1. Chapter 12 Forecasting Russell and Taylor Operations and Supply Chain Management, 8th Edition

2. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-2

3. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-3

4. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-4

5. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-5

6. Lecture Outline Strategic Role of Forecasting in Supply Chain ManagementStrategic Role of Forecasting in Supply Chain Management Components of Forecasting DemandComponents of Forecasting Demand Time Series MethodsTime Series Methods Forecast AccuracyForecast Accuracy Time Series Forecasting Using ExcelTime Series Forecasting Using Excel Regression MethodsRegression Methods © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-6

7. Learning Objectives Discuss the strategic role of forecasting in supply chain management Describe the forecasting process and identify the components of forecasting demand Forecast demand using various time series models, including exponential smoothing, and trend and seasonal adjustments Discuss and calculate various methods for evaluating forecast accuracy Use Excel to create various forecast models Develop forecasting models with linear and multiple regression analysis © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-7

8. Forecasting Predicting the future Qualitative forecast methods subjective Quantitative forecast methods based on mathematical formulas © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-8

9. Strategic Role of Forecasting in Supply Chain Management Accurate forecasting determines inventory levels in the supply chain Continuous replenishment supplier & customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery Variations of continuous replenishment quick response—the way retailers accommodate ‘fads’ JIT (just-in-time) VMI (vendor-managed inventory) stockless inventory THESE SYSTEMS RELY HEAVILY ON ACCURATE SHORT-TERM FORECASTS © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-9

10. The Effect of Inaccurate Forecasting © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-10

11. Forecasting Quality Management Accurately forecasting customer demand is a key to providing good quality service Strategic Planning Successful strategic planning requires accurate forecasts of future products and markets © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-11

12. Components of Forecasting Demand Time frame Demand behavior Causes of behavior © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-12

13. Time Frame Indicates how far into the future is forecast Short-range forecast typically encompasses the immediate future up to six months Use for detailed scheduling of goods and services Medium-range forecast Six months to two years 18 months is a typical medium-range forecast Addresses aggregate planning—what HR, what inventory, what technology Long-range forecast usually encompasses a period of time longer than two years out to say 50 years with 5 years being a typical long-range forecast Used to make capital investment decisions—what facilities located where, by when? © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-13

14. Demand Behavior Trend a gradual, long-term up or down movement of demand Random variations movements in demand that do not follow a pattern Cycle an up-and-down repetitive movement in demand Seasonal pattern an up-and-down repetitive movement in demand occurring periodically © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-14

15. Forms of Forecast Movement © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-15

16. Forecasting Methods Time series statistical techniques that use historical demand data to predict future demand Regression methods attempt to develop a mathematical relationship between demand and factors that cause its behavior Qualitative use management judgment, expertise, and opinion to predict future demand © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-16

17. Qualitative Methods Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts Delphi method involves soliciting forecasts about technological advances from experts © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-17

18. Forecasting Process 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-18

19. Data Mining Process to analyze large amounts of data A set of IT tools Every day your transaction database is saved into the data warehouse Identify patterns, trends and relationships among and between groups of customers, markets and products This is driven by very low data storage costs 1979: 15 megabyte hard-drive costs $1500 About $100 per megabyte 2017: 5 terabyte Seagate hard drive costs $133 How many megabytes in a terabyte? 1,000,000 So one terabyte should cost $100,000,000 in 1979 $ 5 TB (terabytes) would be $500,000,000 in 1979 $ © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-19

20. 11-20 Forecast when the price of gasoline will return to $3 a gallon : a DELPHI simulation Forecast when the price of gasoline will return to $3 a gallon Write your answer on a piece of paper

21. I’m a politician trying to sell you on the idea that as a country we should impose tariffs on imports We run a $750 billion trade deficit with the rest of the world—that is exports minus imports Our major trading partners are China, Mexico and Canada In order to have balanced trade with these countries what should happen? That would generate a lot of jobs in this country It would increase our annual GDP from $18T to nearly $19T Tell me why that may not be a good idea? © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-21

22. Time Series Time is often the independent variable in forecasting Assumes that what has occurred in the past will continue to occur in the future Relate the forecast to only one factor - time Include naïve forecast moving average exponential smoothing linear trend line © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-22

23. Moving Average Naive forecast demand in current period is used as next period’s forecast Simple moving average uses average demand for a fixed sequence of periods good for stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-23

24. Moving Average: Naïve Approach Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Nov - FORECAST © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-24

25. Moving Average: Naïve Approach PROBLEM: Too Much Volatility! Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH - 120 90 100 75 110 50 75 130 110 90 Nov - FORECAST © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-25

26. Simple Moving Average MA n = n i = 1  DiDi n where n =number of periods in the moving average D i =demand in period i © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-26

27. 3-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDi 3 MOVING AVERAGE © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-27

28. 3-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDi 3 = 90 + 110 + 130 3 = 110 orders for Nov – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MOVING AVERAGE © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-28

29. 5-month Simple Moving Average MA 5 = 5 i = 1  DiDi 5 Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MOVING AVERAGE © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-29

30. 5-month Simple Moving Average MA 5 = 5 i = 1  DiDi 5 = 90 + 110 + 130+75+50 5 = 91 orders for Nov Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-30

31. Smoothing Effects © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-31

32. Weighted Moving Average Adjusts moving average method to more closely reflect data fluctuations WMA n = i = 1  W i D i where W i = the weight for period i, between 0 and 100 percent  W i = 1.00 n © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-32

33. Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 WMA 3 = 3 i = 1  W i D i November Forecast © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-33

34. Weighted Moving Average Example 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-34

35. Exponential Smoothing Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method Smoothing constant, α applied to most recent data © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-35

36. Exponential Smoothing 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-36

37. 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 Effect of Smoothing Constant © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-37

38. Exponential Smoothing (α=0.30) F 2 =  D 1 + (1 -  )F 1 F 3 =  D 2 + (1 -  )F 2 F 13 =  D 12 + (1 -  )F 12 PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-38

39. Exponential Smoothing (α=0.30) 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 PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-39

40. Exponential Smoothing FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 13Jan– © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-40

41. Exponential Smoothing 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-41

42. Exponential Smoothing © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-42

43. Adjusted Exponential Smoothing 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 ≤  ≤  © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-43

44. Adjusted Exponential Smoothing (β=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 T 3 =  (F 3 - F 2 ) + (1 -  ) T 2 AF 3 = F 3 + T 3 T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 AF 13 = F 13 + T 13 = © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-44

45. Adjusted Exponential Smoothing (β=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-45

46. Adjusted Exponential Smoothing FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan3737.00–– 2Feb4037.000.0037.00 3Mar4138.500.4538.95 4Apr3739.750.6940.44 5May 4538.370.0738.44 6Jun5038.370.0738.44 7Jul 4345.841.9747.82 8Aug 4744.420.9545.37 9Sep 5645.711.0546.76 10Oct5250.852.2858.13 11Nov5551.421.7653.19 12Dec 5453.211.7754.98 13Jan–53.611.3654.96 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-46

47. Adjusted Exponential Smoothing FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 13Jan– © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-47

48. Adjusted Exponential Smoothing Forecasts © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-48

49. Linear Trend Line 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-49

50. Least Squares Example x (PERIOD) y (DEMAND) xyx 2 173 240 341 437 545 650 743 847 956 1052 1155 1254 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-50

51. Least Squares Example x = y = b = = a = y - bx  xy - nxy  x 2 - nx 2 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-51

52. Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-52

53. Least Squares Example x (PERIOD) y (DEMAND) xyx 2 173371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-53

54. Least Squares Example 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-54

55. Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-55

56. Seasonal Adjustments   Repetitive increase/ decrease in demand   Use seasonal factor to adjust forecast Seasonal factor = S i = DiDDiD © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-56

57. Seasonal Adjustment 2002 12.68.66.317.5 2003 14.110.37.518.2 2004 15.310.68.119.6 DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = D1DD1D S 2 = = D2DD2D S 4 = = D4DD4D S 3 = = D3DD3D © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-57

58. Seasonal Adjustment SF 1 = (S 1 ) (F 5 ) = SF 2 = (S 2 ) (F 5 ) = SF 3 = (S 3 ) (F 5 ) = SF 4 = (S 4 ) (F 5 ) = y=y= For 2005 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-58

59. Seasonal Adjustment 2002 12.68.66.317.545.0 2003 14.110.37.518.250.1 2004 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1DD1D 42.0 148.7 S 2 = = = 0.20 D2DD2D 29.5 148.7 S 4 = = = 0.37 D4DD4D 55.3 148.7 S 3 = = = 0.15 D3DD3D 21.9 148.7 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-59

60. Seasonal Adjustment 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-60

61. Forecast Accuracy Forecast error difference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-61

62. Mean Absolute Deviation (MAD) where t = period number D t = demand in period t F t = forecast for period t n = total number of periods  = absolute value   D t - F t  n MAD = © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-62

63. 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 PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t | © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-63

64. MAD Calculation   D t - F t  n MAD= © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-64

65. 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 | © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-65

66. MAD Calculation   D t - F t  n MAD= = = 4.85 53.39 11 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-66

67. Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD =  |D t - F t |  D t Cumulative error E =  e t Average error E = etnetn © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-67

68. Comparison of Forecasts FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30)4.859.6%49.314.48 Exponential smoothing (  = 0.50)4.048.5%33.213.02 Adjusted exponential smoothing3.817.5%21.141.92 (  = 0.50,  = 0.30) Linear trend line2.294.9%–– © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-68

69. Forecast Control Tracking signal monitors the forecast to see if it is biased high or low 1 MAD ≈ 0.8 б Control limits of 2 to 5 MADs are used most frequently Tracking signal = =  (D t - F t ) MAD E MAD © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-69

70. Tracking Signal Values 13737.00––– 24037.003.003.003.00 34137.903.106.103.05 43738.83-1.834.272.64 54538.286.7210.993.66 65040.299.6920.684.87 74343.20-0.2020.484.09 84743.143.8624.344.06 95644.3011.7036.045.01 105247.814.1940.234.92 115549.065.9446.175.02 125450.843.1549.324.85 DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-70

71. Tracking Signal Values 13737.00––– 24037.003.003.003.00 34137.903.106.103.05 43738.83-1.834.272.64 54538.286.7210.993.66 65040.299.6920.684.87 74343.20-0.2020.484.09 84743.143.8624.344.06 95644.3011.7036.045.01 105247.814.1940.234.92 115549.065.9446.175.02 125450.843.1549.324.85 DEMANDFORECAST,ERROR  E = PERIODD 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-71

72. Tracking Signal Plot © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-72

73. Statistical Control Charts  =  (D t - F t ) 2 n - 1 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-73   Using  we can calculate statistical control limits for the forecast error   Control limits are typically set at  3    Mean squared error (MSE)   Average of squared forecast errors

74. Statistical Control Charts © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-74

75. Time Series Forecasting Using Excel Excel can be used to develop forecasts: Moving average Exponential smoothing Adjusted exponential smoothing Linear trend line © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-75

76. Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts =B5*(C11-C10)+ (1-B5)*D10 =C10+D10 =ABS(B10-E10) =SUM(F10:F20) =G22/11 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-76

77. Demand and Exponentially Smoothed Forecast Click on “Insert” then “Line” © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-77

78. Data Analysis Option © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-78

79. Forecasting With Seasonal Adjustment © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-79

80. Forecasting With OM Tools © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-80

81. Regression Methods Linear regression mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation Correlation a measure of the strength of the relationship between independent and dependent variables © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-81

82. Linear Regression 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-82

83. Linear Regression Example xy (WINS)(ATTENDANCE) xyx 2 436.3 640.1 641.2 853.0 644.0 745.6 539.0 747.5 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-83

84. Linear Regression Example x = y = b = a = y - bx  xy - nxy 2  x 2 - nx 2 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-84

85. Linear Regression Example xy (WINS)(ATTENDANCE) xyx 2 436.3145.216 640.1240.636 641.2247.236 853.0424.064 644.0264.036 745.6319.249 539.0195.025 747.5332.549 49346.72167.7311 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-85

86. Linear Regression Example 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-86

87. Linear Regression Example ||||||||||| 012345678910 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-87

88. Correlation and Coefficient of Determination Correlation, r Measure of strength of relationship Varies between -1.00 and +1.00 Coefficient of determination, r 2 Percentage of variation in dependent variable resulting from changes in the independent variable © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-88

89. Linear Regression Example xy (WINS)(ATTENDANCE) xyx 2 436.3145.216 640.1240.636 641.2247.236 853.0424.064 644.0264.036 745.6319.249 539.0195.025 747.5332.549 49346.72167.7311 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-89

90. Linear Regression Example 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-90

91. n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Computing Correlation © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-91

92. 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 Computing Correlation © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-92

93. Regression Analysis With Excel =INTERCEPT(B5:B12,A5:A12) =CORREL(B5:B12,A5:A12) =SUM(B5:B12) © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-93

94. Regression Analysis with Excel © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-94

95. Regression Analysis With Excel © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-95

96. Multiple Regression 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 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-96

97. Multiple Regression With Excel r 2, the coefficient of determination Regression equation coefficients for x 1 and x 2 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-97

98. Multiple Regression Example y = 19,094.42 + 3560.99 x 1 +.0368 x 2 Attendance for 7 wins and $60,000 promotion y = © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-98

99. Multiple Regression Example y = 19,094.42 + 3560.99 x 1 +.0368 x 2 Attendance for 7 wins and $60,000 promotion y = 19,094.42 + 3560.99 (7) +.0368 (60,000) = 46,229.35 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-99

100. Copyright 2014 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-100