SeDFAM: Semiconductor Demand Forecast Accuracy Model

Transcription

1 UTDallas.edu/ Metin SeDFAM: Semiconductor Demand Forecast Accuracy Model Metin Çakanyıldırım School of Management University of Texas at Dallas Robin Roundy School of Operations Research Cornell University IIE Portland Conference 23

2 UTDallas.edu/ Metin 2 Semiconductor Industry Industry Characteristics High Technology - Competition leads to Short Product Life Cycles and Frequent Line Width Changes Volatile Demand Fab financing: tool prices Business Contribution: Quantify Risk and Uncertainty Capacity acquisition Customer service: meet market demand Tool utilization

3 UTDallas.edu/ Metin 3 Goals of the Research Forecast Modeling. Covariances of product demands; substitutes - complements 2. Signal deteriorating forecasts 3. Forecast simulation

4 UTDallas.edu/ Metin 4 Demand Modeling A hierarchical model: Product families by general functionality, i.e. memory Products by functionality and line width, i.e. memory CMOS 2 Level of detail driven by capacity planning For families with persistent demands Products have transient demands Family demands are often correlated: Memory and CPU chips Correlations can often be strong. Correlation among the products of the same family e.g. between (memory,cmos8) and (memory,cmos) 2. Correlation among the products of different product families e.g. between (memory,cmos), (X86,CMOS)

5 UTDallas.edu/ Metin 5 Notation p, q: families (e.g. ASICS, X86) tec, tec+: a line width and its successor (e.g. CMOS, CMOS2) (p, tec): a product (e.g. (memory, CMOS)) d p,tec s,t : demand forecast made in s for t for a product (p, tec) d p s,t : demand forecast made in s for t for a family p d p s,t = tec d p,tec s,t H : forecast horizon

6 UTDallas.edu/ Metin 6 Inputs to Forecast Evolution Forecast history for a product (p, tec) Lags Jan... Sep... Dec d p,tec jan,jan... d p,tec sep,sep... d p,tec dec,dec t s = 2 d p,tec nov,jan... d p,tec jul,sep... d p,tec oct,dec H d p,tec jan H,jan... d p,tec sep H,sep... d p,tec dec H,dec

7 UTDallas.edu/ Metin 7 Heath-Jackson Framework for Family Demands d p t,t d p s,t. d p s,t s- d p s,t s d p t,t t v p s,t = d p s,t d p s,t d p t,t d p s,t v p s,t uncorrelated with v p s+,t Distribution of v p s,t depends on t s v p s,t correlated with vs,r q v s = [vs,t]: p Family forecast update vector at time s

8 UTDallas.edu/ Metin 8 SeDFAM Fractional Forecasts: f p,tec s,t : Fraction of demand for family p line width tec or shorter, forecasted from s for t Analyzing Fractional Forecasts f p,tec s,t = linewidth tec dp,tec s,t d p s,t Heath-Jackson approach is not directly applicable Apply a nonlinear transformation mapping Fractional Forecasts to Perceived Ages Apply Heath-Jackson to Perceived Age Forecasts

9 UTDallas.edu/ Metin 9 Computing Perceived Ages from Fractional Forecasts R(δ) f p,tec s,t δ p,tec s,t L δ Perceived age update u p,tec s,t = δ p,tec s,t δ p,tec s,t

10 UTDallas.edu/ Metin Perceived Age Update Vectors Construct iid update vectors u 4 s = [us,s X86,4,..., u X86,4 s,s+h, umem,4 s,s,..., u Mem,4 P C,4 s,s+h, ups,s,...] iid: updates for different technologies are independent u 6 s = [u X86,6 s,s,..., u X86,6 s,s+h, umem,6 s,s,..., u Mem,6 P C,6 s,s+h, up s,s,...] iid: updates created in different time periods are independent u 6 s+ = [u X86,6 s+,s+,..., ux86,6 s+,s+h, umem,6 s+,s+,..., umem,6 s+,s+h Data is missing if (X86, 6) production ends before s + H, up P C,6 s+,s+,...] u tec s N(, Σ), use EM (Expectation Maximization) algorithm by Schafer (997)

11 UTDallas.edu/ Metin Summary: SeDFAM Estimation Procedure Inputs : Demand forecasts, d p,tec s,t. Estimate family forecast update covariance matrix, ˆΛ 2. Fit ramp function ˆR to fractional forecasts 3. Compute perceived age forecasts δ p,tec s,t = ˆR (f p,tec s,t ) 4. Estimate perceived age forecast update covariance matrix, ˆΣ (using the EM algorithm) 5. Use ˆR, ˆΛ, ˆΣ to compute variances and covariances of demands as seen in period r

12 UTDallas.edu/ Metin 2 Step 5 of SeDFAM Estimation Procedure Computing variance of R(δ p,tec s,t ) is complicated because R is not linear Options: Monte-Carlo Sampling or Numerical Integration R is a quadratic spline with 3 knots Knots define regions of integration in R 2 We use Monte-Carlo Sampling

13 UTDallas.edu/ Metin 3 Flowchart for Simulating Forecasts Test accuracy of SeDFAM in estimating capacity demand covariances Perceived Ages δ p,tec r,t = p,tec r,t I r. Perceived Age Updates = (U p,tec s,t ) N(, Σ). U tec s Family Demands d p r,t = Dp r,t I r. Family Demand Updates V s = (V p s,t ) N(, Λ). Perceived Age Forecasts p,tec s,t = p,tec s,t + U p,tec s,t. Family Demand Forecasts D p s,t = Dp s,t + V p s,t. Fractional Demand Forecasts F p,tec s,t = R( p,tec s,t ) Product Demand Forecast D p,tec s,t = D p s,t (F p,tec s,t F p,tec+ s,t ), see (??).

14 UTDallas.edu/ Metin 4 Biases Lag bias: E(update), simple modification of forecast evolution Nonlinearity bias: Fractional forecasts = R (perceived ages) perceived ages unbiased implies fractional forecasts biased Small when R is close to linear.

15 UTDallas.edu/ Metin 5 Capacity Demanded from a Critical Tool A critical tool Used for technologies tec = and tec = 2, and for families A and B Consider capacity demands for a critical tool with processing times, c p,tec tec = tec = 2 A..3 B.7.

16 UTDallas.edu/ Metin 6 Experimental Design Simulation Model Historical Forecasts up to period now N independent evolutions from period now on Estimated covariance matrix of forecasts generated in now True covariance matrix of forecasts generated in now

17 UTDallas.edu/ Metin 7 Heuristics Allocation: Family variances are allocated to technologies Proportional to forecasted volume Proportion: Update is proportional to the forecast d p,tec t h,t dp,tec t,t d p,tec t h,t ξ h Assume ξ h, h =..H has the same distribution for (p, tec) t [Variance of error in d p,tec t,t ] = (d p,tec now,t) 2 var(ξ t now ) Neither Allocation nor Proportion capture correlations (time-wise or among families)

18 UTDallas.edu/ Metin 8 Results: Capacity Acquisition Customer Service: P(meet customer demand) targeted at 84. %. Method LT=2 LT=4 LT=6 LT=8 LT= LT=2 Aver SeDFAM Allocation Proportion Tool Utilization : E(excess capacity / mean demand for capacity) Method LT=2 LT=4 LT=6 LT=8 LT= LT=2 Aver True SeDFAM Allocation Proportion

19 UTDallas.edu/ Metin 9 Robustness Analysis C s,t : forecast (from s for t) of the critical tool capacity required Γ: covariance matrix of [C now+,now+,..., C now+h+,now+h+ ] Performance measure: F (Γ) = (Estimated Γ) (T rue Γ) (T rue Γ) Properties varied without significant effect on performance: Skewness of ramp curves Forecast horizon, H Magnitude of covariances in perceived age updates Correlations across families & time in family demand & age updates

20 UTDallas.edu/ Metin 2 Robustness Analysis: Forecast History.4.35 x, o, +, * : individual runs with 9, 6, 45, 3 months of forecast history.3.25 F(Γ) month aver. 45 month aver. 6 month aver. 9 month aver Starting Months for Replications SedFAM estimates Γ more accurately with longer forecast history

21 UTDallas.edu/ Metin 2 Tests with Industrial Data Model assumptions pass statistical tests with the industrial data Perceived age stationarity tested visually: 5 Perceived age update Ramp age

22 UTDallas.edu/ Metin 22 Product Family Demands 5 DREC MPZ RSP 5 SAPC MPCN MXS SPC 5 SREC Quarters 2 3 Quarters

23 UTDallas.edu/ Metin 23 Data Analysis Select Families: SAPC, SREC, DREC, MXS Life Cycles for MPZ, RSP ended Life Cycles for MPCN, SPC started Make demand stationary Family SAPC SREC DREC MXS Exponent

24 UTDallas.edu/ Metin 24 Family and Fractional Forecasts 3 Family Forecasts Fractional Ramp Forecasts SAPC 2 SAPC SREC 2 SREC DREC 2 DREC MXS 2 MXS Quarters Quarters

25 UTDallas.edu/ Metin 25 Resolution of Uncertainty in Family Forecasts Family Demand Coefficient of Variation in Years DREC, mean= SAPC, mean= MXS, mean= Forecast Lag in Years SREC, mean= Forecast Lag in Years

26 UTDallas.edu/ Metin 26 Resolution of Uncertainty in Perceived Age Forecasts 3 Perceived Age Forecasts, Standard Deviation of Error in Years DREC SAPC SREC Forecast Lag in Years

27 UTDallas.edu/ Metin 27 Correlations in Family Demands DREC SAPC MXS SREC DREC DREC SAPC SAPC-2 MXS MXS SREC SREC DREC and SAPC subtitutes. MXS and SREC complements.

28 UTDallas.edu/ Metin 28 Correlations in Perceived Ages DREC SAPC SREC DREC DREC SAPC SAPC SREC SREC-2-57

29 UTDallas.edu/ Metin 29 Effectiveness of SeDFAM in estimating Γ, in % All key assumptions are statistically verified Correlations: Strong or weak Update Frequency Only impacts SeDFAM performance thru amount of data available Bayesian approach; Computationally stable, but sensitive to prior Sample size Size of F (Γ) by Quarters Aver Λ, Σ Λ, Σ F (Γ) Annu,Quar,Bay. 5, x Semi,Quar,Bay., 22 4x Quar,Quar,Bay. 2, 5 6x Quar,Quar,Fre. 2, 5 6x

30 UTDallas.edu/ Metin 3 Conclusion SeDFAM accurately estimates forecast error variances & correlations is robust requires about 48 periods of history for good performance benefits. quantify risk and uncertainty 2. signals deteriorating forecasts 3. forecast simulation