Hadi Zaklouta3.56 Fall 2009A Decision Tree and Binomial Lattice Analysis of flexibility` Automotive demand is highly uncertain, making flexibility an interesting and valuable approach to system design` Two vehicle productions are under investigation from the perspective of an assembly plant: SUV and small cars` Combining both assembly systems into one assembly plant using shared tools may yield more profits under uncertainty` Delaying plant capacity decisions may also be more profitable` Hypothetical automotive assembly system for manufacturing SUV and small cars using either separate facilities or shared facilities. ` Two sources of flexibility: ◦ Capacity decision making flexibility over time: can we adjust capacity investments?◦ Production flexibility: can both cars be produced on same line? Scenarios (I‐IV)Capacity decision making flexibilityYes NoAssembly line production flexibilityYes IIINo III IV` Sources of uncertainty: first year demand and subsequent growth rates for either product given alongside probabilitiesDemand projections are based on automotive market volatility up to dateExpected Demand in first period S.Dev of Exp.DemandSubsequent growth ratesmall cars 300000 10% -5% to+4%SUVs 130000 10% -4 to -15%SUV Small CarMarket Demand Demand P(D) Demand P(D)Very High 200000 0.10 425,000 0.10High 160000 0.25 375,000 0.25Average 130000 0.30 300,000 0.30Low 100000 0.25 220,000 0.25Very Low 60000 0.10 180,000 0.10EV 130000 300,000S.Dev. 12,665 28,755Standard Deviation (%) 10% 10%YR 1 Market Demand/Growth rateSUV growth rates and probabilities‐0.30 ‐0.20 ‐0.10 0.00 0.10Very High 0.05 0.1 0.275 0.325 0.25High 0.05 0.15 0.35 0.3 0.15Average 0.1 0.2 0.3 0.225 0.175Low 0.15 0.225 0.35 0.2 0.075Very low 0.2 0.3 0.3 0.15 0.05YR1 Market Demand/Growth rateSmall Car growth rates and probabilities‐0.20 ‐0.10 0.00 0.08 0.15Very High 0.05 0.1 0.275 0.325 0.25High 0.05 0.15 0.35 0.3 0.15Average 0.1 0.2 0.3 0.225 0.175Low 0.15 0.225 0.35 0.2 0.075Very low 0.2 0.3 0.3 0.15 0.05` In scenarios I-IV the primary decision variable is assembly line capacity given in # lines where each line can produce a fixed number of vehicles and each has its own costSUV Small Car Multiproduct assemblyUnit Price ($k) 30 20 ‐Capacity of line (1000s) 30 50 40Variable Cost ($k) 20 12 ‐Cost of Equipment/line ($m) 60 50 75Figure 8: Prices, variable costs of product types and annual capacities and equipment costs per line of single vehicle style assemblies and multistyle assembly.Plant DesignSUV_Single StyleSMALL CAR_Single StyleMultiStyleLargest 7916Large 6814Average 5 6 11Small 4 5 8Smallest 2 4 6Summary of important system parameters5 possible optimal capacity decisions for each system` Two decision tree analyses over two years corresponding to both flexible and inflexible capacity decision making cases were conducted for each assembly system (single style vs. multi style). ……………………………………………………………………………………Capacity decision making-inflexibleCapacity decision making-flexible……………………………………………………………………………………` Optimal capacity flexible and capacity inflexible strategies arederived for each assembly system (based on ENPV)Assembly System Best Strategy# LinesNPV of Expected ProfitSUV Single Style Build Large 6 $1,756,057,475Small Car Single Style Build Large 8 $3,424,910,740Multi Style Build Large 14 $4,391,184,9 14Optimal capacity decisions for capacity inflexible scenariosSUV Single Style ULTIMATE FLEXIBLE STRATEGYD1followed by D2 if Yr 1 Market Demand is:NPV of Expected Profits6 lines 6‐Large Very Low$1,759,733,287"Build Large" 6‐Large Low6‐Large Average6‐Large High7‐ Largest Very HighSmall Car Single Style ULTIMATE FLEXIBLE STRATEGYD1followed by D2 if Yr 1 Market Demand is: NPV of Expected Profits8 lines 8‐Large Very Low$3,440,404,665"Build Large" 8‐Large Low8‐Large Average8‐Large High9‐ Largest Very HighMulti style ULTIMATE FLEXIBLE STRATEGYD1 followed by D2 if Yr 1 Market Demand is:NPV of Expected Profits14 lines 14‐ Large Very Low$4,419,756,155"Build Large" 14‐ Large Low14‐ Large Average14‐ Large High16‐ Largest Very HighOptimal capacity decisions for capacity flexible scenariosSurprising result: In all cases, production flexibility is not as profitable as keeping separate lines!` Small Car Single Style assembly system demonstrates the highest increase in ENPV and highest value of capacity decision making flexibility: ~$15.5m` Increases in ENPV indicate value of capacity flexibility is positive, but return on investments (ENPV/CapEx) suggest flexibility not worthpursuing!*production flexibility not profitable` 6 year period lattice analysis was conducted on single style assembly systems to explore value of adding capacity decision making flexibility` Important derived parameters: (system modeled in monthly periods):Average Growth rates Standard Deviationsg(annual) g(monthly) sdev(annual) sdec(monthly)SUV -0.09 -0.00783 0.03 0.0087Small Car 0 0 0.025 0.0072Annual u,d,p valuesSUV Small Caru 1.00870 1.00724d 0.99138 0.99281p 0.04803 0.50000Monthly u,d,p valuesSUV Small Caru1.1095 1.0905d0.9012 0.9170P0.05 0.5c)` Optimal inflexible and flexible designs were identified for each single style assembly system based on ENPV` Inflexible design consists of fixed capacity decision` Flexible design consists of a decision set {D1,D2} with option of exercising expansion to D2ENPV of all designs for single style SUV and small car assembly systems. Yellow represents optimal capacity inflexible strategy,red represents optimal capacity flexible strategy` Flexible Strategies modeled as call optionsSUV demand projections and strategy for exercising Call OptionYear 0 1 2 3 4 5 6Demand (000s) 140 155.3321 172.3433 191.2175 212.1587 235.3933 261.1724126.1813 140 155.3321 172.3433 191.2175 212.1587113.7265 126.1813 140 155.3321 172.3433102.5011 113.7265 126.1813 14092.38367 102.5011 113.726583.26491 92.3836775.04622Optimal strategy: Excercise CALL NO NOYES YES YES YES4 lines to 5 lines OPTION ? NO NO NOYES YESNO NO NOYESNO NO NONO NONOSmall Car demand projections and strategy for exercising Call OptionYear 0 123456Demand (000s) 300 327.139 356.733 389.0042 424.1947 462.5687 504.4142275.1125 300 327.139 356.733 389.0042 424.1947252.2895 275.1125 300 327.139 356.733231.36 252.2895 275.1125 300212.1667 231.36 252.2895194.5657 212.1667178.4248Optimal strategy: