Flexibility in Multidisciplinary Design: Theory and Experimental ValidationMichel-Alexandre Cardin, PhD CandidateProf. Olivier de WeckESD.77/16.888Lecture 212Outline Introduction Flexibility in Systems Design Emphasis on “Infrastructures” Garage Case Example Experimental Research Design of Experiment Preliminary Analysis and Results Discussion3Risk CategoriesTechnicalRiskCost RiskScheduleRiskMarket/ThreatChangeSchedule SlipsProgrammaticRisk4Value at Risk ConceptValue at Risk (VAR) recognizes fundamental reality: actual value of any design or project can only be known probabilisticallyBecause of inevitable uncertainty in Future demands on systemFuture performance of technologyMany other market, political factorsSystems that Suffered Because of Unmitigated Risk5B-58 Hustler (1960-70)… Originally intended to fly at high altitudes and speeds to avoid Soviet fighters, the introduction of highly accurate Soviet surface-to-air missiles forced the B-58 into a low-level penetration role that severely limited its range and strategic value. This led to a brief operational career between 1960 and 1969.Iridium Constellation (1997-)Iridium went public in 1997 with an ambitious plan to use a 66-satellite constellation of low earth orbit satellites to compete with the mobile phone companies in the market for wireless communications. But for a host of reasons … there were a host of regulatory, marketing and technical complications. By 1999, the company had filed Chapter 11.6Value at Risk DefinitionValue at Risk (VAR) definition: A loss that will not be exceeded at some specified confidence level “We are p percent certain that we will not loose more than V dollars on this project”VAR easy to see on cumulative probability distribution (see next figure)7VAR Cumulative Distribution Function Look at distribution of NPV of designs A, B: 90% VAR for NPVA is -$91M 90% VAR for NPVB is $102MCDF0%20%40%60%80%100%-400 -200 0 200 400 600NPVCumulative ProbabilityNPVA NPVB 90% VAR for NPVA90%VAR for NPVB 10% CDF Probability8VAR and Flexibility VAR is a common financial concept It stresses downside losses, risks However, designers also need to look at upside potential: “Value of Gain”  Flexibility in design provides value by both: Decreasing downside risk Increasing upside potential See next figure9Sources of Value for FlexibilityCut downside ; Expand UpsideValue-at-Risk-and-Gain (VARG)Cumulative ProbabilityValueOriginaldistributionDistribution withflexibilityCut downside risksExpand upside potential10Why Focus on Flexibility? Uncertainty affects future performance Wide-spread engineering practice is very “deterministic” Optimize to “fixed” objectives or forecasts Easy to be “sub-optimal” in the real world Sensitivity analysis done ex post Flexibility shown to improve expected value and performance significantly (10% to 80% vs. initial design) Example case studies in aerospace, automotive, mining, oil, real estate industries See  http://ardent.mit.edu/real_options/Common_course_materials/papers.html http://strategic.mit.edu11What Do We Mean by “Flexibility”? Citygroup Campus, Court Square One and Two, Long Island, New YorkStart smallerReduce exposure to downside risk of overcapacityExpand when neededExtra gains on upside opportunityPearson and Wittels, 200812Other Real-World Examples Ponte 25 de Abril, Lisbon Bluewater commercial center parking garage, U.K.Estudio Mario Novais, iblioteca de Arte-Fundação , Calouste, Gulbenkian (1966)http://en.wikipedia.org/wiki/File:Ponte25Abril1.jpg13Parking Garage Project ExampleValuing Options by Spreadsheet: Parking Garage Case ExampleRichard de Neufville, Stefan Scholtes and Tao Wang -- ASCE Journal of Infrastructure Systems, Vol.12, No.2. pp. 107-111, 200614Intended “Take-Aways” Design project for fixed objective (mission or specifications) is engineering base case Can use optimization as discussed in this class Recognizing uncertainty different design (because of system non-linearities) Harnessing flexibility even better design (it avoids costs, expands only as needed)15Parking Garage Case Garage in area where population expands New commercial/retail opportunities Actual demand is necessarily uncertain Demand drives capacity for # of parking spots Design Opportunity: Strengthened structure Enables future addition of floor(s) (flexibility) Costs more initially (flexibility costs) for same capacity Design issue: is extra cost worthwhile?16Parking Garage Case Details Demand At start is for 750 spaces Over next 10 years is expected to rise (exponentially) by another 750 spaces After year 10 maybe 250 more spaces could be 50% off the projections, either way; Annual volatility for growth is 10% Consider 20 years Average annual revenue/space used = $10,000 The discount rate taken to be 12%17Parking Garage Details (Cont) Costs annual operating costs (staff, cleaning, etc.) = $2,000 /year/space available (note: spaces used is often < spaces available) Annual lease of the land = $3.6 Million  construction cost = $16,000/space + 10% for each level above the first level Site can accommodate 200 cars per level18Step 1: Set Up Base CaseDemand growth as predicted, no variability0 1 2 3 19 20Demand 750 893 1,015 1,688 1,696Capacity 1,200 1,200 1,200 1,200 1,200Revenue $7,500,000 $8,930,000 $10,150,000 $12,000,000 $12,000,000Recurring CostsOperating cost $2,400,000 $2,400,000 $2,400,000 $2,400,000 $2,400,000Land leasing cost $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000Cash flow $1,500,000 $2,930,000 $4,150,000 $6,000,000 $6,000,000Discounted Cash Flow $1,339,286 $2,335,778 $2,953,888 $696,641 $622,001Present value of cash flow $32,574,736Capacity costs for up to two levels $6,400,000Capacity costs for levels above 2 $16,336,320Net present value$6,238,416Yearcapex= capital expenditures=initial investment19Optimal Design for Base Case No Uncertainty-15 -10 -5 05102 3 4 5 6 7 8 9Number of FloorsExpected NPV ($, Millions)Traditional NPVoptimalunder-capacity(lost revenue)over-capacity(too much capex)20Step 2: Simulate Uncertainty 0100200300400500600-17.8 -15.6 -13.5 -11.3 -9.2 -7.0 -4.9 -2.7 -0.6 1.6 3.7 5.9 8.0Frequency 5-floor design Simulated Mean 6-floor design Deterministic ResultLower demand => Loss Higher demand => Gain