1. A Finger in the Wind: Forecasting Techniques for Capacity Planning Linwood Merritt Bank of America May, 2005 lin.merritt@bankofamerica.com

2. SCMG Spring 2005 L Merritt, page 2 Purpose of Presentation Robust Capacity Planning entails the analysis of data to project future demand. This analysis can be as simple as a linear trend of historical demand data, and can be as complex as multivariate regression using business drivers combined with analysis of changing business functionality. This presentation is intended as a “Forecasting 101” introduction to trending techniques, and discusses the use of Excel and SAS to perform trend analysis of computer resources and produce Capacity Planning forecasts.

3. SCMG Spring 2005 L Merritt, page 3  Date-based trending Linear Exponential  Business driver trending Single variable Multiple variables Categories of Forecasting Approaches

4. SCMG Spring 2005 L Merritt, page 4 Comparison of Tools  Basic analysis of a relatively small amount of data: spreadsheet product such as Excel.  Automation of projections over a large amount of data and instances: programming language such as SAS.

5. SCMG Spring 2005 L Merritt, page 5 Date-Based Trending  “Steering by your wake:” using the past to predict the future.  Linear: use of “Least Squares” algorithm; single answer to set of differential equations.  Exponential: “Least Squares” trending of exponents.

6. SCMG Spring 2005 L Merritt, page 6 Types of Growth  Linear: straight line (same delta each interval)  Exponential: compound growth (same percentage each interval)

7. SCMG Spring 2005 L Merritt, page 7 Linear Calculations  Linear: straight line (y = b + mx) Linear annual growth: take difference of projections one-year- apart. Linear monthly growth = (annual growth difference) / 12

8. SCMG Spring 2005 L Merritt, page 8 Linear Growth Example  Jan 2004 = 100, Jan 2005 = 120  Linear Annual Growth = 120-100 = 20 Monthly Growth = 20/12 = 1.67 Monthly projections = 100, 101.7, 103.3, … Annual Projections = 100, 120, 140, …

9. SCMG Spring 2005 L Merritt, page 9 Exponential Calculations  Exponential: compound growth (y = b * m x ) log (y) = log b + x * log m y’ = b’ + m’ x Take linear trend of log(y), convert back with exp(y). Compound annual growth: take ratio of projections one-year- apart. Compound monthly growth = (compound annual growth) (1/12)

10. SCMG Spring 2005 L Merritt, page 10 Exponential Growth Example  Jan 2004 = 100, Jan 2005 = 120  Compound Annual Growth = 120/100 = 1.2 Jan 2005 is 120% of Jan 2004, a 20% compound annual growth. Monthly Growth = 1.2 (1/12) = 1.015 Monthly projections = 100, 101.5, 103.1, … Annual Projections = 100, 120, 144, …

11. SCMG Spring 2005 L Merritt, page 11 Linear Regression Basics  Formula: y = b + mx x = independent variable (Date or Business Driver) y = dependent variable (Result) m = “slope” of straight line Excel: “X Variable 1” SAS: date or business driver coefficient b = Intercept Excel (if date-based): # days since 12/31/1899 SAS (if date-based): # days since 1/1/1960

12. SCMG Spring 2005 L Merritt, page 12 Linear Date-Based Trending Using Excel “Trend” Function =TREND($B$2:$B$32,$A$2:$A$32,A2)

13. SCMG Spring 2005 L Merritt, page 13 Regression Statistics` Multiple R0.863991366 R Square0.746481081 Adjusted R Square0.73773905 Standard Error33085.82124 Observations31 ANOVA dfSSMSFSignificance F Regression193473879391 85.389885143.83704E-10 Residual29317454754481094671567 Total301.25219E+11 CoefficientsStandard Errort StatP-valueLower 95% Intercept-7118703.027816014.4395-8.7237463981.32806E-09-8787640.858 X Variable 1201.896571721.848706469.2406647573.83704E-10157.2109253 MonthJan-04Feb-04Mar-04Apr-04May-04 550742.04557000.84562855.84569114.63575171.53 =+$B$17+$B$18*B20 Intercept + (X Variable 1) * Month Excel Data Analysis Regression Tool

14. SCMG Spring 2005 L Merritt, page 14 Linear Date-Based Trending in SAS proc reg noprint data=cmg outest=reglin tableout; model hist = date / selection=rsquare; data proj; set reglin (in=r) cmg (in=c); retain il dl 0; if r then do; if hist = -1; il = intercept; dl = date; delete; end; projl = il + date*dl;

15. SCMG Spring 2005 L Merritt, page 15 SAS “Proc Reg” Output Obs _MODEL_ _TYPE_ _DEPVAR_ _RMSE_ Intercept date hist _IN_ _P_ _EDF_ _RSQ_ 1 MODEL1 PARMS hist 33085.82 -2693937.76 201.897 -1 1 2 29 0.74648 Obs date hist projl 1 01JAN01 350000 329665.30 2 01FEB01 340000 335924.09 3 01MAR01 410000 341577.19 4 01APR01 320000 347835.99 37 01JAN04. 550742.04 38 01FEB04. 557000.84 39 01MAR04. 562855.84 40 01APR04. 569114.63 41 01MAY04. 575171.53

16. SCMG Spring 2005 L Merritt, page 16 Exponential Date-Based Trending Using Excel “Growth” Function =GROWTH($B$2:$B$32,$A$2:$A$32,A2)

17. SCMG Spring 2005 L Merritt, page 17 Exponential Date-Based Trending Using Logarithms =EXP(TREND($C$2:$C$32,$A$2:$A$32,A2))

18. SCMG Spring 2005 L Merritt, page 18 Exponential Date-Based Trending in SAS proc reg noprint data=cmg outest=regexp tableout; model histl = date / selection=rsquare; histl = log(hist); data proj; set regexp (in=r) cmg (in=c); retain il dl 0; if r then do; if hist = -1; ie = intercept; de = date; delete; end; proje = exp (ie + date*de);

19. SCMG Spring 2005 L Merritt, page 19 SAS Exponential Regression Output Obs _MODEL_ _TYPE_ _DEPVAR_ _RMSE_ Intercept date histl _IN_ _P_ _EDF_ _RSQ_ 1 MODEL1 PARMS histl 0.081097 5.49908.000482211 -1 1 2 29 0.73655 Obs date hist proje 1 01JAN01 350000 334592.56 2 01FEB01 340000 339631.79 3 01MAR01 410000 344248.56 4 01APR01 320000 349433.23 37 01JAN04. 567326.04 38 01FEB04. 575870.44 39 01MAR04. 583980.04 40 01APR04. 592775.26 41 01MAY04. 601412.86

20. SCMG Spring 2005 L Merritt, page 20 Linear vs. Exponential Results

21. SCMG Spring 2005 L Merritt, page 21 Footnote: SAS/Graph Linear Trending symbol1 i=rl color=blue v=w h=.5; proc gplot data=cmg; plot hist * date / regeqn;

22. SCMG Spring 2005 L Merritt, page 22 Business Driver Based Forecasting  Linear “least squares” regression using business driver instead of date as independent variable  Formula: y = b + mx x = independent variable (Business Driver) y = dependent variable (Result) m = “slope” of straight line Excel: “X Variable 1” SAS: business driver coefficient b = Intercept

23. SCMG Spring 2005 L Merritt, page 23 Business Driver Based Forecasting Steps  Map business drivers to servers.  Use historical data to correlate.  Use business driver projections to build forecast.

24. SCMG Spring 2005 L Merritt, page 24 Single Business Driver Trending Using Excel “Trend” Function =TREND($B$2:$B$32,$C$2:$C$32,C2)

25. SCMG Spring 2005 L Merritt, page 25 Excel “Tools,” “Data Analysis,” “Regression”

26. SCMG Spring 2005 L Merritt, page 26 Single Business Driver Trending Using Excel Data Analysis =+Business1!$B$17+Business1!$B$18*H2 Intercept + (X Variable 1) * BusDriverA

27. SCMG Spring 2005 L Merritt, page 27 Single Business Driver Trending in SAS proc reg noprint data=cmg outest=regbusa tableout ; model hist = busa / selection=rsquare; data proj; set regbusa (in=a) cmg (in=c); retain ia da 0; if a then do; if hist = -1; ia = intercept; da = busa; delete; end; proja = ia + busa*da;

28. SCMG Spring 2005 L Merritt, page 28 SAS Business Driver Regression Output Obs _MODEL_ _TYPE_ _DEPVAR_ _RMSE_ Intercept busa hist _IN_ _P_ _EDF_ _RSQ_ 1 MODEL1 PARMS hist 33330.20 128231.62 59.0956 -1 1 2 29 0.74272 Obs date hist busa proja 1 01JAN01 350000 3500 335066.38 2 01FEB01 340000 3600 340975.94 3 01MAR01 410000 3700 346885.51 4 01APR01 320000 3900 358704.64 37 01JAN04. 7900 595087.21 38 01FEB04. 7800 589177.65 39 01MAR04. 7900 595087.21 40 01APR04. 8000 600996.78 41 01MAY04. 8200 612815.91

29. SCMG Spring 2005 L Merritt, page 29 Multiple Business Drivers  Linear “least squares” multivariate regression using multiple business drivers as independent variables  Formula: y = b + ma + nb + … a, b, … = independent variables (Business Drivers) y = dependent variable (Result) m, n, … = coefficients of each Business Driver

30. SCMG Spring 2005 L Merritt, page 30 Multiple Business Driver Trending Using Excel “Trend” Function =TREND($B$2:$B$32, $C$2:$D$32,C2:D2)

31. SCMG Spring 2005 L Merritt, page 31 Multiple Business Drivers Using Excel Data Analysis Regression

32. SCMG Spring 2005 L Merritt, page 32 Excel Data Analysis of Multiple Variables

33. SCMG Spring 2005 L Merritt, page 33 = Business2!$B$17 +Business2!$B$18*'Regression Data'!H2 +Business2!$B$19*'Regression Data'!I2 Intercept + (X Variable 1) * BusDriverA + (X Variable 2) * BusDriverB Data Analysis Projections for Multiple Business Drivers

34. SCMG Spring 2005 L Merritt, page 34 Multiple Business Driver Trending in SAS proc reg noprint data=cmg outest=regbusab tableout ; model hist = busa busb / selection=rsquare; data proj; set regbusab (in=b) cmg (in=c); retain ib da db 0; if b then do; if hist = -1 and _IN_ = 2; ib = intercept; da = busa; db = busb; delete; end; projb = ib + busa*da + busb*db;

35. SCMG Spring 2005 L Merritt, page 35 SAS Multivariate Regression Output Obs _MODEL_ _TYPE_ _DEPVAR_ _RMSE_ Intercept busa busb hist _IN_ _P_ _EDF_ _RSQ_ 1 MODEL1 PARMS hist 33330.20 128231.62 59.0956. -1 1 2 29 0.74272 2 MODEL1 PARMS hist 54624.94 205255.71. 253.480 -1 1 2 29 0.30895 3 MODEL1 PARMS hist 33901.16 131950.59 60.1175 -10.300 -1 2 3 28 0.74301 Obs date hist busa busb projb 1 01JAN01 350000 3500 500 337211.58 2 01FEB01 340000 3600 600 342193.28 3 01MAR01 410000 3700 640 347793.01 4 01APR01 320000 3900 800 358168.43 37 01JAN04. 7900 1000 596578.32 38 01FEB04. 7800 1020 590360.56 39 01MAR04. 7900 950 597093.34 40 01APR04. 8000 990 602693.07 41 01MAY04. 8200 980 614819.58

36. SCMG Spring 2005 L Merritt, page 36 Negative Coefficient  A negative coefficient should send a warning flag: Intercept = 131950.59 X Variable 1 = 60.1175 X Variable 2 = -10.300 For 01JAN04, Projection = 131950.6 + 60.1*7900 - 10.3*1000 = 596578 If Business Driver B decreases, the projection increases: Projection = 131950.6 + 60.1*7900 - 10.3*500 = 601729 If the business driver increases enough, the projection may be negative!

37. SCMG Spring 2005 L Merritt, page 37 proc nlin noprint data=cmg outest=regnlin maxiter=10000 method=NEWTON; parms intercept=0 Ren1 =.00000003 Ren2 =.00000003; bounds 0<=Intercept,0<=Ren1, 0<=Ren2; model hist = intercept + busa*Ren1 + busb*Ren2; data proj; set regnlin (in=n) cmg (in=c); retain ni na nb 0; if n then do; if _TYPE_ =: 'FINAL'; ni = intercept; na = ren1; nb = ren2; delete; end; projn = ni + busa*na + busb*nb; Negative Coefficients Nonlinear regression of a linear equation (w/ bounds on coefficients)

38. SCMG Spring 2005 L Merritt, page 38 SAS Non-Linear Regression Output Obs _TYPE_ _STATUS_ _NAME_ _ITER_ _SSE_ intercept Ren1 Ren2 1 ITER 2 Iteration 0 5.6357E12 0.00 0.00 3E-8 2 ITER 2 Iteration 1 5.6357E12 0.00 0.00 1.081384E-8 3 ITER 2 Iteration 2 5.6357E12 0.00 0.00 4.818163E-9 4 ITER 2 Iteration 3 5.6357E12 0.00 0.00 1.070866E-9 5 ITER 2 Iteration 4 5.6357E12 0.00 0.00 4.8535E-10 6 ITER 2 Iteration 5 5.6357E12 0.00 0.00 1.19403E-10 7 ITER 2 Iteration 6 5.6357E12 0.00 0.00 5.04498E-12 8 ITER 2 Iteration 7 5.6357E12 0.00 0.00 -6.6429E-11 9 ITER 2 Iteration 8 5.6357E12 0.00 0.00 -8.8765E-11 10 ITER 2 Iteration 9 5.6357E12 0.00 0.00 -9.5745E-11 11 ITER 2 Iteration 10 5.6357E12 0.00 0.00 -9.7926E-11 12 ITER 2 Iteration 11 5.6357E12 0.00 0.00 -9.9289E-11 13 ITER 2 Iteration 12 5.6357E12 0.00 0.00 -9.9715E-11 14 ITER 2 Iteration 13 5.6357E12 0.00 0.00 -9.9981E-11 15 ITER 2 Iteration 14 5.6357E12 0.00 0.00 -9.9992E-11 16 ITER 2 Iteration 15 5.6357E12 0.00 0.00 -9.9998E-11 17 ITER 2 Iteration 16 5.6357E12 0.00 0.00 -9.9998E-11 18 ITER 2 Iteration 17 32216155095 128231.62 59.10 0 19 FINAL 0 Converged. 32216155095 128231.62 59.10 0 20 COVB 0 Converged intercept. 32216155095 1063952717.10 -207093.13 0 21 COVB 0 Converged Ren1. 32216155095 -207093.13 41.71 0 22 COVB 0 Converged Ren2. 32216155095 0.00 0.00 0

39. SCMG Spring 2005 L Merritt, page 39 SAS Non-Linear Regression Results Obs date hist busa busb projn 1 01JAN01 350000 3500 500 335066.38 2 01FEB01 340000 3600 600 340975.94 3 01MAR01 410000 3700 640 346885.51 4 01APR01 320000 3900 800 358704.64 37 01JAN04. 7900 1000 595087.21 38 01FEB04. 7800 1020 589177.65 39 01MAR04. 7900 950 595087.21 40 01APR04. 8000 990 600996.78 41 01MAY04. 8200 980 612815.91

40. SCMG Spring 2005 L Merritt, page 40 Business Driver Scenario Analysis  Example: Business initiative with incremental daily projections  Approach: Create new monthly totals for affected business driver(s). Run Business Driver based projections with new business driver forecast.

41. SCMG Spring 2005 L Merritt, page 41 Business Driver Scenario Example Sum daily projections for each month New Business Driver projections (add Scenario to baseline, create new graphical projections) Create document with text and graphical analysis

42. SCMG Spring 2005 L Merritt, page 42 Factoring Functionality Growth  Single business driver  Compare business driver growth with resource metric growth  Calculation: (Business Driver input) / (Business Driver Trended) * (Resource Trended)

43. SCMG Spring 2005 L Merritt, page 43 Functionality Trending Using Growth Comparisons =+D2/E2*C2 BusA/(Trended BusA) * (Trended Hist)

44. SCMG Spring 2005 L Merritt, page 44 Functionality Regression Using Date and Business Drivers =TREND($C$2:$C$32, $A$2:$B$32,A2:B2)

45. SCMG Spring 2005 L Merritt, page 45 Comparison of Results

46. SCMG Spring 2005 L Merritt, page 46 Using Growth Rates =IF($C3>0,+D3*$C3^(1/12),D3*$B3^(1/12))

47. SCMG Spring 2005 L Merritt, page 47 Growth Rate Calculations (Bulk Capacity Planning) (#Years) =( Log(Threshold) - Log(Base) ) / Log(1+AnnualGrowth) (#Years) =(UpgradeDate - BaseDate) / 365.25 UpgradeDate = 365.25 * (Log(Threshold)-Log(Base)) / Log(1+AnnualGrowth%) + BaseDate Examples: Base Date = September 2003, Base Utilization = 60%, Threshold = 80%, Annual Growth =20% Base Date = September 2003, Base Utilization = 50%, Threshold = 80%, Annual Growth =15% Base Date = September 2003, Base Utilization = 40%, Threshold = 70%, Annual Growth =25%

48. SCMG Spring 2005 L Merritt, page 48 Bulk Capacity Planning Example =365.25 * (LOG(D14)-LOG(C14)) / LOG(1+E14) + B14 365 * (LOG(Upgrade%)-LOG(Base CPU%))/LOG(1+CAGR%) + Base Date

49. SCMG Spring 2005 L Merritt, page 49 Conditional Formatting

50. SCMG Spring 2005 L Merritt, page 50 Mainframe Workload Projections Mainframe Average Dayshift Projected MIPS by Month System Group AUG04 SEP04 OCT04 NOV04 DEC04 JAN05 CAGR Av/Pk _______ __________________________ ______ ______ ______ ______ ______ ______ ______ ______ Node 1 425.0 431.5 438.1 444.8 451.6 458.5 20.0%.7500 Application A 11.1 11.5 11.9 12.3 12.7 13.2 50.0%.4400 Application B 2.2 2.3 2.4 2.5 2.6 2.7 50.0%.8298 Application C 28.7 25.2 22.2 19.5 17.2 15.1 -78.2%.6461 Application D 14.1 14.3 14.6 14.8 15.1 15.3 22.1%.6258 Application E 1.4 1.0 0.7 0.5 0.4 0.3 -98.1%.6518 Application F 6.8 5.9 5.1 4.4 3.8 3.3 -81.7%.8257 Application G 15.0 15.5 16.0 16.6 17.1 17.7 50.0%.5037 Small 163.6 163.5 163.3 163.2 163.1 162.9 -1.0%.7539

51. SCMG Spring 2005 L Merritt, page 51 Automated Workload Trending Exponential TrendingWorkload DataTrended Resource by Month Override Resource and Growth Rates

52. SCMG Spring 2005 L Merritt, page 52 Other Options  Lag variables as input to regression  Adjustment factors for upgrades  Other regression techniques  Automatic batch runs  “Start Date” configuration  Actual vs. Projected analysis  Timewise regression

53. SCMG Spring 2005 L Merritt, page 53 proc reg noprint data=forecast outest=regdata tableout ; by machine shift; model cpureg = %CtReg / selection=rsquare noint; Automated SAS Regression with Open Number of Business Drivers

54. SCMG Spring 2005 L Merritt, page 54 Actual vs. Projected

55. SCMG Spring 2005 L Merritt, page 55 Individual Actual vs. Projected Analysis Count =232 Avg Error=0.25439 Application ServerBus1Bus2Bus3Bus4Bus5Bus7 ServA0.233 ServB0.585 ServC0.454 ServD0.343 ServD0.596 ServE0.108

56. SCMG Spring 2005 L Merritt, page 56 Actual vs. Projected Graphical Analysis

57. SCMG Spring 2005 L Merritt, page 57 Aggregate Actual vs. Projected (Relative)

58. SCMG Spring 2005 L Merritt, page 58 Aggregate (Average Actual vs. Average Projected)

59. SCMG Spring 2005 L Merritt, page 59 Aggregate Actual vs. Projected (Absolute)

60. SCMG Spring 2005 L Merritt, page 60 Timewise Regression (Proc Forecast)

61. SCMG Spring 2005 L Merritt, page 61 Summary  There are many types of regression trending approaches.  The most useful output is often “compound annual growth.”  “Mileage will vary:” Each situation should be addressed individually.

62. SCMG Spring 2005 L Merritt, page 62 Thanks! Linwood Merritt Bank of America lin.merritt@bankofamerica.com