Forecasting ppt @ doms

1. Forecasting

5. The Effect of Inaccurate Forecasting 12-

10. Forms of Forecast Movement 12- Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement

13. Forecasting Process 12- 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data No Yes

16. Moving Average: Naïve Approach 12- Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 ORDERS MONTH PER MONTH - 120 90 100 75 110 50 75 130 110 90 Nov - FORECAST

17. Simple Moving Average 12- MA n = n i = 1  D i n where n = number of periods in the moving average D i = demand in period i

18. 3-month Simple Moving Average 12- Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH MA 3 = 3 i = 1  D i 3 = 90 + 110 + 130 3 = 110 orders for Nov – – – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 110.0 MOVING AVERAGE

19. 5-month Simple Moving Average 12- Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH – – – – – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE MA 5 = 5 i = 1  D i 5 = 90 + 110 + 130+75+50 5 = 91 orders for Nov

20. Smoothing Effects 12- 150 – 125 – 100 – 75 – 50 – 25 – 0 – | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Actual Orders Month 5-month 3-month

22. Weighted Moving Average Example 12- MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 WMA 3 = 3 i = 1  W i D i = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders November Forecast

24. Exponential Smoothing 12- F t +1 =  D t + (1 -  ) F t where: F t +1 = forecast for next period D t = actual demand for present period F t = previously determined forecast for present period   = weighting factor, smoothing constant

25. Effect of Smoothing Constant 12- 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t + 0.80 F t If  = 0, then F t +1 = 0  D t + 1 F t = F t Forecast does not reflect recent data If  = 1, then F t +1 = 1  D t + 0 F t =  D t Forecast based only on most recent data

26. Exponential Smoothing (α=0.30) 12- F 2 =  D 1 + (1 -  ) F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 =  D 2 + (1 -  ) F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 =  D 12 + (1 -  ) F 12 = (0.30)(54) + (0.70)(50.84) = 51.79 PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54

27. Exponential Smoothing 12- FORECAST, F t + 1 PERIOD MONTH DEMAND (  = 0.3) (  = 0.5) 1 Jan 37 – – 2 Feb 40 37.00 37.00 3 Mar 41 37.90 38.50 4 Apr 37 38.83 39.75 5 May 45 38.28 38.37 6 Jun 50 40.29 41.68 7 Jul 43 43.20 45.84 8 Aug 47 43.14 44.42 9 Sep 56 44.30 45.71 10 Oct 52 47.81 50.85 11 Nov 55 49.06 51.42 12 Dec 54 50.84 53.21 13 Jan – 51.79 53.61

28. Exponential Smoothing 12- 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Actual Orders Month  = 0.50  = 0.30

29. Adjusted Exponential Smoothing 12- AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor T t +1 =  ( F t +1 - F t ) + (1 -  ) T t where T t = the last period trend factor  = a smoothing constant for trend 0 ≤  ≤ 

30. Adjusted Exponential Smoothing (β=0.30) 12- PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54 T 3 =  ( F 3 - F 2 ) + (1 -  ) T 2 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = 38.5 + 0.45 = 38.95 T 13 =  ( F 13 - F 12 ) + (1 -  ) T 12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = 53.61 + 1.36 = 54.97

31. Adjusted Exponential Smoothing 12- FORECAST TREND ADJUSTED PERIOD MONTH DEMAND F t +1 T t +1 FORECAST AF t +1 1 Jan 37 37.00 – – 2 Feb 40 37.00 0.00 37.00 3 Mar 41 38.50 0.45 38.95 4 Apr 37 39.75 0.69 40.44 5 May 45 38.37 0.07 38.44 6 Jun 50 38.37 0.07 38.44 7 Jul 43 45.84 1.97 47.82 8 Aug 47 44.42 0.95 45.37 9 Sep 56 45.71 1.05 46.76 10 Oct 52 50.85 2.28 58.13 11 Nov 55 51.42 1.76 53.19 12 Dec 54 53.21 1.77 54.98 13 Jan – 53.61 1.36 54.96

32. Adjusted Exponential Smoothing Forecasts 12- 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Actual Demand Period Forecast (  = 0.50) Adjusted forecast (  = 0.30)

33. Linear Trend Line 12- y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x b = a = y - b x where n = number of periods x = = mean of the x values y = = mean of the y values  xy - nxy  x 2 - nx 2  x n  y n

34. Least Squares Example 12- x (PERIOD) y (DEMAND) xy x 2 1 73 37 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650

35. Least Squares Example 12- x = = 6.5 y = = 46.42 b = = =1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 3867 - (12)(6.5)(46.42) 650 - 12(6.5) 2  xy - nxy  x 2 - nx 2 78 12 557 12

36. 12- Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units 70 – 60 – 50 – 40 – 30 – 20 – 10 – | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Actual Demand Period Linear trend line

38. Seasonal Adjustment 12- 2002 12.6 8.6 6.3 17.5 45.0 2003 14.1 10.3 7.5 18.2 50.1 2004 15.3 10.6 8.1 19.6 53.6 Total 42.0 29.5 21.9 55.3 148.7 DEMAND (1000’S PER QUARTER) YEAR 1 2 3 4 Total S 1 = = = 0.28 D 1  D 42.0 148.7 S 2 = = = 0.20 D 2  D 29.5 148.7 S 4 = = = 0.37 D 4  D 55.3 148.7 S 3 = = = 0.15 D 3  D 21.9 148.7

39. Seasonal Adjustment 12- SF 1 = ( S 1 ) ( F 5 ) = (0.28)(58.17) = 16.28 SF 2 = ( S 2 ) ( F 5 ) = (0.20)(58.17) = 11.63 SF 3 = ( S 3 ) ( F 5 ) = (0.15)(58.17) = 8.73 SF 4 = ( S 4 ) ( F 5 ) = (0.37)(58.17) = 21.53 y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17 For 2005

42. 12- MAD Example 1 37 37.00 – – 2 40 37.00 3.00 3.00 3 41 37.90 3.10 3.10 4 37 38.83 -1.83 1.83 5 45 38.28 6.72 6.72 6 50 40.29 9.69 9.69 7 43 43.20 -0.20 0.20 8 47 43.14 3.86 3.86 9 56 44.30 11.70 11.70 10 52 47.81 4.19 4.19 11 55 49.06 5.94 5.94 12 54 50.84 3.15 3.15 557 49.31 53.39 PERIOD DEMAND, D t F t (  =0.3) ( D t - F t ) | D t - F t |

44. Other Accuracy Measures 12- Mean absolute percent deviation (MAPD) MAPD =  |D t - F t |  D t Cumulative error E =  e t Average error E =  e t n

45. Comparison of Forecasts 12- FORECAST MAD MAPD E ( E ) Exponential smoothing (  = 0.30) 4.85 9.6% 49.31 4.48 Exponential smoothing (  = 0.50) 4.04 8.5% 33.21 3.02 Adjusted exponential smoothing 3.81 7.5% 21.14 1.92 (  = 0.50,  = 0.30) Linear trend line 2.29 4.9% – –

47. Tracking Signal Values 12- 1 37 37.00 – – – 2 40 37.00 3.00 3.00 3.00 3 41 37.90 3.10 6.10 3.05 4 37 38.83 -1.83 4.27 2.64 5 45 38.28 6.72 10.99 3.66 6 50 40.29 9.69 20.68 4.87 7 43 43.20 -0.20 20.48 4.09 8 47 43.14 3.86 24.34 4.06 9 56 44.30 11.70 36.04 5.01 10 52 47.81 4.19 40.23 4.92 11 55 49.06 5.94 46.17 5.02 12 54 50.84 3.15 49.32 4.85 DEMAND FORECAST, ERROR  E = PERIOD D t F t D t - F t  ( D t - F t ) MAD – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17 TRACKING SIGNAL TS 3 = = 2.00 6.10 3.05

48. Tracking Signal Plot 12- 3  – 2  – 1  – 0  – -1  – -2  – -3  – | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 Tracking signal (MAD) Period Exponential smoothing (  = 0.30) Linear trend line

50. Statistical Control Charts 12- Errors 18.39 – 12.24 – 6.12 – 0 – -6.12 – -12.24 – -18.39 – | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 Period UCL = +3  LCL = -3 

52. Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts 12- =B5*(C11-C10)+ (1-B5)*D10 =C10+D10 =ABS(B10-E10) =SUM(F10:F20) =G22/11

53. Demand and Exponentially Smoothed Forecast 12- Click on “Insert” then “Line”

54. Data Analysis Option 12-

55. Forecasting With Seasonal Adjustment 12-

56. Forecasting With OM Tools 12-

58. Linear Regression 12- y = a + bx a = y - b x b = where a = intercept b = slope of the line x = = mean of the x data y = = mean of the y data  xy - nxy  x 2 - nx 2  x n  y n

59. Linear Regression Example 12- x y (WINS) (ATTENDANCE) xy x 2 4 36.3 145.2 16 6 40.1 240.6 36 6 41.2 247.2 36 8 53.0 424.0 64 6 44.0 264.0 36 7 45.6 319.2 49 5 39.0 195.0 25 7 47.5 332.5 49 49 346.7 2167.7 311

60. Linear Regression Example 12- x = = 6.125 y = = 43.36 b = = = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 346.9 8  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

61. Linear Regression Example 12- | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 60,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = 18.46 + 4.06 x Wins, x Attendance, y y = 18.46 + 4.06(7) = 46.88, or 46,880 Attendance forecast for 7 wins

63. Computing Correlation Copyright 2011 John Wiley & Sons, Inc. 12- n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947

64. Regression Analysis With Excel 12- =INTERCEPT(B5:B12,A5:A12) =CORREL(B5:B12,A5:A12) =SUM(B5:B12)

65. Regression Analysis with Excel 12-

66. Regression Analysis With Excel 12-

67. Multiple Regression 12- Study the relationship of demand to two or more independent variables y =  0 +  1 x 1 +  2 x 2 … +  k x k where  0 = the intercept  1 , … ,  k = parameters for the independent variables x 1 , … , x k = independent variables

68. Multiple Regression With Excel 12- r 2 , the coefficient of determination Regression equation coefficients for x 1 and x 2

69. Multiple Regression Example 12- y = 19,094.42 + 3560.99 x 1 + .0368 x 2 y = 19,094.42 + 3560.99 (7) + .0368 (60,000) = 46,229.35