MIest 16888 Today' s Topics Multidisciplinary System · An mdo value framework Design Optimization(MSDO) Lifecycle cost models Design for Value Value metrics valuation techniques Lecture 24 Value-based mdo 10May2004 Aircraft example Spacecraft Example Karen willcox Olivier de weck Acknowledgments: Jacob Markish and Ryan Peoples e Massachusetts Institute of Technology.Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology.Prof de Weck and Prof Willco Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics Lest Optimal Design Design Example We need to design a particular portion of the wing Traditionally, design has focused on performance Traditional approach: balance the aero& structural requirements, e.g. for aircraft design We should consider cost: what about an option that is very cheap to optimal= minimum weight manufacture but performance is worse? Increasingly, cost becomes important manufacturing cost? → aerodynamics? structural dynamics? 85% of total lifecycle cost is locked in by the end of aircraft demand?← preliminary design aircraft price? environmental impact? But minimum weight≠ minimum cost≠ maximum value How do we trade performance and cost? What is an appropriate value metric? How much performance are we willing to give up for $100 saved? What is the impact of the low-cost design on price and demand of this aircraft? What is the impact of this design decision on the other aircraft I build? e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics What about market uncertainty?
1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design for Value Lecture 24 10 May 2004 Karen Willcox Olivier de Weck Acknowledgments: Jacob Markish and Ryan Peoples Multidisciplinary System Multidisciplinary System Design Optimization (MSDO) Design Optimization (MSDO) 2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Today’s Topics Today’s Topics • An MDO value framework • Lifecycle cost models • Value metrics & valuation techniques • Value-based MDO • Aircraft example • Spacecraft Example 3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Optimal Design Optimal Design • Traditionally, design has focused on performance e.g. for aircraft design optimal = minimum weight • Increasingly, cost becomes important • 85% of total lifecycle cost is locked in by the end of preliminary design. • But minimum weight z minimum cost z maximum value • What is an appropriate value metric? 4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design Example Design Example • We need to design a particular portion of the wing • Traditional approach: balance the aero & structural requirements, minimize weight • We should consider cost: what about an option that is very cheap to manufacture but performance is worse? aerodynamics? • How do we trade performance and cost? • How much performance are we willing to give up for $100 saved? • What is the impact of the low-cost design on price and demand of this aircraft? • What is the impact of this design decision on the other aircraft I build? • What about market uncertainty? structural dynamics? manufacturing cost? aircraft demand? aircraft price? tooling? environmental impact?
Mlesd Value Optimization Framework 50 Mlesd Challenges b Cost and revenue are difficult to model Modu often models are based on empirical data how to predict for new designs Uncertainty of market Perto ng program leng Module de Valuing flexibility Performance/financial groups even more uncoupled than Massachusetts Institute of Technology -Prof de Weck and Prof willcox e Massachusetts Insttute of Technology. Prof de Weck and Prof Willcox Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics MIest Cost Model Lifecycle Cost Need to model the lifecycle Modul cost of the system Life cycle e Design-Manufacture erforman Module "Value"metric Lifecycle cost Total cost of program over 85% of Total LCC is locked Revenu in by the end of preliminary Time (From Roskam, Figure 2. e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox B Massachusetts Insttute of Technology-Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Module “Value” metric Performance Module Aerodynamics Structures Weights Mission Stability & Control Revenue Module Value Optimization Framework Value Optimization Framework Manufacturing Tooling Design Operation Market factors Fleet parameters Competition “Optimal” design 6 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Challenges Challenges • Cost and revenue are difficult to model – often models are based on empirical data – how to predict for new designs • Uncertainty of market • Long program length • Time value of money • Valuing flexibility • Performance/financial groups even more uncoupled than engineering disciplines 7 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Model Cost Model Need to model the lifecycle cost of the system. Life cycle : Design - Manufacture - Operation - Disposal Lifecycle cost : Total cost of program over life cycle 85% of Total LCC is locked in by the end of preliminary design. Cost Module “Value” metric Performance Module Revenue Module 8 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Lifecycle Cost Lifecycle Cost 0 20 40 60 80 100 65% Conceptual design Preliminary design, system integration Detailed design Manufacturing and acquisition Operation and support Disposal Time Impact on LCC (%) 85% 95% (From Roskam, Figure 2.3)
Mlesd Non-Recurring Cost 16888 M|歌 d Development Cost Model男 Cost incurred one time only Cashflow profiles based on beta curve Engineering airframe design/analysi Typical development time -6 years configuration control Learning effects captured-span, cost Toolin. systems engineering Ing design of tools and fixtures fabrication of tools and fixtures development support ght testing from Markish) e Massachusetts Institute of Technology.Prof de Weck and Prof Willcox e Massachusetts Insttute of normalized time prof de Weck and Prof Willcox Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept. of Aeronautics and Astronautics Lest Recurring Cost Learning Curve Cost incurred per unit As more units are made, the recurring cost per Labor unit decreases fabrication assembly This is the learning curve effect Material to manufacture e.g. Fabrication is done more quickly, less raw material aterial is wasted purchased outside production Y=Y urchased equipment Production support Y number of hours to produce unit X n= log b/log 2 production tooling support b= learning curve factor (-80-100%) engineering support B Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox e Massachusetts Institute of Technology- Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
9 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Non-Recurring Cost Recurring Cost Cost incurred one time only: Engineering - airframe design/analysis - configuration control - systems engineering Tooling - design of tools and fixtures - fabrication of tools and fixtures Other - development support - flight testing Engineering Tooling Other 10 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Development Cost Model Development Cost Model • Cashflow profiles based on beta curve: • Typical development time ~6 years • Learning effects captured – span, cost 1 1 ( ) (1 ) D E c t Kt t 0 0.01 0.02 0.04 0.05 0.06 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 normalized time Support Tool Fab Tool Design ME Engineering normalized cost (from Markish) 11 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Recurring Cost Recurring Cost Cost incurred per unit: Labor - fabrication - assembly - integration Material to manufacture - raw material - purchased outside production - purchased equipment Production support - QA - production tooling support - engineering support Labor Material Support 12 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Learning Curve Learning Curve As more units are made, the recurring cost per unit decreases. This is the learning curve effect. e.g. Fabrication is done more quickly, less material is wasted. n x Y Y x 0 Yx = number of hours to produce unit x n = log b/log 2 b = learning curve factor (~80-100%)
MIest Learning Curve 16888 Mlesd Airplane Related Operating Costs 50, CAPITAL COSTS: CASH AIRPLANE RELATED Financing OPERATING COSTS Crew b=09 0.55 reduced by CAROC Maintenance a factor of GPE Depreciation GPE Maintenance Control Communications Unit number Typical LC slopes: Fab 90%, Assembly 75%, Material 98% CAROC is only 60%ownership costs are significant e Massachusetts Institute of Technology - Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology.Prof de Weck and Prof Willco ngineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics MIest Value metric What is value? Objective function could be different for each stakeholder Need to provide a e.g. manufacturer Vs airline vs. flying public quantitative metric that Program related parameters vs technical parameters incorporates cost, performance and cost, price, production quantity, timing revenue information Traditionally program-related design uncoupled from technical design erforman "Value" metric Module In optimization, need to Custoner es Customer value derived from about what metric we choose Shareholder value derived is directly related to customer Revenu satisfaction e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox 16 From Markish, Engineering Systems Division and Dept of Aeronautics and Astronautics Fig. 1, pg 20 e Massachusetts Institute of Technology- Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
13 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Learning Curve Learning Curve 0.55 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 Unit number Cost of unit b=0.9 Typical LC slopes: Fab 90%, Assembly 75%, Material 98% Every time production doubles, cost is reduced by a factor of 0.9 14 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics CASH AIRPLANE RELATED OPERATING COSTS: Crew Fuel Maintenance Landing Ground Handling GPE Depreciation GPE Maintenance Control & Communications Airplane Related Operating Costs Airplane Related Operating Costs CAROC is only 60% - ownership costs are significant! CAROC 40% 60% Capital Costs CAPITAL COSTS: Financing Insurance Depreciation 15 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value Metric Value Metric Need to provide a quantitative metric that incorporates cost, performance and revenue information. In optimization, need to be especially carefully about what metric we choose... Cost Module “Value” metric Performance Module Revenue Module 16 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics What is Value? What is Value? • Objective function could be different for each stakeholder e.g. manufacturer vs. airline vs. flying public • Program related parameters vs. technical parameters cost, price, production quantity, timing • Traditionally program-related design uncoupled from technical design Customer Value Shareholder Value Product Quality Schedule Cost Economic Value Added Demand Revenue EBIT System Design Price From Markish, Fig. 1, pg 20 Customer value derived from quality, timeliness, price. Shareholder value derived from cost and revenue, which is directly related to customer satisfaction
MIest Value metrics 16888 Valuation Techniques Traditional Metrics Augmented Metrics How much will I need to invest? performance cost How much will I get back? weight revenue When will I get my money back speed profit How much is this going to cost me? quietness How are you handling risk& uncertainty? emissions Investment Criteria commonality Net present value The definition of value will vary depending on your system Discounted payback and your role as a stakeholder, but we must define a Internal rate of return quantifiable metric · Return on investment e Massachusetts Institute of Technology - Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology. Prof de Weck and Prof Willco ngineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics Mlesd Net Present Value(NPV) Discounted Cash Flow(DCF) E5.71 Measure of present value of various cash flows in different Forecast the cash flows, Co, C1,., C of the project over its economic life Cash flow in any given period discounted by the value of a Treat investments as negative cash flow dollar today at that point in the future Determine the appropriate opportunity cost of capital "Time is money (i.e. determine the a dollar tomorrow is worth less today since if properly Use opportunity cost of capital to discount the future invested, a dollar today would be worth more tomorrow cash flow of the project Rate at which future cash flows are discounted is Sum the discounted cash flows to get the net present determined by the discount rate"or " hurdle rate value(NPV) Discount rate is equal to the amount of interest the investor could earn in a single time period(usually a year) if s/he were to invest in a"safer investment e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox e Massachusetts Institute of Technology- Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
17 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value Metrics Value Metrics performance weight speed Traditional Metrics cost revenue profit quietness emissions commonality ... Augmented Metrics The definition of value will vary depending on your system and your role as a stakeholder, but we must define a quantifiable metric. 18 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Valuation Techniques Valuation Techniques Investor questions: • How much will I need to invest? • How much will I get back? • When will I get my money back? • How much is this going to cost me? • How are you handling risk & uncertainty? Investment Criteria • Net present value • Payback • Discounted payback • Internal rate of return • Return on investment 19 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Net Present Value (NPV) Net Present Value (NPV) • Measure of present value of various cash flows in different periods in the future • Cash flow in any given period discounted by the value of a dollar today at that point in the future – “Time is money” – A dollar tomorrow is worth less today since if properly invested, a dollar today would be worth more tomorrow • Rate at which future cash flows are discounted is determined by the “discount rate” or “hurdle rate” – Discount rate is equal to the amount of interest the investor could earn in a single time period (usually a year) if s/he were to invest in a “safer” investment 20 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Discounted Cash Flow (DCF) Discounted Cash Flow (DCF) • Forecast the cash flows, C0, C1, ..., CT of the project over its economic life – Treat investments as negative cash flow • Determine the appropriate opportunity cost of capital (i.e. determine the discount rate r) • Use opportunity cost of capital to discount the future cash flow of the project • Sum the discounted cash flows to get the net present value (NPV) NPV C0 C1 1 r C2 1 r 2 ! CT 1 r T
MIest DCF example 16888 Mlesd Risk-Adjusted Discount Rate 55.9 DCF analysis assumes a fixed schedule of cash flows What about uncertainty Peric Discount Fac Cash Flow Present Value Common approach: use a risk-adjusted discount rate -150,000 150,000 The discount rate is often used to reflect the risk 0935 100.000 associated with a project the riskier the project, use a 0.873 +300000 +261,000 Typical discount rates for commercial aircraft programs Discount rate =7% s18400 Issues with this approach? e Massachusetts Institute of Technology.Prof de Weck and Prof Willcox 22 e Massachusetts Insttute of Technology Prof de Weck and Prof. willcox gineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics Mlesd Net Present Value(NPV) Payback Period How long it takes before entire initial investment is NPy recovered through revenue (1+r) Insensitive to time value of money, i.e. no discounting Gives equal weight to cash flows before cut-off date no weight to cash flows after cut-off date Cannot distinguish between projects with different 口 Cashflow Difficult to decide on appropriate cut-off date Program Time, t lyrs e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox @ Massachusetts Insttute of Technology- Prof de Weck and Prof willcox Engineering Systems Division pt of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
21 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics DCF example DCF example Period Discount Factor Cash Flow Present Value 0 1 -150,000 -150,000 1 0.935 -100,000 -93,500 2 0.873 +300000 +261,000 Discount rate = 7% NPV = $18,400 22 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Risk-Adjusted Discount Rate Adjusted Discount Rate • DCF analysis assumes a fixed schedule of cash flows • What about uncertainty? • Common approach: use a risk-adjusted discount rate • The discount rate is often used to reflect the risk associated with a project: the riskier the project, use a higher discount rate • Typical discount rates for commercial aircraft programs: 12-20% • Issues with this approach? 23 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Net Present Value (NPV) Net Present Value (NPV) 0 (1 ) T t t t C NPV r ¦ -1500 -1000 -500 0 500 1000 1500 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Cashflow DCF (r=12%) Program Time, t [yrs] Cashflow, Pt [$] 24 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Payback Period Payback Period • How long it takes before entire initial investment is recovered through revenue • Insensitive to time value of money, i.e. no discounting • Gives equal weight to cash flows before cut-off date & no weight to cash flows after cut-off date • Cannot distinguish between projects with different NPV • Difficult to decide on appropriate cut-off date
Mlesd Discounted payback 16888 Internal rate of return(IRR) Payback criterion modified to account for the time Investment criterion is"rate of return must be greater value of money than the opportunity cost of capital Internal rate of return is equal to the discount rate for Cash flows before cut-off date are discounted which the NPv is equal to zero Overcomes objection that equal weight is given to C all flows before cut-off date NPV=Co+ (1+/R Cash flows after cut-off date still not given any IRR solution is not unique weight Multiple rates of return for same project iRR doesnt always correlate with NPV NPV does not always decrease as discount rate Increases e Massachusetts Institute of Technology.Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology Prof de Weck and Prof. willcox gineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics Mlesd Return on Investment(ROI) Decision Tree AnalysiS(DTA) Return of an action divided by the cost NPV analysis with different future scenarios of that action Weighted by probability of event occurring ROI- revenue-cost cost Need to decide whether to use actual or discounted cashflows e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox @ Massachusetts Insttute of Technology- Prof de Weck and Prof willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
25 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Discounted payback Discounted payback • Payback criterion modified to account for the time value of money – Cash flows before cut-off date are discounted • Overcomes objection that equal weight is given to all flows before cut-off date • Cash flows after cut-off date still not given any weight 26 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Internal rate of return (IRR) Internal rate of return (IRR) • Investment criterion is “rate of return must be greater than the opportunity cost of capital” • Internal rate of return is equal to the discount rate for which the NPV is equal to zero • IRR solution is not unique – Multiple rates of return for same project • IRR doesn’t always correlate with NPV – NPV does not always decrease as discount rate increases NPV C0 C1 1 IRR C2 1 IRR 2 ! CT 1 IRR T 0 27 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Return on Investment (ROI) Return on Investment (ROI) • Return of an action divided by the cost of that action • Need to decide whether to use actual or discounted cashflows revenue cost cost ROI 28 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Decision Tree Analysis (DTA) Decision Tree Analysis (DTA) • NPV analysis with different future scenarios • Weighted by probability of event occurring
Mlesd Real Options Valuation Approach 50 Mlesd Dynamic Programming Problem Formulation In reality: The firm Cashflows are uncertain Portfolio of designs ability to make decisions as future unfolds Sequential development phases e View an aircraft program as a series of making investment decisions · The market Sale price is steady Spending money on development today gives Quantity demanded is unpredictable the option to build and sell aircraft at a later Units built units demanded date Problem objective Better valuation metriC: expected NPV from Which aircraft to design? dynamic programming algorithm (Markish, Which aircraft to produce? 2002) When? e Massachusetts Institute of Technology.Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology Prof de Weck and Prof. willcox gineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics MIled Dynamic Programming: Problem 50 MId Dynamic Programming: Operating 1639 Modes How to model decision making? St 2. Control variables 湖m如mm 4. Profit function 47101 Solution: E (S )=max I, (S, ", +E.(s,ap)I Solve iteratively CAPACTY e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox e Massachusetts Insttute of Technology . Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
29 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Real Options Valuation Approach Real Options Valuation Approach ¾ In reality: ¾Cashflows are uncertain ¾Ability to make decisions as future unfolds ¾ View an aircraft program as a series of investment decisions ¾ Spending money on development today gives the option to build and sell aircraft at a later date ¾ Better valuation metric: expected NPV from dynamic programming algorithm (Markish, 2002) 30 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Dynamic Programming: Problem Formulation Problem Formulation • The firm: – Portfolio of designs – Sequential development phases – Decision making • The market: – Sale price is steady – Quantity demanded is unpredictable – Units built = units demanded • Problem objective: – Which aircraft to design? – Which aircraft to produce? – When? 31 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Problem Dynamic Programming: Problem Elements Elements 1. State variables st 2. Control variables ut 3. Randomness 4. Profit function 5. Dynamics • Solution: • Solve iteratively. > @¿ ¾ ½ ¯ ® ( ) 1 1 ( ) max ( , ) t t t t t 1 t 1 u t t E F s r F s s u t S 32 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Operating Dynamic Programming: Operating Modes How to model decision making?
MIest Example: BWB 16888 M|歌 d Example: BWB Simulation run男 Blended-Wing-Body (BWB Proposed new jet transport concept 250-seat, long range Part of a larger family sharing 224262830 time years) common centerbody bays wings 8-=,p222 e Massachusetts Institute of l ecnnology-PToT ae wecx ana Hr gineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept, of Aeronautics and Astronautics Lest Example: BWb Importance of Fle Traditional Design Optimization ◆ dynamic programming Objective function -deterministic NPV usually minimum Performance Model Design vector attributes of design e.g. planform geometry function J(x) vector X 357y形284610 Performance model 08171270 5 contains several engineerIng disciplines At baseline of 28 aircraft, DP value is $2. 26B versus deterministic value of $325M e Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox @ Massachusetts Insttute of Technology- Prof. de Weck and Prof willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
33 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Example: BWB • Blended-Wing-Body (BWB): – Proposed new jet transport concept • 250-seat, long range • Part of a larger family sharing common centerbody bays, wings, ... 34 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Simulation Run Example: BWB Simulation Run -4,000,000 -3,000,000 -2,000,000 -1,000,000 0 1,000,000 2,000,000 3,000,000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 time (years) cash flow ($K) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 time (years) operating mode 0 20 40 60 80 100 120 quantity demanded per year mode demand 35 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Importance of Example: BWB Importance of Flexibility Flexibility -10 -5 0 5 10 15 20 25 3 5 7 11 18 28 44 69 108 171 270 initial annual demand forecast program value ($B) dynamic programming deterministic NPV At baseline of 28 aircraft, DP value is $2.26B versus deterministic value of $325M 36 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Traditional Design Optimization Traditional Design Optimization ¾ Objective function: usually minimum weight ¾ Design vector: attributes of design, e.g. planform geometry ¾ Performance model: contains several engineering disciplines Performance Model Optimizer Design vector x Objective function J(x)
Mlesd Coupled MDO Framework 16888 Mlesd Value-Based Optimization Results E50. >Objective function: value metric, e.g. NPV >Boeing BWB case study Simulation model >475 passengers, 7800 nmi range performance and financial Market >Baseline: optimized for minimum GTOW Stochastic element 0. a >Outcomes ost Performance >Comparison of min GTOW and max E[NPV Valuation Model R Demand Traditional NPV vS. stochastiC E[NPV Effect of range requirement on program value Objective >Effect of speed requirement on program value Optimizer Prof de Weck and Prof willcox e Massachusetts Institute of Technology Prof de Weck and Prof. willcox eening Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astro Mlesd Different Objectives, Different Designs 50 Mlesd Deterministic vs Stochastic Valuation 57H Discount rates: 12% and 20% New objective results in Computational expense reduced, but NPV results are tradeoff > Lower structural weight, lower E[NPV] for 12% design =0.58%decrease[relative to E[NPV] for 20% design=3.7% decrease J max-EINPV design Higher fuel burn, lower price A High-Id drives design to reduced development Net result Minimum-GTOW planform costs 2. 3% improvement in value · Traditiona| NPV not Overall design very similar appropriate Constrained to satisfy design As valuation metric As optimization s Unable to move dramatically in design space Maximum-value planform e Massachusetts Institute of Technology Prof de Weck and prof willcox e Massachusetts Insttute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics
37 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Coupled MDO Framework Coupled MDO Framework Performance Model Cost Revenue Optimizer Valuation Market VD Price, Demand Cost Design vector x Objective function J(x) ¾Objective function: value metric, e.g. NPV ¾Simulation model: performance and financial ¾Stochastic element 38 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value-Based Optimization Results Based Optimization Results ¾Boeing BWB case study ¾475 passengers, 7800 nmi range ¾Baseline: optimized for minimum GTOW ¾Outcomes ¾Comparison of min GTOW and max E[NPV] designs ¾Traditional NPV vs. stochastic E[NPV] ¾Effect of range requirement on program value ¾Effect of speed requirement on program value 39 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Different Objectives, Different Designs Different Objectives, Different Designs ¾ New objective results in tradeoff: ¾Lower structural weight, lower cost ¾Higher fuel burn, lower price ¾ Net result 2.3% improvement in value ¾ Overall design very similar ¾Constrained to satisfy design requirements ¾Unable to move dramatically in design space Minimum-GTOW planform Maximum-value planform 40 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Deterministic vs. Stochastic Valuation Deterministic vs. Stochastic Valuation • Discount rates: 12% and 20% – Computational expense reduced, but NPV results are negative – E[NPV] for 12% design = 0.58% decrease – E[NPV] for 20% design = 3.7% decrease • Highrd drives design to reduced development costs • Traditional NPV not appropriate – As valuation metric – As optimization objective relative to max-E[NPV] design -10 -8 -6 -4 -2 0 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Program Year Relative Cash Flow r_d = 12% r_d = 20%
