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Chapter 5 Structured Trade-Offs for Multiple Objective Decisions: Multi-Attribute Utility Theory Methods to assign weights to objectives and measures Methods to create a non-linear single utility function for a measure when appropriate Most of the chapter’s tables and figures are included in the file. Instructor must decide how many and which examples to use. ©Chelst & Canbolat Value-Added Decision Making 1 MAUT Process TASKS • Structure STEPS Identify Requirements • Describe Alternatives • Clarify Preferences • Analyze Weighted Sum Synthesize Determine Objectives TECHNIQUES Identify Measures Identify Alternatives Gather data for each alternative for each measure Assign weights Conduct Sensitivity Analysis Create a common scale for each measure Conduct Comparative Analysis ©Chelst & Canbolat Value-Added Decision Making Creativity & Expert Judgment Individual Analyses Swing Weight & Mid-Level Splitting Evaluate Hybrid Alternative(s) Chapter 5 2 Weights and Utility Functions Decision maker(s) preferences Weights (across objectives and measures) reflect the relative value assigned to individual objectives and individual measures Utility function (Scale within a measure) Deterministic Reflects relative value (utility) of increasing or decreasing a measure Linear utility function is default relative value is strictly proportional to the measure Probabilistic Reflects attitude towards risk 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 3 (Maximize) Additive utility function: A weighted sum of n different utility functions takes on the following form for assumed linear additive independence between measures and objectives: 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 4 Assign weights to objectives and measures Tradeoffs 9/19/2011 Direct assessment of weights SMART method – swing weights Top-Down – hierarchical ©Chelst & Canbolat Value-Added Decision Making Chapter 5 5 Tradeoffs:Value and Technical Decision Process rs e ak ts M igh n e o i is s W c s D e sse A Value Tradeoff 9/19/2011 E Un ngi de ne rs e rs ta nd & M Re an la ag tio e n s rs hi p Engineers & Managers Struggle ©Chelst & Canbolat Value-Added Decision Making Technical Tradeoff Chapter 5 6 Example of Tradeoff Types : Cost and Service retail outlet Technical trade-off How much will waiting time decrease by adding one more cashier? (queuing theory) How much will customer satisfaction improve if waiting time is reduced by two minutes? Value trade-off How much would a company be willing to spend to reduce waiting time by two minutes? How much more would a customer be willing to pay to reduce waiting time by two minutes? ©Chelst & Canbolat Value-Added Decision Making Chapter 5 7 Difference Confusing for Experienced Managers and Decision Makers Value Tradeoffs are NOT Technical Relationship Tradeoffs Experienced Managers and Designers routinely make technical relationship tradeoffs. They are less comfortable with softer issue of value tradeoffs ©Chelst & Canbolat Value-Added Decision Making Chapter 5 8 Example: Light Bulb Selection Classic tradeoff: Cost vs. Performance Bill Frail has recently been promoted to a product development manager position and he will move to his new office. His new office is being repaired now. He will select light bulbs for the office. In the office, there are 10 bulb fixtures. What is the best bulb for Mr. Frail? How much value does he place on performance relative to cost? 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 9 Activity: Directly assign weights to performance and cost for bulb selection – Weights must sum to one. Measure Weight Performance ………... Cost ………... Sum Total 1 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 10 Data: Three Alternative Bulbs 9/19/2011 10 lamps each with a bulb, 3000 hours a year per lamp Bulb life 60 & 75 W bulbs: 1500 hours (20 bulbs/year) Long-life 100 W bulb:3000 hours (10 bulbs/year) Electric rate: $0.10/kWh Annual Operating Cost: kWh/year*0.10 Bulb Watt Annual Operating . Cost ($) Annual Purchase Cost ($) Total Annual Cost ($) 60 180 9 189 75 225 10 235 100 300 15 315 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 11 No alternative is best on both measures Total Annual Cost ($) 350 300 250 75 Watt 200 150 100 9/19/2011 100 Watt 60 Watt 65 75 Bulb Watts ©Chelst & Canbolat Value-Added Decision Making 110 Chapter 5 12 Determining Weights: Consider ranges Swing Weight method – Two Measures Rank the alternatives by considering the measure ranges Assign 100 points to the highest ranked measure range Assess the relative importance of “swinging” the next highest ranked criterion as a percentage of the highest ranked selection criterion's 100 point Swing Weight. Compute each measure’s relative weight by normalizing the individual Swing Weights. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 13 Activity:Assign weights 10 bulbs Fill in the table below: look at the ranges & assign points, Calculate normalized final weight. Measure Least Preferred Value Most Preferred Value Rank Order Performance 60w 100w …… .…. …… Annual Cost $350 $150 …… .…. …… Total Points ….. Final Weight 1.00 Do not be surprised if there are significant differences from previously assigned weights that ignored ranges. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 14 Repeat Activity:Assign weights for 1000 bulbs (Inexpensive motel) Replace 1000 bulbs – Cost Range Changed Measure Least Preferred Value Most Preferred Value Rank Order Points Final Weight Performance 60w 100w ….. ….. ….. Annual Cost $35,000 $15,000 ….. ….. ….. ….. 1 Total Do not be surprised if there are significant differences from previously assigned weights. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 15 Range specification should impact assignment of weights Different weights for different ranges as well as different decision contexts (office or hotel) Minimum Range to use when assigning weights: Difference between best and worst measures for alternatives considered. Preferable: Pick a range that is realistic for the problem and allows for the possibility of other realistic alternatives to be added The new alternatives may have values outside a too narrowly specified initial range. 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 16 Interpretation of Weights – Range Impact Assume performance rated highest and cost is 2nd most important. Assume the range on cost was assigned 67 points relative to the 100 points for the highest ranked range Weights are 100/167 = .60 and 67/167 = .40 Assume Performance range of 40 watts (60 to 100 watts) This means that an alternative earns 0.60 utility units as the performance increases by 40 watts. = Every watt increase adds 0.015 utility to total score Now imagine the same assigned weights but a broader range from 25 to 100 watts This means an alternative earns 0.60 utility units as the performance increases by 75 watts. = Every watt increase adds ONLY 0.008 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 17 Weight Assignment Interview Question Wrong phrasing: How much weight to cost? Appropriate phrasing A: How much weight for a cost that ranges from $350 to $150 relative to a performance range of 60 to 100 watts B: How much weight for cost that ranges from $400 to $100 relative to performance range of 60 to 100 watts Answers to A and B should be different. Assume 1000 bulbs instead of just 10. C: How much weight for cost that ranges from $35000 to $15000 relative to performance range of 60 to 100 watts 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 18 Next step – Common units Single Utility Scale the Relative Values of a Measure Proportional – Linear: DEFAULT assumption 2. Choose curve’s rough shape and evaluate points 3. Mid-level splitting 4. Direct Assessment – for category variables 1. 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 19 Proportional Scores (SUF): Bulb Selection Assign 0 and 1 for worst and best levels of each objective, respectively SUFp (100 Watt)=1 (Best) & SUFp (60 Watt)=0 (Worst) SUFc ($150)=1(Best) & SUFc ($350)=0 (Worst) A general formula for the linear utility score SUFi (x i) x WorstValue BestValue WorstValue The 75 Watt bulb’s performance: SUFp (75 Watt) 75 60 0.375 100 60 The 75 Watt bulb’s utility for cost: SUFc (75 Watt) 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 235 350 0.575 150 350 Chapter 5 20 Activity: Proportional Scores for Light Bulb Cost range was $150 (best) to $350 (worst) Calculate the utility score for cost measure for the 60-watt and 100-watt bulbs The 60 Watt bulb’s utility for cost: SUFc ($189)= The 100 Watt bulb’s utility for cost: SUFc ($315)= 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 21 SUF : Bulb Selection – Linearity Assumptions Performance 60 Watt Bulb 0 75 Watt Bulb 0.375 100 Watt Bulb 1 Cost 0.805 0.575 0.175 1.00 1.00 100 Watt 0.90 0.80 60 Watt 0.80 0.70 Utility Utility 0.60 0.50 0.40 0.60 75 Watt 0.40 75 Watt 0.30 100 Watt 0.20 0.20 0.10 0.00 60 Watt 0.00 150 60 9/19/2011 75 100 Performance (Watt) 200 250 300 350 Cost ($) Linear Utility Going from 61 to 60 watts performance has the same value in utility as going from 100 to 99 watts ©Chelst & Canbolat Value-Added Decision Making Chapter 5 22 Calculate TOTAL Utility Score This decision maker less concerned about price and more concerned about performance. It is his lamps he must see by. Assigns 0.40 to cost and 0.60 to performance Calculate the TOTAL utility score for a 60 watt bulb U=wpSUFp(Performance)+wcSUFc(Cost) U(60 Watt)=0.60*(0.00)+0.40*(0.805)=0.322 Activity: calculate utility of 75 watt bulb __________________________________ Activity: calculate utility of 100 watt bulb __________________________________ ©Chelst & Canbolat Value-Added Decision Making Chapter 5 23 Calculate Total Utility U=WpSUFp(Performance)+WcSUFc(Cost) The weighted utilities U(60 Watt)= 0.60 *(0.000)+0.40*(0.805)=0.322 U(75 Watt)= 0.60 *(.375)+ 0.40 *(0.575)=0.455 Alternative Utility 100-Watt Bulb 0.675 75-Watt Bulb 0.454 60-Watt Bulb 0.317 Maximize Performance Minimize Cost ©Chelst & Canbolat Value-Added Decision Making Chapter 5 24 Moneymark – financial service phone line Activity: Rank, assign points and calculate weights Strategy 4 staff 5 staff 6 staff Objective Minimize waiting time Annual Cost (Dollars) Waiting Time (Minutes) 115,200 144,000 172,800 11.1 1.9 0.5 Least Most Rank Points Weight Preferred Preferred Order Measure Waiting time (minutes) Annual cost Minimize cost (dollars) 12 0 175,000 115,000 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 25 Assume 0.4 weight for cost Waiting Servers Time Utility 4 11.1 0.075 5 1.9 0.842 6 0.5 0.958 Cost Dollars Utility $115,200 0.997 $144,000 0.517 $172,800 0.037 Total Score Utility 0.444 0.712 0.590 Weights how much money would manager be willing to spend to reduce waiting time from 11.1 minutes to 1.9 minutes and to 0.5 minutes) Alternative Utility 5 staff 6 staff 4 staff 0.712 0.590 0.444 Waiting Time Cost ©Chelst & Canbolat Value-Added Decision Making Chapter 5 26 Interview Process: Relative importance weights Discuss measure ranges Define goals and measures Provide measure level ranges State assumptions Condition the Responses Provide relevant information Elicit / Verify Responses Conduct interview Record response / rationale Check “belief” of sub-totals 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 27 Whose Values and Weights to be traded off? Decision Maker(s) represent values organization Senior executives Customer or Subject Matter Expert(s) reflect values of the ultimate customer or end user. Marketing experts or representative users Engineers who understand relationship between design parameters and performance on key measures of interest. Financial services phone line Waiting time is customer perspective Cost is company perspective 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 28 Activity – used car: large number of measures Preferred Objective Reliability Total Cost Aesthetics Measure Least Most Mileage 130,000 80,000 Dependability ratings 2 circles 4 circles Purchase cost Mpg Maintenance Annual Longevity Color Interior Exterior $6,500 20 mpg $600 5 years Dark Poor Poor Neither works 2 None $2,500 30 mpg $400 3 years Light Excellent Excellent A/C & Heater Accessories Seating Capacity Sound System Rank Order Points Weight Measure Both work 6 or more Radio & CD Sum 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 29 Other Weighting Methods Direct Tradeoffs How much is it worth in dollars to increase the value of this other measure Large Hierarchy Allocate weight to broad categories with range awareness Rank order: reliability, total cost, aesthetics, and accessories Directly assign weights to each major category Subdivide the allocation with each category Within aesthetics Rank order: color, interior and exterior Directly assign local weights to each measure Global weight = product of objective weight and local measure weight 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 30 Hierarchical Approach – Top down Objective Rank Weights Objective 3 0.20 Measure Least Most Mileage 125,000 80,000 Dependability 2 circles 4 circles Purchase cost $6,000 $1,000 Total Cost mpg Maintenance Longevity Color 20 mpg $600 5 years Dark 30 mpg $400 3 years Light 1 0.40 Aesthetics Interior Poor Excellent 4 0.15 Exterior Poor Excellent A/C & Heater Neither work Both work 2 6 or more None Radio & CD Reliability Accessories Seating Sound System 2 Sum 9/19/2011 0.25 Rank Weight Measure Weight Global 2 0.45 0.09 1 0.55 0.11 1 2 4 2 2 0.4 0.25 0.1 0.25 0.4 0.16 0.10 0.04 0.10 0.04 3 0.15 0.015 1 0.45 0.045 3 0.3 0.075 2 0.3 0.075 1 0.4 0.10 1 ©Chelst & Canbolat Value-Added Decision Making 31 Utility or Value Function common scale Convert score on each measure to a point on a zero-to-one scale Default assumption = linearity or proportional 9/19/2011 Often reasonable assumption or approximation Construct nonlinear function Approximate shape Direct assessment Mid-level splitting (time consuming) ©Chelst & Canbolat Value-Added Decision Making Chapter 5 32 Motivate Need for Non-Linear Utility Function Home Choice: 3, 4 , or 5 bedrooms Are 4 bedrooms midway in value between 3 and 5? Kitchen remodeling: range is 12 weeks to 18 weeks Are 15 weeks midway in value between 12 and 18? Waiting Time on Phone: range is 0 to 12 minutes Is 6 minutes midway in value between 0 and 12? Suggest a measure with a non-linear utility function Describe Context ______________________________ 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 33 Activity: Direct Assessment - Bedrooms SUF(5) =1 SUF(3) = 0 SUF(4) = ? Which change produces a greater value improvement? If Change 1 – Improve from 3 to 4 SUF(4) > 0.5 If Change 2 – Improve from 4 to 5 SUF(4) < 0.5 9/19/2011 Which is greater for you _________________ Specify your SUF(4) = _________ ©Chelst & Canbolat Value-Added Decision Making Chapter 5 34 Common Units of “Utility” Conversion To Common Units Single-Measure Utility Function (SUF) 1 Decreasing Rate of Value Constant Rate of Value Increasing Rate of Value Combination 0 9/19/2011 Measure Level There is no right or wrong SUF for a measure. Shape of SUF depends on the context and personal preferences. Preferences should be captured well enough to understand and analyze the current situation. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 35 Management “Targets” for Measures lead to Non-Linear Utility Function **Over-Emphasis on achieving a specific Target leads to an extremely non-linear utility function. Steep curve near target and until target is achieved Relatively flat curve past target 1 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Utility 0 Target Measure Shallower SUF allows for more tradeoff opportunities Chapter 5 36 Key: SELECT Shape of Curve Decreasing rate of value - Concave Small increments in the measure add “significant” value. Less and less value added as approaching most preferred level. (e.g. each additional bedroom) Increasing rate of value - Convex small increments from least preferred level add “little” value. As level improves each additional fixed increment has even greater value. Largest incremental value occurs as measure approaches most preferred value. (e.g. NBA Draft 24th to 23rd and 2nd to 1st) Combination – S shaped Small increases from least preferred value or as approach most preferred add significant value. (e.g. acceleration for normal car driver) 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 37 How Much Non-Linear Detail? Office space 1500 sq feet adequate Could make do with 1000 sq feet Could use extra space up to 2000 sq feet 1.00 Utility 0.75 0.50 0.25 0.00 1000 1200 1400 1600 1800 2000 Floor Area 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 38 Mid-Level splitting Specify Utility and Find Value Mid-level Splitting: continuous measures 1. 2. 3. 9/19/2011 Divide utility range between 0 and 1 into equal intervals Determine measure level with 0.5 utility Determine measure level with 0.25 utility Determine measure level with 0.75 utility ©Chelst & Canbolat Value-Added Decision Making Chapter 5 39 Activity: Mid-Level Splitting - Time Waiting on hold Step 1 Step 2 Step 3 Utility Minutes 0 12 0.5 X 1 0 0 12 0.25 Y 0.5 X Specified in step 1 0.5 X Specified in step 1 0.75 Z 1 0 ©Chelst & Canbolat Value-Added Decision Making Specify X= Y= Z= Chapter 5 40 Nancy Chicila of MONEYMARK – interview Range from 0 to 12 minutes – Find X0.5 Let M = (Best level + Worst level)/2 = 6 = midpoint of total range U(0) = 1 and U(12) = 0 Ask which change produces a greater value improvement. • Change 1: Improve from 12 to 6 min • Change 2: Improve from 6 to 0 If, for example, the answer is that Change 2 has a greater impact, this implies U(6) − U(12) < 0.5 and U(0) − U(6) > 0.5 Because U(0) = 1 and U(12) = 0 then U(6) < 0.5 and the “time” value X0.5 < 6 minutes. In Nancy’s opinion, unless the waiting decreases to less than 5 minutes, the utility score does not reach 0.5. She sets 4 minutes as the 0.5 level. X0.5 = 4. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 41 Nancy Chicila of MONEYMARK – interview Find X0.25 & X0.25 In this example, X0.5 = 4 Calculate midpoint (12 + 4)/2 = 8 • Change 1: Is there greater value in improving from 12 to 8? • Change 2: Or is there greater value in improving from 8 to 4? Nancy preferred Change 2. X0.25 < 8 minutes, and she set X0.25 = 7. Calculate midpoint (4 − 0)/2 = 2 • Change 1: Is there greater value in improving from 4 to 2? • Change 2: Is there greater value in improving from 2 to 0? Nancy viewed change 2 as more significant, since it eliminated all waiting time. She then sets the midpoint at 1.5 min, which means that X0.75 = 1.5. ©Chelst & Canbolat Value-Added Decision Making Chapter 5 42 Nancy’s Mid-level splitting for waiting on hold 1 1 1 Utility Utility Utility 0 0 0 0. 12. Waiting Time (Minutes) 0. 0. Waiting Time (Minutes) Level: 7 Utility: 12. Waiting Time (Minutes) 12. Level: 1.5 Utility: 0.75 0.25 Preference Set = NEW PREF. SET ©Chelst & Canbolat Value-Added Decision Making Chapter 5 43 Comparison of linear and non-linear utility increases difference between 6 and 5 servers Servers 4 5 6 Time 11.1 1.9 0.5 Utility of time Linear Non-Linear 0.08 0.03 0.84 0.70 0.96 0.91 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 44 Rank ordering unchanged but total score gap between 1st and 2nd narrowed Linear Utility for Waiting Time Alternative Utility 5 staff 0.712 6 staff 0.590 4 staff 0.444 Waiting Time Cost Non-linear Utility for Waiting Time Alternative Utility 5 staff 6 staff 4 staff 0.626 0.558 0.419 Waiting Time Cost ©Chelst & Canbolat Value-Added Decision Making Chapter 5 45 Two ways of representing Uncertainty Include Probabilistic data for a specific measure in the Data Matrix for various alternatives Three-Point Estimate Discrete Distribution - approximations Continuous Distribution SEPARATE Risk Measure Separate Measure – label Low Risk (Most Preferred), Medium, and High Risk (Least preferred) 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Inclusion of Uncertainty in MAUT: Bulbs random number of hours of operation affects operating cost Bulb Annual Probability Operating Cost $275 0.4 $300 0.3 $350 0.3 ©Chelst & Canbolat Value-Added Decision Making Separate Risk Measure Less risky vs more risky alternative Supplier Choice – More information or Less Used Car – More variability by brand in reliability Worker – Current employee vs. new employee for MGT Activity – Example and Context ____________ ©Chelst & Canbolat Value-Added Decision Making Word description of risk level of suppliers Word description? Low risk/uncertainty Medium risk/uncertainty High risk/uncertainty ©Chelst & Canbolat Value-Added Decision Making Uncertainty: Impact and Implementations in LDW Uncertainty range may lead to changes in rankings depending upon which values actually occurred (example kitchen remodeler) Logical Decisions Allows for explicit incorporation of values and their probabilities Linear utility function rankings will be based on expected value of each uncertain variable Utility (Expected value) = Expected value of utility Non-linear utility Cannot simply use expected values 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 50 Uncertainty within measures: Cost & Delay Input uncertainty into data for measure Measure Total labor cost Total material cost Build Rite $34,000 $20,000 0% (p=0.33) 2% (p=0.34) 7% (p=0.33) 13 weeks Quality Build $26,000 $12,000 2% (p=0.33) 5% (p=0.34) 9% (p=0.33) 10 weeks Cost Conscious $25,000 $10,000 6% (p=0.33) 9% (p=0.34) 15% (p=0.33) 9 weeks Weeks of delay On time (p=0.33), 1 week late (p=0.34) 2 weeks late (p=0.33) 1 week late(p=0.33) 2 weeks late(p=0.34) 3 weeks late (p=0.33) 2 weeks late (p=0.33) 3 weeks late (p=0.34) 4 weeks late (p=0.33) Cleanliness scale Follow-up and resolution scale Creativity scale Brand & store reputation scale Percent use of subcontractors Fit and finish scale Years in business Quality of references scale Clean Adequate Highly creative Top of line 25% Excellent 12 (Good) Excellent Messy Highly responsive Creative 2nd Best Brand 40% Good 8 (OK) Good Dirty Adequate Mundane 2nd Best Brand 65% Good 22 (Excellent) OK Cost overrun history Duration kitchen unavailable ©Chelst & Canbolat Value-Added Decision Making Chapter 5 51 Figure 5.15: Stacked bar results for kitchen remodeling Alternative Utility Build Rite 0.651 Quality Build 0.630 Cost Conscious 0.462 Max. Quality 9/19/2011 Min. Cost Min. Hassle ©Chelst & Canbolat Value-Added Decision Making Kitchen remodeler: uncertainty for cost & delay scores overlap in top 2 alternatives Alternative Build Rite Quality Build Cost Conscious Utility 0.651 0.630 0.462 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 53 Group Decision Making: Practical Influence diagrams and goals hierarchy provide structured group communication approach consensus Decomposition in objectives, measures, weights and utilities allows for multiple inputs and perspectives Separates data collection and expert judgment from weighting process Rationales for weights Understanding of core differences Logical Decisions allows the analyst to simultaneously incorporate separate weights for multiple decision makers Often even though weights differ, rank orderings may not differ ©Chelst & Canbolat Value-Added Decision Making Chapter 5 54 Additional Concepts Arrow’s impossibility theorem for consistent group decisions Non-additive utility functions Motivation Formula 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 55 Arrow’s Impossibility Theorem: Consistent group aggregation of preferences Arrow and average of preferences Arrow and majority rule vote Yes No Result A>B 2 1 A>B B>C 2 1 B>C A>C 1 2 A<C SME 1 SME 2 SME 3 Average A 1 3 2 2 B 2 1 3 2 C 3 2 1 2 ©Chelst & Canbolat Value-Added Decision Making Chapter 5 56 Non-linear additive utility function Multiplicative form U= k1u1(x1) + k2u2(x2) + (1- k1- k2) u1(x1) u2(x2) Craftsmanship (k1+ k2 < 1) Gap &Misalignment measures Bad on either undermines craftsmanship Competitiveness (k1+ k2 > 1) Pricing & Styling measures Excellent on either makes products competitive ©Chelst & Canbolat Value-Added Decision Making Chapter 5 57 Craftsmanship (k1+ k2 < 1) Gaps and Misalignment measures U= 0.2u1(x1) + 0.2u2(x2) + (0.6)u1(x1) u2(x2) 1 2 3 4 5 Poor on either undermines craftsmanship Alternative Excellent and poor Very good and weak Both very good Both good Both OK 0.2 Gap 1 0.9 0.9 0.75 0.5 Weights 0.2 Misalignment 0 0.1 0.9 0.75 0.5 ©Chelst & Canbolat Value-Added Decision Making 0.6 Product 0 .09 0.81 0.56 0.25 Total 0.2 .25 0.85 0.64 0.35 Chapter 5 58 Competitiveness (k1+ k2 > 1) Pricing & Styling measures U= 0.8u1(x1) + 0.8u2(x2) + (-0.6) u1(x1) u2(x2) 1 2 3 4 5 Excellence on either product competitive Alternative Excellent and poor Very good and weak Both very good Both good Both OK 0.8 Price 1 0.9 0.9 0.75 0.5 Weights 0.8 Styling 0 0.1 0.9 0.75 0.5 ©Chelst & Canbolat Value-Added Decision Making -0.6 Product 0 .09 0.81 0.56 0.25 Total 0.8 .75 0.95 0.86 0.5 Chapter 5 59 MAUT Process TASKS • Structure STEPS Identify Requirements • Describe Alternatives • Clarify Preferences • Analyze Weighted Sum Synthesize Determine Objectives TECHNIQUES Identify Measures Identify Alternatives Gather data for each alternative for each measure Assign weights Conduct Sensitivity Analysis Create a common scale for each measure Conduct Comparative Analysis ©Chelst & Canbolat Value-Added Decision Making Creativity & Expert Judgment Individual Analyses Swing Weight & Mid-Level Splitting Evaluate Hybrid Alternative(s) Next Chapter Chapter 5 60 Additional Figures from text 5.8 Used car scores 5.17, 5.19 and 5.20 Nuclear emergency management 5.21 and 5.23 Coating Process 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making 61 Figure 5.8: Ranking of the alternatives for the used car example Alternative Utility Chevrolet Cavalier Honda Civic Ford Ranger Mazda Miata 0.613 0.470 0.440 0.411 Total Cost Aesthetics 9/19/2011 Accessories Reliability ©Chelst & Canbolat Value-Added Decision Making Figure 5.17: Goals hierarchy for nuclear emergency management case Thyroid cancer Health Other cancers Positive effects Overall SocioPsychological Negative effects Cost Political cost 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Figure 5.19: Ranking nuclear emergency management strategies-base case scenario 9/19/2011 ©Chelst & Canbolat Value-Added Decision Making Figure 5.20: Ranking nuclear emergency management strategies-worst case scenario Alternative 9/19/2011 Utility Strategy 0 0.043 Strategy 1 0.431 Strategy 2 0.636 Strategy 3 0.762 Strategy 4 0.781 Costs Other cancers Political cost Soc. psych negative Soc. psych positive Thyroid cancer ©Chelst & Canbolat Value-Added Decision Making Figure 5.21: Goals hierarchy for coating process selection Max. Performance Max. Reliability Select the Best Coating Process Min. Cost Max. Flexibility Flexibilityc Min. Weight Weight Max. Coating Control Min. Foreign Material Foreign Material Min. Facilities & Tooling Facilities & Tooling Cost Min. Labor Labor Cost Min. Material Min. Scrap Min. Development Time 9/19/2011 c Coating Control c Material Cost Scrap Cost Development Time ©Chelst & Canbolat Value-Added Decision Making Figure 5.23: Stacked bar ranking for the coating processes Alternative Utility Selective Spray 0.702 Sil-Gel Potting 0.650 Coat and Extract 0.596 Minimize Cost Maximize Reliability Minimize Development Time 9/19/2011 Maximize Performance ©Chelst & Canbolat Value-Added Decision Making