1. Chapter 4 Forecasting

2. Ch. 4: What is covered? Moving AverageMoving Average Weighted Moving AverageWeighted Moving Average Exponential SmoothingExponential Smoothing Trend ProjectionsTrend Projections Seasonal Index/Adjusted-ForecastSeasonal Index/Adjusted-Forecast MAD, CE, Bias, MSE, MAPDMAD, CE, Bias, MSE, MAPD Linear Regression, r, r 2Linear Regression, r, r 2

3. Ch. 4: What is not covered? Trend Adjusted Exponential SmoothingTrend Adjusted Exponential Smoothing Tracking SignalTracking Signal By-Hand computation of anything done by ExcelBy-Hand computation of anything done by Excel –a and b using Least Squares –MAD, CE, Bias, MSE, MAPD, r and r 2 Multiple RegressionMultiple Regression

4. Forecasting Predicting future events Predicting future events Usually demand behavior over a time frame Usually demand behavior over a time frame Qualitative methods Qualitative methods Based on subjective methods Based on subjective methods Quantitative methods Quantitative methods Based on mathematical formulas Based on mathematical formulas

5. Demand Behavior Trend Trend gradual, long-term up or down movement gradual, long-term up or down movement Cycle Cycle up & down movement repeating over long time frame up & down movement repeating over long time frame Seasonal pattern Seasonal pattern periodic oscillation in demand which repeats periodic oscillation in demand which repeats Random movements follow no pattern Random movements follow no pattern

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

7. Moving Average MA n = n i = 1  DiDiDiDi n where n =number of periods in the moving average D i =demand in period i Average several periods of data Average several periods of data Dampen, smooth out changes Dampen, smooth out changes Use when demand is stable with no trend or seasonal pattern Use when demand is stable with no trend or seasonal pattern

8. Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDiDiDi 3 = 90 + 110 + 130 3 = 110 orders for Nov Simple Moving Average

9. Jan120– Feb90 – Mar100 – Apr75103.3 May11088.3 June5095.0 July7578.3 Aug13078.3 Sept11085.0 Oct90105.0 Nov –110.0 ORDERSTHREE-MONTH MONTHPER MONTHMOVING AVERAGE Simple Moving Average

10. Jan120– Feb90 – Mar100 – Apr75103.3 May11088.3 June5095.0 July7578.3 Aug13078.3 Sept11085.0 Oct90105.0 Nov –110.0 ORDERSTHREE-MONTH MONTHPER MONTHMOVING AVERAGE MA 5 = 5 i = 1  DiDiDiDi 5 = 90 + 110 + 130 + 75 + 50 5 = 91 orders for Nov Simple Moving Average

11. Jan120– – Feb90 – – Mar100 – – Apr75103.3 – May11088.3 – June5095.099.0 July7578.385.0 Aug13078.382.0 Sept11085.088.0 Oct90105.095.0 Nov –110.091.0 ORDERSTHREE-MONTHFIVE-MONTH MONTHPER MONTHMOVING AVERAGEMOVING AVERAGE

12. Smoothing Effects 150 150 – 125 125 – 100 100 – 75 75 – 50 50 – 25 25 – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov 5-month 3-month Actual Orders Month

13. Weighted Moving Average WMA n = i = 1  Wi DiWi DiWi DiWi Di where W i = the weight for period i, between 0 and 100 percent  W i = 1.00 Adjusts moving average method to more closely reflect data fluctuations Adjusts moving average method to more closely reflect data fluctuations

14. Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90

15. Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 November forecast WMA 3 = 3 i = 1  Wi DiWi DiWi DiWi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders

16. 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 Averaging method Averaging method Weights most recent data more strongly Weights most recent data more strongly Reacts more to recent changes Reacts more to recent changes Widely used, accurate method Widely used, accurate method Exponential Smoothing

17. Effect of Smoothing Constant 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 0 = 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

18. PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 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 Exponential Smoothing

19. FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3) 1Jan37– 2Feb4037.00 3Mar4137.90 4Apr3738.83 5May 4538.28 6Jun5040.29 7Jul 4343.20 8Aug 4743.14 9Sep 5644.30 10Oct5247.81 11Nov5549.06 12Dec 5450.84 13Jan–51.79 Exponential Smoothing

20. FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb4037.0037.00 3Mar4137.9038.50 4Apr3738.8339.75 5May 4538.2838.37 6Jun5040.2941.68 7Jul 4343.2045.84 8Aug 4743.1444.42 9Sep 5644.3045.71 10Oct5247.8150.85 11Nov5549.0651.42 12Dec 5450.8453.21 13Jan–51.7953.61 Exponential Smoothing

21. 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Orders Month Exponential Smoothing Forecasts

22. 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Orders Month  = 0.30 Exponential Smoothing Forecasts

23. 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213  = 0.50 Actual Orders Month  = 0.30 Exponential Smoothing Forecasts

24. Mean Absolute Deviation (MAD) where t = the period number t = the period number D t = demand in period t D t = demand in period t F t = the forecast for period t F t = the forecast for period t n = the total number of periods n = the total number of periods  = the absolute value  D t - F t  n MAD =

25. MAD Example 13737.00 24037.00 34137.90 43738.83 54538.28 65040.29 74343.20 84743.14 95644.30 105247.81 115549.06 125450.84 557 PERIODDEMAND, D t F t (  =0.3)

26. MAD Example 13737.00–– 24037.003.003.00 34137.903.103.10 43738.83-1.831.83 54538.286.726.72 65040.299.699.69 74343.20-0.200.20 84743.143.863.86 95644.3011.7011.70 105247.814.194.19 115549.065.945.94 125450.843.153.15 55749.3153.39 PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |

27. MAD Example 13737.00–– 24037.003.003.00 34137.903.103.10 43738.83-1.831.83 54538.286.726.72 65040.299.699.69 74343.20-0.200.20 84743.143.863.86 95644.3011.7011.70 105247.814.194.19 115549.065.945.94 125450.843.153.15 55749.3153.39 PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |  D t - F t  n MAD= = = 4.45 53.39 12

28. Other Accuracy Measures Average error = bias E = etetnnetetnnn Mean squared error = E = e2te2tnne2te2tnnn

29. y = a + bx where a =intercept (at period 0) b =slope of the line x =the time period y =forecast for demand for period x Linear Trend Line

30. y = a + bx where a =intercept (at period 0) b =slope of the line x =the 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 Linear Trend Line

31. x (PERIOD) y (DEMAND) 137 240 341 437 545 650 743 847 956 1052 1155 1254 78557 Least Squares Example

32. x (PERIOD) y (DEMAND) xyx 2 137371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650 Least Squares Example

33. x (PERIOD) y (DEMAND) xyx 2 137371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650 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

34. Least Squares Example x (PERIOD) y (DEMAND) xyx 2 173371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650 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 Linear trend line y = 35.2 + 1.72 x

35. Least Squares Example x (PERIOD) y (DEMAND) xyx 2 173371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650 Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13) y = 57.56 units

36. Linear Trend Line 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Demand Period

37. Linear Trend Line 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Demand Period Linear trend line

38. Seasonal Adjustments Repetitive increase/ decrease in demand Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

39. Seasonal Adjustment 1999 12.68.66.317.545.0 2000 14.110.37.518.250.1 2001 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total

40. Seasonal Adjustment 1999 12.68.66.317.545.0 2000 14.110.37.518.250.1 2001 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD42.0148.7 S 2 = = = 0.20 D2D2DDD2D2DD 29.5148.7 S 4 = = = 0.37 D4D4DDD4D4DD 55.3148.7 S 3 = = = 0.15 D3D3DDD3D3DD21.9148.7

41. Seasonal Adjustment 1999 12.68.66.317.545.0 2000 14.110.37.518.250.1 2001 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S i 0.280.200.150.37

42. Seasonal Adjustment 1999 12.68.66.317.545.0 2000 14.110.37.518.250.1 2001 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S i 0.280.200.150.37 y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17 For 2002

43. Seasonal Adjustment SF 1 = (S 1 ) (F 4 )SF 3 = (S 3 ) (F 4 ) = (0.28)(58.17) = 16.28= (0.15)(58.17) = 8.73 SF 2 = (S 2 ) (F 4 )SF 4 = (S 4 ) (F 4 ) = (0.20)(58.17) = 11.63= (0.37)(58.17) = 21.53 1999 12.68.66.317.545.0 2000 14.110.37.518.250.1 2001 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S i 0.280.200.150.37 y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17 For 2002

44. Causal Modeling with Linear Regression Study relationship between two or more variables Study relationship between two or more variables Dependent variable y depends on independent variable x y = a + bx Dependent variable y depends on independent variable x y = a + bx

45. Correlation Correlation, r Correlation, r Measure of strength of relationship Measure of strength of relationship Varies between -1.00 and +1.00 Varies between -1.00 and +1.00 1.00 => an increase in the independent variable results in a linear increase in the dependent 1.00 => an increase in the independent variable results in a linear increase in the dependent -1.00 => an increase in the independent variable results in a linear decrease in the dependent -1.00 => an increase in the independent variable results in a linear decrease in the dependent 0.0 => there does not seem to be a linear relationship between the 0.0 => there does not seem to be a linear relationship between the

46. Coefficient of Determination Coefficient of determination, r 2Coefficient of determination, r 2 –Percentage of variation in dependent variable resulting from changes in the independent variable