1. 1 Learning Objectives When you complete this chapter, you should be able to : Identify or Define:  Forecasting  Types of forecasts  Time horizons  Approaches to forecasts

2. 2 Learning Objectives When you complete this chapter, you should be able to : Describe or Explain:  Moving averages  Exponential smoothing  Trend projections  Regression and correlation analysis  Measures of forecast accuracy

3. 3 What is Forecasting?  Process of predicting a future event ??

4. 4  Short-range forecast  Up to 1 year, generally less than 3 months  Purchasing, job scheduling, workforce levels, job assignments, production levels  Medium-range forecast  3 months to 3 years  Sales and production planning, budgeting  Long-range forecast  3 + years  New product planning, facility location, research and development Forecasting Time Horizons

5. 5 Types of Forecasts  Economic forecasts  Address business cycle – inflation rate, money supply, housing starts, etc.  Technological forecasts  Predict rate of technological progress  Impacts development of new products  Demand forecasts  Predict sales of existing product

6. 6 Strategic Importance of Forecasting  Human Resources – Hiring, training, laying off workers  Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share  Supply-Chain Management – Good supplier relations and price advance

7. 7 Seven Steps in Forecasting  Determine the use of the forecast  Select the items to be forecasted  Determine the time horizon of the forecast  Select the forecasting model(s)  Gather the data  Make the forecast  Validate and implement results

8. 8 The Realities!  Forecasts are seldom perfect  Most techniques assume an underlying stability in the system  Product family and aggregated forecasts are more accurate than individual product forecasts

9. 9 Forecasting Approaches  Used when situation is vague and little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods

10. 10 Forecasting Approaches  Used when situation is ‘stable’ and historical data exist  Existing products  Current technology  Involves mathematical techniques  e.g., forecasting sales of color televisions Quantitative Methods

11. 11 Overview of Qualitative Methods  Jury of executive opinion  Pool opinions of high-level executives, sometimes augment by statistical models  Delphi method  Panel of experts, queried iteratively

12. 12 Overview of Qualitative Methods  Sales force composite  Estimates from individual salespersons are reviewed for reasonableness, then aggregated  Consumer Market Survey  Ask the customer

13. 13  Involves small group of high-level managers  Group estimates demand by working together  Combines managerial experience with statistical models  Relatively quick  ‘Group-think’ disadvantage Jury of Executive Opinion

14. 14 Sales Force Composite  Each salesperson projects his or her sales  Combined at district and national levels  Sales reps know customers’ wants  Tends to be overly optimistic

15. 15 Delphi Method  Iterative group process, continues until general agreement is reached  3 types of participants  Decision makers  Staff  Respondents Staff (Administering survey) Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments)

16. 16 Consumer Market Survey  Ask customers about purchasing plans  What consumers say, and what they actually do are often different  Sometimes difficult to answer

17. 17 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

18. 18  Set of evenly spaced numerical data  Obtained by observing response variable at regular time periods  Forecast based only on past values  Assumes that factors influencing past and present will continue influence in future Time Series Forecasting

19. 19 Trend Seasonal Cyclical Random Time Series Components

20. 20 Components of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation Figure 4.1

21. 21  Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration Trend Component

22. 22  Regular pattern of up and down fluctuations  Due to weather, customs, etc.  Occurs within a single year Seasonal Component Number of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

23. 23  Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships Cyclical Component 05101520

24. 24  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating Random Component MTWTFMTWTFMTWTFMTWTF

25. 25 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

26. 26 Naive Approach  Assumes demand in next period is the same as demand in most recent period  e.g., If May sales were 48, then June sales will be 48  Sometimes cost effective and efficient

27. 27 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

28. 28  MA is a series of arithmetic means  Used if little or no trend  Used often for smoothing  Provides overall impression of data over time Moving Average Method Moving average = ∑ demand in previous n periods n

29. 29 January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 Moving Average Example101213 (10 + 12 + 13)/3 = 11 2 / 3

30. 30 Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales 30 30 – 28 28 – 26 26 – 24 24 – 22 22 – 20 20 – 18 18 – 16 16 – 14 14 – 12 12 – 10 10 – Actual Sales Moving Average Forecast

31. 31  Used when trend is present  Older data usually less important  Weights based on experience and intuition Weighted Moving Average Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

32. 32 January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / 2 Weighted Moving Average101213 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

33. 33 Moving Average And Weighted Moving Average 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average Figure 4.2

34. 34 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

35. 35 Exponential Smoothing New forecast =last period’s forecast +  (last period’s actual demand – last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0    1)

36. 36 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

37. 37 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= 142 +.2(153 – 142)

38. 38 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= 142 +.2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

39. 39  Form of weighted moving average  Weights decline exponentially  Most recent data weighted most  Requires smoothing constant (  )  Ranges from 0 to 1  Subjectively chosen  Involves little record keeping of past data Exponential Smoothing

40. 40 Impact of Different  225 225 – 200 200 – 175 175 – 150 150 – |||||||||123456789123456789|||||||||123456789123456789 Quarter Demand  =.1 Actual demand  =.5

41. 41 Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error= Actual demand - Forecast value = A t - F t

42. 42 Common Measures of Error Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD) MAD = ∑ |actual - forecast| n Mean Squared Error (MSE)Mean Squared Error (MSE) MSE = ∑ (forecast errors) 2 n

43. 43 Common Measures of Error Mean Absolute Percent Error (MAPE) MAPE = 100 ∑ |actual i - forecast i |/actual i n n i = 1

44. 44 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100

45. 45 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100 MAD = ∑ |deviations| n = 84/8 = 10.50 For  =.10 = 100/8 = 12.50 For  =.50

46. 46 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100 MAD10.5012.50 = 1,558/8 = 194.75 For  =.10 = 1,612/8 = 201.50 For  =.50 MSE = ∑ (forecast errors) 2 n

47. 47 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100 MAD10.5012.50 MSE194.75201.50 = 45.62/8 = 5.70% For  =.10 = 54.8/8 = 6.85% For  =.50 MAPE = 100 ∑ |deviation i |/actual i n i = 1

48. 48 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100 MAD10.5012.50 MSE194.75201.50 MAPE5.70%6.85%

49. 49 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

50. 50 Trend Projections Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique y = a + bx ^ where y= computed value of the variable to be predicted (dependent variable) a= y-axis intercept b= slope of the regression line x= the independent variable (in this case time) ^

51. 51 Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^

52. 52 Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^ Least squares method minimizes the sum of the squared errors (deviations)

53. 53 Least Squares Method Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx

54. 54 Least Squares Example b = = = 10.54 ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(4 2 ) a = y - bx = 98.86 - 10.54(4) = 56.70 TimeElectrical Power YearPeriod (x)Demandx 2 xy 1999174174 20002794158 20013809240 200249016360 2003510525525 2004614236852 2005712249854 ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

55. 55 Least Squares Example b = = = 10.54  xy - nxy  x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(4 2 ) a = y - bx = 98.86 - 10.54(4) = 56.70 TimeElectrical Power YearPeriod (x)Demandx 2 xy 1999174174 20002794158 20013809240 200249016360 2003510525525 2004614236852 2005712249854  x = 28  y = 692  x 2 = 140  xy = 3,063 x = 4y = 98.86 The trend line is y = 56.70 + 10.54x ^

56. 56 Least Squares Example ||||||||| 199920002001200220032004200520062007 160 160 – 150 150 – 140 140 – 130 130 – 120 120 – 110 110 – 100 100 – 90 90 – 80 80 – 70 70 – 60 60 – 50 50 – Year Power demand Trend line, y = 56.70 + 10.54x ^

57. 57 Least Squares Requirements 1.We always plot the data to insure a linear relationship 2.We do not predict time periods far beyond the database 3.Deviations around the least squares line are assumed to be random

58. 58 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

59. 59 Associative Forecasting Used when changes in one or more independent variables can be used to predict the changes in the dependent variable Most common technique is linear regression analysis We apply this technique just as we did in the time series example

60. 60 linear regression analysis Forecasting an outcome based on predictor variables using the least squares technique y = a + bx ^ where y= computed value of the variable to be predicted (dependent variable) a= y-axis intercept b= slope of the regression line x= the independent variable though to predict the value of the dependent variable ^

61. 61 Associative Forecasting Example SalesLocal Payroll ($000,000), y($000,000,000), x 2.01 3.03 2.54 2.02 2.01 3.57 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll

62. 62 Associative Forecasting Example Sales, y Payroll, xx 2 xy 2.0112.0 3.0399.0 2.541610.0 2.0244.0 2.0112.0 3.574924.5 ∑y = 15.0∑x = 18∑x 2 = 80∑xy = 51.5 x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 b = = =.25 ∑xy - nxy ∑x 2 - nx 2 51.5 - (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx = 2.5 - (.25)(3) = 1.75

63. 63 Associative Forecasting Example 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll y = 1.75 +.25x ^ Sales = 1.75 +.25(payroll) If payroll next year is estimated to be $600 million, then: Sales = 1.75 +.25(6) Sales = $325,000 3.25

64. 64 Sy,x. To measure the accuracy of the regression estimates, we must compute the standard error of the estimate, Sy,x. This computation is called the standard deviation of the regression. It measures the error from the dependent variable y, to the regression line, rather than to the mean. Standard Error of the Estimate

65. 65 Standard Error of the Estimate wherey=y-value of each data point y c =computed value of the dependent variable, from the regression equation n=number of data points S y,x = ∑(y - y c ) 2 n - 2

66. 66 Standard Error of the Estimate Computationally, this equation is considerably easier to use We use the standard error to set up prediction intervals around the point estimate S y,x = ∑y 2 - a∑y - b∑xy n - 2

67. 67 Associative Forecasting Example Sales, y Payroll, xx 2 xy 2.0112.0 3.0399.0 2.541610.0 2.0244.0 2.0112.0 3.574924.5 ∑y = 15.0∑x = 18∑x 2 = 80∑xy = 51.5 x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 b = = =.25 ∑xy - nxy ∑x 2 - nx 2 51.5 - (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx = 2.5 - (.25)(3) = 1.75

68. 68 Standard Error of the Estimate 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll 3.25 S y,x = = ∑y 2 - a∑y - b∑xy n - 2 39.5 - 1.75(15) -.25(51.5) 6 - 2 S y,x =.306 The standard error of the estimate is $30,600 in sales

69. 69 coefficient of correlation Regression line merely describe the relationship among variables. Another way to evaluate the relationship between two variable is to compute the coefficient of correlation.

70. 70  How strong is the linear relationship between the variables?  Correlation does not necessarily imply causality!  Coefficient of correlation, r, measures degree of association  Values range from -1 to +1 Correlation

71. 71 Correlation Coefficient r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

72. 72 Correlation Coefficient r = n∑xy - ∑x∑y [n∑x 2 - (∑x) 2 ][n∑y 2 - (∑y) 2 ] y x (a)Perfect positive correlation: r = +1 y x (b)Positive correlation: 0 < r < 1 y x (c)No correlation: r = 0 y x (d)Perfect negative correlation: r = -1

73. 73  Coefficient of Determination, r 2, measures the percent of change in y predicted by the change in x  Values range from 0 to 1  Easy to interpret Correlation For the Nodel Construction example: r =.901 r 2 =.81

74. 74 Multiple Regression Analysis If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables y = a + b 1 x 1 + b 2 x 2 … ^ Computationally, this is quite complex and generally done on the computer

75. 75 Multiple Regression Analysis y = 1.80 +.30x 1 - 5.0x 2 ^ In the Nodel example, including interest rates in the model gives the new equation: An improved correlation coefficient of r =.96 means this model does a better job of predicting the change in construction sales Sales = 1.80 +.30(6) - 5.0(.12) = 3.00 Sales = $300,000

76. 76 Have nice day!