation) 02/26/12
4. Investment in Automation Boss Controls (BC) is gearing up to manufacture an option to be made available on 1 million new cars world-wide. Initial estimates are that the take rate for the option could be as low as 30% or as high as 50%. Assume the 50% take rate has a 0.6 probability of occurring. The plan calls for BC to deliver the option to the OEM’s at a price of $60. Timothy O’Leary, VP for imaginative products, is considering two alternatives that differ significantly in the level of investment in automation and the related variable cost of production. Low Investment = $8M Variable Cost = $27 per option ======================================================================= High Investment = $13M Variable Cost = $14 per option 02/26/12
5. Schematic of Boss Controls Without data & symmetricrectangle  decisioncircle  random event Automation Investment Decision Demand Uncertainty 02/26/12
6. Information Content in Decision Tree Tree Construction – Layout -- Information regarding relationships (& sequence) between decisions and uncertainty. Probabilities - Information regarding uncertainty Assigned to branches of random events Value - Information regarding cost or profits or parameters Associated with all branches: events and decisions Formula captures how the values interrelate. Specific Goal: Maximize or Minimize Expected Value Implied Real Goal: Update Intuition 02/26/12
7. Figure 10.1: A basic decision tree with one decision node and one random node 02/26/12
8. Figure 10-2: Influence diagram for capacity planning example Competitor Actions Sales Total Revenue How Much Capacity Actual Yield Total Profit Total Cost Star Electronic, a cellular phone manufacturer, is exploring optimum production capacity for a new phone. The new product requires a new production line and there is uncertainty regarding its yield. Management is focusing on three capacity options. Their competitor’s new product may have either marginal or significant impact on the demand for Star’s new product, which could be high, medium, or low. 02/26/12
9. Figure 10.3: Schematic tree for capacity planning example Sales How Much Capacity Competitor Actions Yield 02/26/12
10. Figure 10.4 Design change asymmetric tree Manufacturing Savings Solves Problem Manufacturing Savings Yes Warranty Costs Yes No No Warranty Costs Make Design Change It is only 6 months before the vehicle launch of the MX36. A sound emanating from the instrument panel has been detected on some test drives. However, engineers are not able to reproduce the sound in a controlled environment. They are fairly certain the problem is from a series of three assembled parts. They have a new single modular design that can be implemented quickly and should solve the problem. There is a potential added benefit from the modular design: reduced manufacturing and assembly cost. 02/26/12
11. Figure 10.5: Influence diagram for machine planning for capacity example: sequential decisionsMachine type  number of machines Competitor’s Actions Total Demand Initial Yield Annual Production Total Revenue Learning Curve Net Profit Total Cost Machine Type How Many Machines 02/26/12
12. Figure 10.6: Schematic tree for machine planning for capacity example Total Demand Learning How Many Machines Competitor Actions Type of Machine Yield 02/26/12
13. Controlled Forest Fire Case A fire set under controlled conditions is an important tool in managing the national forests of the United States. These fires are used to clear away forest residue that might otherwise turn a minor fire into a major conflagration. A prescribed burn might be used to clear an area as small as 15 acres in the Tahoe National Forest in Nevada or as large 2000 acres in the Prescott National Forest in Arizona. They are also utilized to enhance wildlife habitat and prepare a site for seedlings. However, planning and executing a controlled fire is a complex and risky process. The spread of a fire is affected by uncertainty surrounding the environmental conditions and the fire's behavior once it is started. Decision makers must decide under what conditions to start a fire and the level of resources to made available on-site as the controlled fire is initiated. The final outcome is also uncertain as to its effects on vegetation, soil, timber, hazards, and wildlife. Once a fire plan has been established, decision makers still must make a careful assessment of current and forecasted weather conditions before going ahead. 02/26/12
14. Figure 10.7: Controlled forest fire (Cohan et al. 1984) – Information  delay 2nd decision Random Event Decision Node Commit Test Burn Initiate Environmental Fire Real-Time Fire Resources? Outcome Full Burn? Conditions Behavior Burn Decisions Effects - Wind - Intensity - Continue - Vegetation - Preferred - Temp - Rate - Modify - Soil - Acceptable - Humidity - Spotting - Stop - Timber - Unacceptable - Stability - Smoke - Escape - Hazards - Flame Length - Wildlife 02/26/12
15. Sequential and Conditional Decisions Sequential Decisions Two or more decisions in sequence followed by one ore more random events Schematic tree Conditional Decisions A decision followed by a random event followed by another decision followed by more random events Optimal second decision depends on the first decision and the outcome of the first random event. Schematic tree 02/26/12
16. Activity: Conditional Decisions A sequence of decisions with random events in between A random event corresponds to gaining information before the next decision Describe your own example of a sequence of decisions and random events interspersed. _________________ 02/26/12
17. Probability Decision Tree BasicsMaking Choices Through Analysis Decisions = Square Nodes Branches = Alternatives Random Events = Circle Nodes Branches = Set of Outcomes Probabilities  attached to every branch from a random (circle) node Values (Intermediate)  Numbers stored on some branches Values of each decision alternative and sequence of probabilistic outcomes Final Numbers just appear at end of tree branches. Specific math formula  used to calculate the Final Values Value Storage in SOFTWARE varies by software package 02/26/12
18. Basic Analytic steps Tree Construction - generally straightforward Asymmetric trees can be complex Calculation of End Point Values Textbook Trivial Real-world decisions can involve complicated formulae or even complex spreadsheets Minimize (or Maximize) Expected Value - Tree Rollback - Trivial calculation of Expected Value E(X) =  X P(X) 02/26/12
19. Results “Analysis” Compare Expected Values Compare Risk Profiles Magnitude of downside risk Probability of worst case scenario Robustness of optimal strategy with regard to Probabilities Values and other parameters 02/26/12
20. Advanced Tree Analysis Value & Risk Management Max improvement – Expected Value of Perfect Control (EVPC) Change Probability or Value of a negative (or positive) outcome and calculate its impact on the expected value of the optimal strategy. Attitude towards risk - utility theory Integrate risk and multiple objectives Sequentially – Risk profile input into multiple objectives Precision Tree Software does NOT allow you to track on the tree multiple values/objectives (e.g. cost & time) of the same decision while optimizing one specific objective function. Create parallel trees. Input single MAUT formula 02/26/12
21. Investment in AutomationConstruct and Solve Probability Decision Tree Boss Controls (BC) is gearing up to manufacture an option to be made available on 1 million new cars world-wide. Initial estimates are that the take rate for the option could be as low as 30% or as high as 50%. Assume the 50% take rate has a 0.6 probability of occurring. The plan calls for BC to deliver the option to the OEM’s at a price of $60. Timothy O’Leary, VP for imaginative products, is considering two alternatives that differ significantly in the level of investment in automation and the related variable cost of production. Low Investment = $8M Variable Cost = $27 per option ======================================================================= High Investment = $13M Variable Cost = $14 per option 02/26/12
22. Investment in AutomationStructure Decision Tree 30% Take Low 50% Take Automation Investment 30% Take High 50% Take Names of branches 02/26/12
23. Investment in AutomationInput Data and Solve Probability Decision Tree Input the fixed costs along the appropriate branches Calculate the total variable cost of production at each branch At End value node: Travel along each path from the root node until the end node adding and subtracting costs along the way. Record the values at the end of each branch-path. At Random event node: Roll back the tree – Calculate expected values at every random event node. At the Decision node: Compare the expected values and select the better value. 02/26/12
24. Figure 10.1: A basic decision tree with one decision node and one random node Calculated Expected Value Probability Calculated End Values Values Optimal: Minimize Expected Value 02/26/12
25. Formula to calculate value on Take_Rate branch Total Revenue = Volume*Take_rate*(Price – Variable Cost) Calculate for Low Investment and Low Take_rate = Calculate for High Investment and High Take_rate = OEM’s price of $60. Take_rate is 30% or 50% Variable Cost with low investment = $27 per option Variable Cost with high investment = $14 per option 02/26/12
26. Figure 10.8: - Automation investment: Calculate revenue and end values – sum values along path Calculated Revenue Calculated End Values 02/26/12
27. 60.0% 0.6 50% 10.0 23 TRUE Take Rate 6.32 (=10*0.6 + 0.8*0.4) -13 40.0% 0.4 30% 0.8 13.8 Decision 6.32 (MAX{6.32, 5.86}) 60.0% 0 50% 8.5 16.5 FALSE Take Rate 5.86 (=8.5*0.6 + 1.9*0.4) -8 40.0% 0 30% 1.9 9.9 Rollback TreeRandom event  Calculate expected valueDecision node  Choose better value Calculated Expected Value High Optimal prob. Automation Investment Low Choose smallest Expected Value Non- Optimal. path 02/26/12
28. Risk Profile Expected value is a weighted sum - Multiply the probabilities along the path by the endpoint value Profile – Group equal values and sum their associated probabilities Do NOT expect the Expected Value! $6.32 million WHY? 02/26/12
29. Figure 10.10: Automation Investment - Risk profile 02/26/12
30. Figure 10.11: Automation Investment - Cumulative risk profile 02/26/12
31. Maximum value of risk managementExpected Value of Perfect Control (EVPC) of random event Goal: Determine the value of eliminating Uncertainty or Risk This provides an upper bound on the value of risk management with regard to that uncertainty. Process: Assign probability of “1” to the best outcome of an uncertain event. Recalculate the overall expected value. The NET Improvement in expected value is the EVPC. 02/26/12
32. Expected Value of Perfect Control: Automation Investment Assign probability of “1” to best outcome Net Change: $10 – 6.32 = $3.68 million 100% 1.0 50% 10.0 23 TRUE Take Rate High 10 =10*1 + 0.8*0) -13 0% 0 30% 0.8 13.8 Decision Automation Investment 10 (MAX(10, 8.5)) 100% 0 50% 8.5 16.5 FALSE Take Rate Low 8.5=8.5*1.0 + 1.9*0) -8 0% 0 30% 1.9 9.9 02/26/12
33. Investment in Automation Robustness of Optimal Solution? The “High” investment alternative involves a new technology. Management is concerned that the capital equipment estimate could be off by + 7%. There is even more concern regarding the variable cost estimate that could be off by + 10% The Low investment alternative is well tested and there is hope that continuous improvement could reduce the variable cost by 5%. Because they did not know, they set the take rate probabilities at 0.6 and 0.4 respectively. However, there is a lot of uncertainty regarding this probability. 02/26/12
34. Investment in AutomationRobustness of Optimal Solution Magnitude of Difference = ($6.32M-$5.86M) = $460,000 Investment(s) How much increase in HIGH Investment fixed cost results in change in best decision? Variable Cost(s) How much would the variable cost for Low Investment have to decline to make it preferred? Probability of 30% take rate: Increases? Decreases? What else might change and why? 02/26/12
35. Precision Tree Sensitivity AnalysisOutput – Separate Worksheets Sensitivity – one parameter at a time Multiple lines – Objective function for each decision. Crossing lines  change in optimal decision One line –Objective function for optimal strategy: A change in optimal decision is usually bend in line 02/26/12
36. Figure 10.23: Sensitivity analysis automation investment – fixed cost of high investment 02/26/12
37. Figure 10.24: Expected value of the optimal decision for each value of the fixed cost of high investment. 02/26/12
38. Figure 10.25: Sensitivity analysis automation investment – low take rate probability 02/26/12
39. Figure 10.26: Sensitivity analysis automation investment – variable cost of high investment 02/26/12
40. Figure 10.27: Sensitivity analysis automation investment – variable cost of low investment 02/26/12
41. Figure 10.28: Strategy region graph for two-way sensitivity analysis 02/26/12
42. Make or Buy Decision Decision Context: Manufacture a component yourself or contract with a supplier to manufacture it. There is a design for a component but you are not sure when it comes time to manufacture, that the design will be feasible as is. If not, there will need to be a quick major redesign of the component. If you manufacture it, you expect that with the redesign it will cost 8% more than the original estimate. The decision to make or buy must be made now before you have time to fully check out the design. The demand for the product is also uncertain. If you sign a contract with the supplier for a specific piece price, if the current design turns out to be infeasible, you know the supplier will use the design change as an excuse to increase the price 15%. Continued… 02/26/12
43. Make or Buy Data Costs: Make In-House Facility investment fixed Cost -$55M Variable Cost/ per part If current design works - $100/part If new Design is needed - $108/part Costs: Buy from Supplier Facility investment fixed Cost - $0 Variable Cost/ per part If current design works - $140/part If new Design is needed - $161/part Random Events 1. Design Feasibility (Prob.) Current Design will Work 0.4 Need a Major Redesign 0.6 2. Demand (Volume & Prob.) Low 1.0 million 0.3 Medium 1.25 million 0.5 High 1.5 million 0.2 02/26/12
44. Activity: Construct Schematic TreeMake or Buy Decision 02/26/12
45. Activity: Make or BuyConstruct & Analyze Tree Lay out Tree without numbers. Insert Probabilities. Write BELOW a formula to calculate Total Cost. Total Cost = __________________________ 02/26/12
46. Figure 10.12: Make/Buy structure a) Influence diagram b) Schematic tree 02/26/12
47. Activity: Formula & Construct Tree Use the formula to determine TWO end values Make  Design works  Low Demand = $$_____________ Buy  Design Does Not Work  High Demand = $$_____________ Fill in Tree on slide – Roll it back. 02/26/12
48. Demand Prob. 1 0.3 1.25 0.5 1.5 0.2 Fixed Costs Make 55 Buy 0 0.12 30.0% Low $_______ 1 40.0% Demand Works $$_______ 100 0.2 50.0% Medium 180 1.25 20.0% 0.08 High Current Design 1.5 205 $$________ TRUE Make 55 0.18 30.0% Low 1 163 60.0% Demand Does NOT work 108 187.3 0.3 50.0% Medium 190 1.25 Decision 20.0% 0.12 High 1.5 217 Make or Buy $$__________ 0 30.0% Low 1 140 40.0% Demand Works 0 140 171.5 50.0% 175 Medium 1.25 20.0% 0 Current Design High Make or Buy 1.5 210 $$__________ FALSE Buy 0 0 30.0% Low 161 1 60.0% Demand Does NOT work $$_______ 0 161 Notice the values that are stored on each branch. A formula is used to calculate the end values. 50.0% 201.25 Medium 1.25 0 20.0% High 1.5 $_______ 02/26/12
49. Demand Prob. 1 0.3 1.25 0.5 1.5 0.2 Fixed Costs Make 55 Buy 0 Expected value 0.12 30.0% Low 1 155 40.0% Demand Works 177.5 100 0.2 50.0% Medium 180 1.25 20.0% 0.08 High 1.5 205 Current Design TRUE Make 55 183.38 0.18 30.0% Low 1 163 60.0% Demand Does NOT work 187.3 108 0.3 50.0% Medium 190 1.25 20.0% 0.12 Decision High 1.5 217 Make or Buy 183.38 0 30.0% Low 1 140 40.0% Demand Works 171.5 140 0 50.0% Medium 175 1.25 20.0% 0 High 1.5 210 Current Design FALSE Buy Make or Buy 0 186.935 0 30.0% Low 1 161 60.0% Demand Does NOT work 197.225 161 0 50.0% Medium Expected value 201.25 1.25 20.0% 0 High 1.5 241.5 02/26/12
50. Figure 10.13: Complete Make/Buy decision tree Modify picture 02/26/12
51. Figure 10.14 Partial decision tree Make/Buy 02/26/12
52. Make or Buy: Interpret Answer $183.4 Million (Make) vs. $186.9 Million (Buy) Is the $3.55 Million Difference significant to you? If it were hundreds of millions would it matter more? Don’t Expect the Expected Value!!! 02/26/12
53. Make or Buy: Interpret Answer What is $9 Billion worth of purchases divided by $180 Million per decision?  50 How can you use this number to justify the use of Expected Values?   Is a net $177.5 Million difference significant? 50 x $3.55 M 02/26/12
54. Risk Profile- Sort Ordered: Class Exercise Buy ValueProbability 1. ________ ______ 2. ________ ______ 3. ________ ______ 4. ________ ______ 5. ________ ______ 6. ________ ______ Make ValueProbability 1. ________ ______ 2. ________ ______ 3. ________ ______ 4. ________ ______ 5. ________ ______ 6. ________ ______ What do you notice? 02/26/12
55. Statistics & Risk Profile – Precision Tree Output 02/26/12
56. Figure 10.15: Risk profile for Make/Buy 02/26/12
57. Cumulative Risk Profile: Precision Tree Output MAKE P(X < 180) = ___, P(X<190) = ____, P(X<220) = ____ BUY P(X < 180) = ___, P(X<190) = ____, P(X<220) = ____ 02/26/12
58. Figure 10.16: Cumulative risk profile for Make/Buy 02/26/12
59. Cumulative Risk Profile: What do you observe? P(X < 180) = P(X < 190) = P(X < 220) = Which is better: graph further to the left or to the right when minimizing? IF Stochastic Dominance – no crossing of lines  Strategy is preferred irrespective of risk attitude What would the answer be if the problem Maximized Profit instead of Minimizing Cost? 02/26/12
60. Statistics & Risk Profile – Precision Tree OutputStochastic Dominance of New Alternative “B” 02/26/12
61. Figure 10.18: Cumulative profile showing dominance of Supplier A over Supplier B 02/26/12
62. Asymmetric Decision Tree It is only six months before vehicle launch. On some occasions on test drives, individuals have noticed a sound emanating from the instrument panel. However, engineers are not able to reproduce the sound in a controlled environment. They are pretty sure the problem is from a series of three assembled parts. They have a new single modular design that can be implemented quickly and that should solve the problem. There is a potential added benefit from the modular design: reduced manufacturing and assembly cost. 02/26/12
63. A Design Change Decision Specific Case Volumes 100,000 vehicles One year’s production is relevant Proposed Solves Problem p = .8 Fixed Costs $150,000 Manufacturing Savings $ 0 p = .30 $ 2.50 p = .70 Current Customers Notice 0% warranty p = .50 1% warranty p = .30 5% warranty p = .20 Cost/warranty = $50 02/26/12
64. Design Change - Schematic Tree & Formula Warranty Cost Solves Problem Total Cost Design Changes Mnfg. Savings End Value Current Design: Warranty Claim * Warranty Cost * Volume New Design: Fixed Cost + (Warranty Claim * Warranty Cost * Volume) + (Manufacturing Savings * Volume) 02/26/12
65. Asymmetric Schematic Probability Decision Tree – Design Change Manufacturing Savings Solves Problem Manufacturing Savings Warranty Costs Yes Warranty Costs No Make Design Change 02/26/12
66. Figure 10.19: Decision tree for design change example 02/26/12
67. Figure 10.20: Design change – Risk profile 02/26/12
68. Cumulative Probability For Change Design of Change Design 1.2 1 0.8 1 : Yes 0.6 Cumulative Probability 2 : No 0.4 0.2 0 -500000 -400000 -300000 -200000 -100000 0 100000 200000 Value Design Change – Risk Profile 02/26/12
69. Interpret Risk Profile &Motivate Next Lecture Describe Worst Case Scenario for preferred strategy What is its probability? Describe a Bad Scenario with a substantial probability of occurrence. What is its probability? 02/26/12
70. Answers to Design Change 0.24 30.0% None 0 -150000 Manuf. Savings 80.0% Yes 25000 Warranty Claims 0 0.56 Prob. Percent 70.0% 2.50 0.5 0 250000 100000 0.3 0.01 TRUE Yes Solves Problem 0.2 0.05 -150000 0.03 Volumes 100000 30.0% None 12000 Warranty $ 50 0 -150000 Fixed Costs 150000 Manuf. Savings 50.0% None 25000 0 0.07 Manuf. Savings 70.0% 2.50 Prob. Amount 250000 100000 Warranty Claims 0.3 0 20.0% No 0.7 2.5 0 -40000 0.018 Solves Problem 30.0% None Yes 0.8 0 -200000 No 0.2 Manuf. Savings 30.0% Low -25000 -50000 0.042 70.0% 2.50 50000 250000 30.0% 0.012 None 0 -400000 Manuf. Savings 20.0% High -225000 Decision -250000 0.028 70.0% 2.50 250000 -150000 12000 Change Design 50.0% 0 None 0 0 Warranty Claims FALSE No -65000 0 0 30.0% Low -50000 -50000 20.0% 0 High -250000 -250000 02/26/12

71. Chapter 10 additional Figures

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72. Figure 10.21: Decision tree for capacity expansion case 02/26/12
73. Figure 10.22: Risk profile for capacity expansion case 02/26/12
74. Figure 10.29: Schematic tree of postal automation 02/26/12
75. Figure 10.30: Schematic decision tree for the transmission line problem 02/26/12
76. Figure 10.31: Decision tree for drug development strategy 02/26/12
77. Figure 10.32: Peak and expected peak sales for drug development strategy case 02/26/12