1. Hadi Zaklouta 3.56 Fall 2009 A Decision Tree and Binomial Lattice Analysis of flexibility

2.  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

3.  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 flexibility YesNo Assembly line production flexibility YesIII NoIIIIV

4.  Sources of uncertainty: first year demand and subsequent growth rates for either product given alongside probabilities Demand projections are based on automotive market volatility up to date Expected Demand in first periodS.Dev of Exp.Demand Subsequent growth rate small cars30000010%-5% to+4% SUVs13000010%-4 to -15% SUVSmall Car Market DemandDemandP(D)DemandP(D) Very High2000000.10425,0000.10 High1600000.25375,0000.25 Average1300000.30300,0000.30 Low1000000.25220,0000.25 Very Low600000.10180,0000.10 EV130000300,000 S.Dev. 12,665 28,755 Standard Deviation (%) 10% YR 1 Market Demand /Growth rate SUV growth rates and probabilities -0.30-0.20-0.100.000.10 Very High0.050.10.2750.3250.25 High0.050.150.350.30.15 Average0.10.20.30.2250.175 Low0.150.2250.350.20.075 Very low0.20.3 0.150.05 YR1 Market Demand/G rowth rate Small Car growth rates and probabilities -0.20-0.100.000.080.15 Very High0.050.10.2750.3250.25 High0.050.150.350.30.15 Average0.10.20.30.2250.175 Low0.150.2250.350.20.075 Very low0.20.3 0.150.05

5.  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 cost SUVSmall CarMultiproduct assembly Unit Price ($k)3020- Capacity of line (1000s)305040 Variable Cost ($k)2012- Cost of Equipment/line ($m)605075 Figure 8: Prices, variable costs of product types and annual capacities and equipment costs per line of single vehicle style assemblies and multistyle assembly. Plant Design SUV_Single Style SMALL CAR_Single StyleMultiStyle Largest7916 Large6814 Average5611 Small458 Smallest246 Summary of important system parameters 5 possible optimal capacity decisions for each system

6.  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-inflexible Capacity decision making-flexible …………

7.  Optimal capacity flexible and capacity inflexible strategies are derived for each assembly system (based on ENPV) Assembly SystemBest Strategy # Lines NPV of Expected Profit SUV Single StyleBuild Large6$1,756,057,475 Small Car Single StyleBuild Large8$3,424,910,740 Multi StyleBuild Large14$4,391,184,914 Optimal capacity decisions for capacity inflexible scenarios SUV Single Style ULTIMATE FLEXIBLE STRATEGY D1 followed byD2if Yr 1 Market Demand is: NPV of Expected Profits 6 lines6-LargeVery Low $1,759,733,287 "Build Large"6-LargeLow 6-LargeAverage 6-LargeHigh 7- LargestVery High Small Car Single Style ULTIMATE FLEXIBLE STRATEGY D1 followe d byD2if Yr 1 Market Demand is:NPV of Expected Profits 8 lines8-LargeVery Low $3,440,404,665 "Build Large"8-LargeLow 8-LargeAverage 8-LargeHigh 9- LargestVery High Multi style ULTIMATE FLEXIBLE STRATEGY D1followed byD2if Yr 1 Market Demand is: NPV of Expected Profits 14 lines 14- LargeVery Low $4,419,756,155 "Build Large"14- LargeLow 14- LargeAverage 14- LargeHigh 16- LargestVery High Optimal capacity decisions for capacity flexible scenarios Surprising result: In all cases, production flexibility is not as profitable as keeping separate lines!

8.  Small Car Single Style assembly system demonstrates the highest increase in ENPV and highest value of capacity decision making flexibility: ~$15.5m

9. SUVSmall CarMulti-style* SingleStyle SUV+Small Car Capacity Decision making flexibility InflexibleFlexibleInflexibleFlexibleInflexibleFlexibleInflexibleFlexible ENPV ($bn) 1.7561.7603.4253.4404.3914.4205.1815.200 P10 ($bn) 0.708 2.084 1.426 2.793 P90 ($bn) 2.4112.3944.6104.6066.207 7.0217.001 Max NPV ($bn) 2.7412.9104.7815.0256.9047.2987.5227.935 Min NPV ($bn) 0.510 1.694 0.837 2.204 CapEX ($bn)*Actual 0.38 - 0.43 - 1.0850.808 Min- 0.38 - 0.43- 1.085 - 0.808 Max**- 0.43 - 0.47 - 1.211-0.902 ENPV/CapEX (%)Actual 459 804 405641 Max- 460 - 808 - 407 - 643 Min- 406 - 734 - 365 - 577  Increases in ENPV indicate value of capacity flexibility is positive, but return on investments (ENPV/CapEx) suggest flexibility not worth pursuing! *production flexibility not profitable

10.  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 ratesStandard Deviations g(annu al)g(monthly)sdev(annual)sdec(monthly) SUV-0.09-0.007830.030.0087 Small Car000.0250.0072 Annual u,d,p values SUV Small Car u1.008701.00724 d0.991380.99281 p 0.04803 0.50000 Monthly u,d,p values SUV Small Car u 1.10951.0905 d 0.90120.9170 P 0.050.5 c)

11. SUV ENPV ($bn) D2 (# lines) 24567 D1 (# lines) 21.4132.0791.5721.4231.414 4-2.07912.07942.07922.0791 5--1.571961.572 6---0.975 7----0.375 S.C. ENPV ($bn) D2 45689 D1 44.5315.5996.2595.8855.413 5-5.5996.2596.0875.904 6--6.2596.4076.355 8---5.8855.890 9----5.413  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 D2 ENPV of all designs for single style SUV and small car assembly systems. Yellow represents optimal capacity inflexible strategy, red represents optimal capacity flexible strategy

12.  Flexible Strategies modeled as call options SUV demand projections and strategy for exercising Call Option Year0123456 Demand (000s)140155.3321172.3433191.2175212.1587235.3933261.1724 126.1813140155.3321172.3433191.2175212.1587 113.7265126.1813140155.3321172.3433 102.5011113.7265126.1813140 92.38367102.5011113.7265 83.2649192.38367 75.04622 Optimal strategy:Excercise CALLNO YES 4 lines to 5 linesOPTION ?NO YES NO YES NO Small Car demand projections and strategy for exercising Call Option Year0123456 Demand (000s)300327.139356.733389.0042424.1947462.5687504.4142 275.1125300327.139356.733389.0042424.1947 252.2895275.1125300327.139356.733 231.36252.2895275.1125300 212.1667231.36252.2895 194.5657212.1667 178.4248 Optimal strategy:Exercise CALLNO YES 6 lines to 8 linesOPTION ?NO YES NO

13.  Again, Small Car Single Style assembly system demonstrates the highest increase in ENPV and highest value of capacity decision making flexibility: ~$148m

14.  Again, increases in ENPV indicate value of capacity flexibility is positive in all cases, but return on investments (ENPV/CapEx) suggest flexibility not worth pursuing! SUVSmall CarMulti-style Capacity Decision making flexibility InflexibleFlexibleInflexibleFlexible Inflexibl e Flexibl e ENPV ($bn) 2.079 6.2596.407 Decision tree analysis has shown that production flexibility is not profitable in all criteria (see Figure 18). Therefore, no further analysis was conducted P10 ($bn) 1.973 5.258 P90 ($bn) 2.467 6.7997.479 Max NPV ($bn) 2.8263.2516.7998.101 Min NPV ($bn) 1.973 4.492 CapEX ($bn) *Actual2.42-3.02- Min-2.42-3.02 Max**-2.87-3.71 ENPV/CapEX (%)Actual85.95 207.06 Max-85.96-211.98 Min-72.42-172.81

15.  Value of production flexibility depends on demand projections (in this example it isn’t worth pursuing)  Value of capacity decision making flexibility depends on system parameters: demand projections, uncertainty, capital costs, profit margin, project lifetime to name a few (in this example most valuable for small car assemblies)  Value of capacity decision making also depends on criteria for evaluation. ENPV and ROI may give different rankings  Lattice Analysis easier to use but more approximate than decision tree analysis