The document discusses various quantitative forecasting techniques including time series methods like moving averages and exponential smoothing. It provides examples of how to calculate 3-period moving averages and exponential smoothing forecasts using sample sales data. Exponential smoothing places more weight on recent observations compared to moving averages. The smoothing constant determines how quickly older data is discounted.

8. Forecast Categories TYPES Qualitative Executive opinions Sales force surveys Delphi method Consumer surveys Quantitative Times series methods Associative (causal) methods

19. Product Demand Charted over 4 Years with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaks Trend component Actual demand line Average demand over four years Demand for product or service Random variation

24. You’re manager of a museum store that sells historical replicas. You want to forecast sales of item (123) for 2000 using a 3 -period moving average. 1995 4 1996 6 1997 5 1998 3 1999 7 Moving Average Example © 1995 Corel Corp.

25. Moving Average Solution

26. Moving Average Solution

27. Moving Average Solution

28. Moving Average Graph 95 96 97 98 99 00 Year Sales 2 4 6 8 Actual Forecast

30. Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average

34. You’re organizing a Kwanza meeting. You want to forecast attendance for 2000 using exponential smoothing (  = .10 ). The 1995 (made in 1994) forecast was 175 . Actual data: 1995 180 1996 168 1997 159 1998 175 1999 190 © 1995 Corel Corp. Exponential Smoothing Example

35. F t = F t -1 +  · ( A t -1 - F t -1 ) Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 1997 159 1998 175 1999 190 2000 NA Exponential Smoothing Solution 175.00 +

36. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10 ( 1997 159 1998 175 1999 190 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

37. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10 (180 - 1997 159 1998 175 1999 190 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

38. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10 (180 - 175.00 ) 1997 159 1998 175 1999 190 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

39. Exponential Smoothing Solution Time Actual Forecast, F t ( α  = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10 (180 - 175.00 ) = 175.50 1997 159 1998 175 1999 190 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

40. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10 (168 - 175.50 ) = 174.75 1998 175 1999 190 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

41. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10(168 - 175.50) = 174.75 1998 175 1999 190 2000 NA 174.75 + .10 (159 - 174.75 ) = 173.18 F t = F t -1 +  · ( A t -1 - F t -1 )

42. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10(168 - 175.50) = 174.75 1998 175 174.75 + .10(159 - 174.75) = 173.18 1999 190 173.18 + .10 (175 - 173.18 ) = 173.36 2000 NA F t = F t -1 +  · ( A t -1 - F t -1 )

43. Exponential Smoothing Solution Time Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10(168 - 175.50) = 174.75 1998 175 174.75 + .10(159 - 174.75) = 173.18 1999 190 173.18 + .10(175 - 173.18) = 173.36 2000 NA 173.36 + .10 (190 - 173.36 ) = 175.02 F t = F t -1 +  · ( A t -1 - F t -1 )

44. Exponential Smoothing Graph Year Sales 140 150 160 170 180 190 93 94 95 96 97 98 Actual Forecast

45. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

46. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% 9% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

47. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% 9% 8.1% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

48. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% 9% 8.1% 90% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

49. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% 9% 8.1% 90% 9% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

50. F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 + ... Forecast Effects of Smoothing Constant  10% 9% 8.1% 90% 9% 0.9% Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2  =  = 0.10  = 0.90

52. How to Choose  Seek to minimize the Mean Absolute Deviation (MAD) If: Forecast error = demand - forecast Then: Note that the sum of all weights in exponential smoothing equals to 1. It is popular because of the simplicity of data keeping.

54. Exponential Smoothing with Trend Adjustment Forecast including trend (FIT t ) = exponentially smoothed forecast (F t ) + exponentially smoothed trend (T t )

55. Exponential Smoothing with Trend Adjustment - continued F t =  (Actual demand this period) + (1-  )(Forecast last period+Trend estimate last period) F t =  (A t-1 ) + (1-  )F t-1 + T t-1 or T t =  (Forecast this period - Forecast last period) + (1-  )(Trend estimate last period T t =  (F t - F t-1 ) + (1-  )T t-1 or

57. Comparison of Forecasts Actual Demand Exponential smoothing Exponential smoothing + Trend

59. b > 0 b < 0 a a Y Time, X Linear Trend Projection Model

61. How to Find a and b: Least Squares Equations Equation: Slope: Y-Intercept: Criteria of finding a and b :

69. Example of Multiplicative Seasonal Model The following trend projection is used to predict quarterly demand: Y = 350 - 2.5t, where t = 1 in the first quarter of 1998. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2000? (10%) Period Projection Adjusted 9 327.5 491.25 10 325 260 11 322.5 354.75 12 320 192

71. Past Data of Nurse Demand: What patterns can be observed?

72. Forecasting Issues During a Product’s Life Introduction Growth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OM Strategy/Issues Company Strategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet

74. Plot of a Tracking Signal Time Lower control limit Upper control limit Signal exceeded limit Tracking signal Acceptable range MAD + 0 -

75. Trend Not Fully Accounted for Pattern of Forecast Error: Identified Only by Observation Time (Years) Error 0 Desired Pattern Time (Years) Error 0

78. Application in Wholesale/Retail Sectors

79. Applications in Marketing

80. Applications in Finance and Accounting