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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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 1 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 2 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) Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 3 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 4 Schematic of Boss Controls Without data & symmetric rectangle decision circle random event Automation Investment Decision Chapter 10 Demand Uncertainty Chelst & Canbolat Value Added Decision Making 02/26/12 5 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 6 Figure 10.1: A basic decision tree with one decision node and one random node Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 7 Figure 10-2: Influence diagram for capacity planning example Sales Competitor Actions How Much Capacity Total Revenue 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 8 Figure 10.3: Schematic tree for capacity planning example How Much Capacity Chapter 10 Yield Competitor Sales Actions Chelst & Canbolat Value Added Decision Making 02/26/12 9 Figure 10.4 Design change asymmetric tree Solves Problem Yes Yes No Make Design Change No Manufacturing Savings Warranty Costs Manufacturing Savings Warranty Costs 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 10 Figure 10.5: Influence diagram for machine planning for capacity example: sequential decisions Machine type number of machines Competitor’s Actions Total Demand Initial Yield Annual Production Learning Curve Machine Type Chapter 10 How Many Machines Total Cost Chelst & Canbolat Value Added Decision Making Total Revenue Net Profit 02/26/12 11 Figure 10.6: Schematic tree for machine planning for capacity example Type of Machine Chapter 10 How Many Machines Yield Learning Chelst & Canbolat Value Added Decision Making Competitor Total Demand Actions 02/26/12 12 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 13 02/26/12 Figure 10.7: Controlled forest fire (Cohan et al. 1984) – Information delay 2nd decision Random Event Commit Resources? Test Burn Outcome - Preferred - Acceptable - Unacceptable Chapter 10 Decision Node Initiate Full Burn? Environmental Conditions - Wind - Temp - Humidity - Stability Fire Behavior - Intensity - Rate - Spotting - Smoke - Flame Length Chelst & Canbolat Value Added Decision Making Real-Time Burn Decisions - Continue - Modify - Stop - Escape Fire Effects - Vegetation - Soil - Timber - Hazards - Wildlife 02/26/12 14 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 15 02/26/12 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. _________________ Chapter 10 Chelst & Canbolat Value Added Decision Making 16 02/26/12 Probability Decision Tree Basics Making 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 17 02/26/12 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) Chapter 10 Chelst & Canbolat Value Added Decision Making 18 02/26/12 Results “Analysis” Compare Expected Values Compare Risk Profiles Magnitude of downside risk Probability of worst case scenario Robustness of optimal strategy Probabilities Values and other parameters Chapter 10 with regard to Chelst & Canbolat Value Added Decision Making 19 02/26/12 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 20 02/26/12 Investment in Automation Construct 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 21 Investment in Automation Structure Decision Tree 30% Take Low 50% Take Automation Investment 30% Take High 50% Take Names of branches Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 22 Investment in Automation Input 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 23 02/26/12 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 24 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 25 02/26/12 Figure 10.8: - Automation investment: Calculate revenue and end values – sum values along path Calculated Revenue Calculated End Values Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 26 Rollback Tree Random event Calculate expected value Decision node Choose better value Calculated Expected Value High 50% TRUE -13 Automation Investment Choose smallest Expected Value Decision 6.32 (MAX{6.32, 5.86}) Low -8 Chapter 10 23 0.6 10.0 Take Rate 6.32 (=10*0.6 + 0.8*0.4) 40.0% 0.4 30% 0.8 13.8 50% FALSE 60.0% 60.0% 16.5 Optimal prob. 0 8.5 Non- Optimal. path Take Rate 5.86 (=8.5*0.6 + 1.9*0.4) 40.0% 0 30% 1.9 9.9 Chelst & Canbolat Value Added Decision Making 27 02/26/12 Risk Profile Do NOT expect the Expected Value! $6.32 million WHY? 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 28 02/26/12 Figure 10.10: Automation Investment - Risk profile 0.6 0.5 Probability 0.4 50% 30% 0.3 0.2 0.1 Chapter 10 Chelst & Canbolat Value Added Decision Making 11 10 9 8 7 6 5 4 3 2 1 0 0 29 02/26/12 Figure 10.11: Automation Investment Cumulative risk profile Cumulative Probability 1 0.8 0.6 50% 30% 0.4 0.2 Chapter 10 Chelst & Canbolat Value Added Decision Making 11 10 9 8 7 6 5 4 3 2 1 0 0 30 02/26/12 Maximum value of risk management Expected 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 31 02/26/12 Expected Value of Perfect Control: Automation Investment Assign probability of “1” to best outcome Net Change: $10 – 6.32 = $3.68 million 100% 50% High Automation Investment TRUE -13 Decision 10 (MAX(10, 8.5)) Take Rate 10 =10*1 + 0.8*0) 0% 30% 13.8 50% Low FALSE -8 Chapter 10 Chelst & Canbolat Value Added Decision Making 23 100% 16.5 1.0 10.0 0 0.8 0 8.5 Take Rate 8.5=8.5*1.0 + 1.9*0) 0% 0 30% 1.9 9.9 02/26/12 32 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 33 02/26/12 Investment in Automation Robustness 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? Chapter 10 Chelst & Canbolat Value Added Decision Making 34 02/26/12 Precision Tree Sensitivity Analysis Output – 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 35 02/26/12 Figure 10.23: Sensitivity analysis automation investment – fixed cost of high investment Expected Value 7.5 7 6.5 High Low 6 5.5 -$12.0 -$12.2 -$12.4 -$12.6 -$12.8 -$13.0 -$13.2 -$13.4 -$13.6 -$13.8 -$14.0 5 High Investment Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 36 Figure 10.24: Expected value of the optimal decision for each value of the fixed cost of high investment. 7.5 Expected Value 7 6.5 6 5.5 Chapter 10 Chelst & Canbolat Value Added Decision Making -$12.0 -$12.2 -$12.4 High Investment -$12.6 -$12.8 -$13.0 -$13.2 -$13.4 -$13.6 -$13.8 -$14.0 5 02/26/12 37 Figure 10.25: Sensitivity analysis automation investment – low take rate probability 8.5 8 Expected Value 7.5 7 6.5 6 High 5.5 Low 5 4.5 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 4 Low Probability Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 38 Figure 10.26: Sensitivity analysis automation investment – variable cost of high investment 7.5 Expected Value 7 6.5 High Low 6 $16.0 $15.5 $15.0 $14.5 $14.0 $13.5 $13.0 $12.5 $12.0 $11.5 5.5 Variable Cost - High Investment Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 39 Figure 10.27: Sensitivity analysis automation investment – variable cost of low investment Expected Value 6.4 6.2 High 6 Low 5.8 $27.2 $27.0 $26.8 $26.6 $26.4 $26.2 $26.0 $25.8 $25.6 5.6 Variable Cost – Low Investment Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 40 Figure 10.28: Strategy region graph for two-way sensitivity analysis Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 41 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… Chapter 10 Chelst & Canbolat Value Added Decision Making 42 02/26/12 Make or Buy Data Random Events 1. Design Feasibility (Prob.) Current Design will Work Need a Major Redesign 0.4 0.6 2. Demand (Volume & Prob.) Low 1.0 million 0.3 Medium 1.25 million 0.5 High 1.5 million 0.2 Chapter 10 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 Chelst & Canbolat Value Added Decision Making 02/26/12 43 Activity: Construct Schematic Tree Make or Buy Decision Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 44 Activity: Make or Buy Construct & Analyze Tree Lay out Tree without numbers. Insert Probabilities. Write BELOW a formula to calculate Total Cost. Total Cost = __________________________ Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 45 Figure 10.12: Make/Buy structure a) Influence diagram Chapter 10 b) Schematic tree Chelst & Canbolat Value Added Decision Making 02/26/12 46 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 47 02/26/12 Low Design Feasibility Prob Make Costs 1 Works Buy Costs Works 0.4 100 140 Does NOT 0.6 108 161 8% 15% Premium 30.0% 40.0% 100 Demand $$_______ Medium 50.0% 1.25 Current Design Make TRUE 55 High 20.0% 1.5 $$________ Low 30.0% 1 Demand 1 1.25 1.5 Prob. 0.3 0.5 0.2 Fixed Costs Make 55 Buy 0 Does NOT work 60.0% 108 $_______ 0.2 180 0.08 205 0.18 163 Demand 187.3 Medium 50.0% High 20.0% 1.25 Decision 0.12 1.5 0.3 190 0.12 217 Make or Buy $$__________ Low 30.0% 1 Works 40.0% Demand 140 171.5 Medium 50.0% High 20.0% 1.25 Make or Buy Current Design Buy FALSE 0 Low 0 210 30.0% 0 161 1 Notice the values that are stored on each branch. A formula is used to calculate the end values. Chelst & Canbolat Value Added Decision Making Demand $$_______ Medium 50.0% High 20.0% 1.25 1.5 48 02/26/12 0 175 1.5 $$__________ Does NOT work 60.0% 161 0 140 0 201.25 0 $_______ Expected value Design Feasibility Prob Works 0.4 Does NOT 0.6 Premium Make Costs 100 108 8% Low Buy Costs 1 Works 140 40.0% 161 177.5 Medium 50.0% High 20.0% 1.25 15% TRUE 55 Prob. 0.3 0.5 0.2 1.5 Current Design 183.38 Low 30.0% 1 Does NOT work 60.0% 108 Decision 0.2 180 0.08 205 0.18 163 Demand 187.3 Medium 50.0% High 20.0% 1.25 Fixed Costs Make 55 Buy 0 0.12 155 Demand 100 Make Demand 1 1.25 1.5 30.0% 1.5 0.3 190 0.12 217 Make or Buy 183.38 Low 30.0% 1 Works 40.0% Demand 171.5 140 Medium 50.0% 1.25 High Make or Buy Buy FALSE 0 20.0% 1.5 Current Design 186.935 Low 30.0% 1 Does NOT work 60.0% 161 Expected value 0 175 0 210 0 161 Demand 197.225 Medium 50.0% High 20.0% 1.25 1.5 Chelst & Canbolat Value Added Decision Making 0 140 49 02/26/12 0 201.25 0 241.5 Figure 10.13: Complete Make/Buy decision tree Modify picture Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 50 Figure 10.14 Partial decision tree Make/Buy Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 51 Make or Buy: Interpret Answer Chapter 10 $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!!! Chelst & Canbolat Value Added Decision Making 52 02/26/12 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 Chapter 10 Chelst & Canbolat Value Added Decision Making 53 02/26/12 Risk Profile- Sort Ordered: Class Exercise Buy Make Value Value Probability Probability 1. ________ ______ 1. ________ ______ 2. ________ ______ 2. ________ ______ 3. ________ ______ 3. ________ ______ 4. ________ ______ 4. ________ ______ 5. ________ ______ 5. ________ ______ 6. ________ ______ 6. ________ ______ What do you notice? Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 54 Statistics & Risk Profile – Precision Tree Output S T A T IS T IC S M a ke D e c is io n M ean 1 8 3 .3 8 M in im u m 1 5 5 .0 0 M a xim u m 2 1 7 .0 0 M ode 1 9 0 .0 0 S td D e v 1 8 .9 7 Chapter 10 P R O F IL E : Buy 1 8 6 .9 4 1 4 0 .0 0 2 4 1 .5 0 2 0 1 .2 5 2 9 .5 8 Chelst & Canbolat Value Added Decision Making M ake # X Buy P X P 1 155 0 .1 2 140 0 .1 2 2 163 0 .1 8 161 0 .1 8 3 180 0 .2 0 175 0 .2 0 4 190 0 .3 0 201 0 .3 0 5 205 0 .0 8 210 0 .0 8 6 217 0 .1 2 242 0 .1 2 02/26/12 55 Figure 10.15: Risk profile for Make/Buy Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 56 C u m u la tiv e P r o b . Cumulative Risk Profile: Precision Tree Output 1 .2 1 : M ake 1 2 : Buy 0 .8 0 .6 0 .4 0 .2 0 120 140 160 180 200 220 240 260 280 V a lue MAKE BUY Chapter 10 P(X < 180) = ___, P(X < 180) = ___, P(X<190) = ____, P(X<220) = ____ P(X<190) = ____, P(X<220) = ____ Chelst & Canbolat Value Added Decision Making 02/26/12 57 Figure 10.16: Cumulative risk profile for Make/Buy Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 58 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? Chapter 10 Chelst & Canbolat Value Added Decision Making 59 02/26/12 Statistics & Risk Profile – Precision Tree Output Stochastic Dominance of New Alternative “B” Make Supplier A Supplier B Design Works ($/ Part) 100 140 147 Premium (If Design does NOT Work) 8% 15% 10% P R O F IL E : M ake S T A T IS T IC S M a k e S u p p lie r A S u p p lie r B S u p p lie r A S u p p lie r B # X P X P X P M ean 1 8 3 .4 1 8 6 .9 1 9 0 .9 1 155 0 .1 2 140 0 .1 2 147 0 .1 2 M in 1 5 5 .0 1 4 0 .0 147 2 163 0 .1 8 161 0 .1 8 162 0 .1 8 M ax 2 1 7 .0 2 4 1 .5 2 4 2 .5 3 180 0 .2 0 175 0 .2 0 184 0 .2 0 M ode 1 9 0 .0 2 0 1 .3 2 0 2 .1 4 190 0 .3 0 201 0 .3 0 202 0 .3 0 1 9 .0 2 9 .6 2 8 .7 5 205 0 .0 8 210 0 .0 8 221 0 .0 8 6 217 0 .1 2 242 0 .1 2 243 0 .1 2 S td D e v Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 60 Figure 10.18: Cumulative profile showing dominance of Supplier A over Supplier B Cumulative Probability 1 0.8 Make 0.6 Suuplier A Supplier B 0.4 0.2 Chapter 10 Chelst & Canbolat Value Added Decision Making 280 260 240 220 200 180 160 140 120 0 02/26/12 61 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. Chapter 10 Chelst & Canbolat Value Added Decision Making 62 02/26/12 A Design Change Decision Specific Case Volumes 100,000 vehicles One year’s production is relevant Current Customers Notice 0% warranty p = .50 1% warranty p = .30 5% warranty p = .20 Cost/warranty = $50 Chapter 10 Proposed Solves Problem p = .8 Fixed Costs $150,000 Manufacturing Savings $0 p = .30 $ 2.50 p = .70 Chelst & Canbolat Value Added Decision Making 02/26/12 63 Design Change - Schematic Tree & Formula Warranty Cost Solves Problem Design Changes Total Cost Mnfg. Savings End Value Current Design: Warranty Claim * Warranty Cost * Volume New Design: Fixed Cost + (Warranty Claim * Warranty Cost * Volume) + (Manufacturing Savings * Volume) Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 64 Asymmetric Schematic Probability Decision Tree – Design Change Solves Problem Yes No Make Design Change Chapter 10 Manufacturing Savings Warranty Costs Manufacturing Savings Warranty Costs Chelst & Canbolat Value Added Decision Making 02/26/12 65 Figure 10.19: Decision tree for design change example Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 66 Figure 10.20: Design change – Risk profile Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 67 Design Change – Risk Profile Cumulative Probability Cumulative Probability For Change Design of Change Design 1.2 1 0.8 1 : Yes 0.6 2 : No 0.4 0.2 0 -500000 -400000 -300000 -200000 -100000 0 100000 200000 Value Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 68 Interpret Risk Profile & Motivate Next Lecture Describe Worst What Case Scenario for preferred strategy is its probability? Describe a Bad Scenario with a substantial probability of occurrence. What Chapter 10 is its probability? Chelst & Canbolat Value Added Decision Making 69 02/26/12 None Warranty Claims Prob. Percent 0.5 0 0.3 0.01 0.2 0.05 Volumes 100000 Warranty $ 50 Fixed Costs 150000 Yes 80.0% 0 Manuf. Savings 25000 70.0% 250000 2.50 Yes TRUE -150000 30.0% 0 Solves Problem 12000 50.0% None 0 Manuf. Savings Prob. Amount 0.3 0 0.7 2.5 Solves Problem Yes 0.8 No 0.2 0.24 -150000 0.56 100000 None Manuf. Savings 25000 2.50 No 20.0% 0 Warranty Claims -40000 None 30.0% -50000 Low 20.0% -250000 Decision 12000 None No FALSE 0 0 0 Warranty Claims -65000 0 Low High Chapter 10 50.0% 0 30.0% -50000 20.0% -250000 -50000 0 -250000 Chelst & Canbolat Value Added Decision Making 30.0% 0 0.018 -200000 70.0% 250000 30.0% 0 0.042 50000 0.012 Manuf. Savings -400000 -225000 2.50 Change Design 0.07 100000 -25000 None 0.03 -150000 70.0% 250000 Manuf. Savings 2.50 High 30.0% 0 70.0% 250000 0.028 -150000 Answers to Design Change 02/26/12 70 Chapter 10 additional Figures Chelst & Canbolat Value Added Decision Making 02/26/12 71 Figure 10.21: Decision tree for capacity expansion case Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 72 Figure 10.22: Risk profile for capacity expansion case 1 Cumulative Probability 0.8 0.6 Old Tech. New Tech. Productivity 0.4 0.2 Chapter 10 Chelst & Canbolat Value Added Decision Making 42 40 38 36 34 32 30 0 02/26/12 73 Figure 10.29: Schematic tree of postal automation Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 74 Figure 10.30: Schematic decision tree for the transmission line problem Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 75 Figure 10.31: Decision tree for drug development strategy Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 76 Figure 10.32: Peak and expected peak sales for drug development strategy case Chapter 10 Chelst & Canbolat Value Added Decision Making 02/26/12 77