1. CHAPTER 2 FORECASTING

2. LEARNING OBJECTIVES Define forecasting, forecasts approaches Understand the three time horizons Describe, Explain and Apply the naïve, moving average, exponential smoothing, and trend method Compute the measures of forecast accuracy Apply a tracking signal

3. Forecasting? Forecast a statement about the future value of a variable of interest. Forecasting the art and science of predicting future events.

4. Forecasts Forecasts affect decisions and activities throughout an organization  Accounting, finance  Human resources  Marketing  Operations  Product / service design

5. Uses of Forecasts AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy OperationsSchedules, MRP, workloads Product/service design New products and services

6. I see that you will get an A this semester.

7. Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

8. Forecasting Time Horizons Short-range forecast Medium-range forecast Long-range forecast

9. Distinguishing Differences Medium/long range- more comprehensive issues and support management decisions regarding planning and products, plants and processes Short-term- employs different methodologies than longer-term Short-term- more accurate than longer-term forecasts

10. Influence of Product Life Cycle Best period to increase market share R&D engineering is critical Practical to change price or quality image Strengthen niche Poor time to change image, price, or quality Competitive costs become critical Defend market position Cost control critical IntroductionGrowthMaturityDecline Company Strategy/Issues Internet search engines Sales Xbox 360 Drive-through restaurants CD-ROMs 3 1/2” Floppy disks LCD & plasma TVs Analog TVs iPods

11. Types of Forecasts Economic forecasts Technological forecasts Demand forecasts

12. 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

13. Forecasting Approaches Qualitative Quantitative

14. Qualitative Approaches Jury of executive opinion Delphi method Sales force composite Consumer market survey

15. Quantitative Approaches Naïve approach Moving average Exponential smoothing Trend projection Linear regression Time-Series Models

16. Time Series Forecasting Set of evenly spaced numerical data  Obtained by observing response variable at regular time periods Forecast based only on past values, no other variables important  Assumes that factors influencing past and present will continue influence in future

17. Time Series Components Trend Seasonal Cycles Random

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

19. Trend Component Overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration

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

21. Cycles Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration 05101520

22. Random Component Erratic, unsystematic, Due to random variation or unforeseen events Short duration and non-repeating MTWTFMTWTFMTWTFMTWTF

23. Naive Approach Assumes demand in next period is the same as demand in most recent period Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

24. Moving Average Method Use a number of historical actual data values to generate a forecast An average of the n most recent periods Useful if can assume that market demand will stay fairly steady over time ∑ demand in previous n periods n Moving average =

25. Moving Average Example 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 101213 (10 + 12 + 13)/3 = 11 2 / 3

26. 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

27. Weighted Moving Average Used when trend or pattern is present Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

28. Weighted Moving Average Example 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 101213 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

29. Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data

30. 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

31. Exponential Smoothing Weighted averaging method based on previous forecast plus a percentage of the forecast error A-F is the error term,  is the % feedback  Weights decline exponentially  Most recent data weighted most Involves little record keeping of past data Requires smoothing constant (  )  Ranges from 0 to 1  Subjectively chosen

32. 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)

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

34. Selecting of Smoothing Constant Chose high values of  when actual demand display an increasing (or decreasing) trend Chose low values of  when demand is relatively stable without any trend Chose low values of  when demand is relatively stable without any trend

35. Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trend ExponentiallyExponentially smoothed (F t ) +(T t )smoothed forecasttrend F t =  (A t - 1 ) + (1 -  )(F t - 1 + T t - 1 ) T t =  (F t - F t - 1 ) + (1 -  )T t - 1

36. Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 217 320 419 524 621 731 828 936 10

37. Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 217 320 419 524 621 731 828 936 10 F 2 =  A 1 + (1 -  )(F 1 + T 1 ) F 2 = (.2)(12) + (1 -.2)(11 + 2) = 2.4 + 10.4 = 12.8 units Step 1: Forecast for Month 2

38. Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.80 320 419 524 621 731 828 936 10 T 2 =  (F 2 - F 1 ) + (1 -  )T 1 T 2 = (.4)(12.8 - 11) + (1 -.4)(2) =.72 + 1.2 = 1.92 units Step 2: Trend for Month 2

39. Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.801.92 320 419 524 621 731 828 936 10 FIT 2 = F 2 + T 1 FIT 2 = 12.8 + 1.92 = 14.72 units Step 3: Calculate FIT for Month 2

40. Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.801.9214.72 320 419 524 621 731 828 936 10 15.182.1017.28 17.822.3220.14 19.912.2322.14 22.512.3824.89 24.112.0726.18 27.142.4529.59 29.282.3231.60 32.482.6835.16

41. Exponential Smoothing with Trend Adjustment Example |||||||||123456789123456789|||||||||123456789123456789 Time (month) Product demand 35 35 – 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – 0 0 – Actual demand (A t ) Forecast including trend (FIT t ) with  =.2 and  =.4

42. Seasonal Variations In Data Regularly repeating movements (upward or downward) in a time series that can be tie to recurring events.  Multiplicative seasonal method a method whereby seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.

43. Seasonal Variations In Data 1.Find average historical demand for each season 2.Compute the average demand over all seasons 3.Compute a seasonal index for each season 4.Estimate next year’s total demand 5.Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season Steps in the process:

44. Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex

45. Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex 0.957 Seasonal index = average 2005-2007 monthly demand average monthly demand = 90/94 =.957

46. Jan808510590940.957 Feb70858580940.851 Mar80938285940.904 Apr9095115100941.064 May113125131123941.309 Jun110115120115941.223 Jul100102113105941.117 Aug88102110100941.064 Sept85909590940.957 Oct77788580940.851 Nov75728380940.851 Dec82788080940.851 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex Seasonal Index Example

47. Jan808510590940.957 Feb70858580940.851 Mar80938285940.904 Apr9095115100941.064 May113125131123941.309 Jun110115120115941.223 Jul100102113105941.117 Aug88102110100941.064 Sept85909590940.957 Oct77788580940.851 Nov75728380940.851 Dec82788080940.851 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex Expected annual demand = 1,200 Janx.957 = 96 1,200 12 Febx.851 = 85 1,200 12 Forecast for 2008 Seasonal Index Example

48. 140 140 – 130 130 – 120 120 – 110 110 – 100 100 – 90 90 – 80 80 – 70 70 – ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Time Demand 2008 Forecast 2007 Demand 2006 Demand 2005 Demand Seasonal Index Example

49. 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

50. 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 ^

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

52. 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) Least Squares Method

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

54. 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

55. Associative Forecasting Example SalesLocal Payroll ($ millions), y($ billions), 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

56. 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 Associative Forecasting Example

57. 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 $6 billion, then: Sales = 1.75 +.25(6) Sales = $3,250,000 3.25 Associative Forecasting Example

58. Standard Error of the Estimate  A forecast is just a point estimate of a future value  This point is actually the mean of a probability distribution 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll 3.25

59. 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 Standard Error of the Estimate

60. 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 Standard Error of the Estimate

61. 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 $306,000 in sales Standard Error of the Estimate

62.  How strong is the linear relationship between the variables?  Coefficient of correlation, r, measures degree of association  Values range from -1 to +1 Correlation r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

63. 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

64. Measuring Forecast Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

65. Mean Absolute Percent Error (MAPE) MAPE = ∑ 100|Actual i - Forecast i |/Actual i n n i = 1 Measuring Forecast Error

66. Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62

67. RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD = ∑ |deviations| n = 82.45/8 = 10.31 For  =.10 = 98.62/8 = 12.33 For  =.50 Comparison of Forecast Error

68. RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 = 1,526.54/8 = 190.82 For  =.10 = 1,561.91/8 = 195.24 For  =.50 MSE = ∑ (forecast errors) 2 n Comparison of Forecast Error

69. RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 = 44.75/8 = 5.59% For  =.10 = 54.05/8 = 6.76% For  =.50 MAPE = ∑ 100|deviation i |/actual i n i = 1 Comparison of Forecast Error

70. RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 MAPE5.59%6.76% Comparison of Forecast Error

71.  Measures how well the forecast is predicting actual values  Good tracking signal has low values  If forecasts are continually high or low, the forecast has a bias error  +ve signal : demand greater then forecast Monitoring and Controlling Forecasts Tracking Signal

72. Tracking signal RSFEMAD= = ∑(Actual demand in period i - Forecast demand in period i)  ∑|Actual - Forecast|/n) Monitoring and Controlling Forecasts Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)

73. Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range

74. Tracking Signal ExampleCumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2

75. Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2 Tracking Signal (RSFE/MAD) -10/10 = -1 -15/7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = +0.5 +35/14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits Tracking Signal Example

76. Forecasting in the Service Sector  Presents unusual challenges  Special need for short term records  Holidays and other calendar events  Unusual events

77. Fast Food Restaurant Forecast 20% 20% – 15% 15% – 10% 10% – 5% 5% – 11-121-23-45-67-89-10 12-12-34-56-78-910-11 (Lunchtime)(Dinnertime) Hour of day Percentage of sales Figure 4.12

78. ?????