1. © 2008 Prentice-Hall, Inc. Chapter 5 To accompany Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna Power Point slides created by Jeff Heyl Forecasting © 2009 Prentice-Hall, Inc.

2. © 2009 Prentice-Hall, Inc. 5 – 2 Introduction Managers are always trying to reduce uncertainty and make better estimates of what will happen in the future This is the main purpose of forecasting Some firms use subjective methods Seat-of-the pants methods, intuition, experience There are also several quantitative techniques Moving averages, exponential smoothing, trend projections, least squares regression analysis

3. © 2009 Prentice-Hall, Inc. 5 – 3 Introduction Eight steps to forecasting : 1.Determine the use of the forecast—what objective are we trying to obtain? 2.Select the items or quantities that are to be forecasted 3.Determine the time horizon of the forecast 4.Select the forecasting model or models 5.Gather the data needed to make the forecast 6.Validate the forecasting model 7.Make the forecast 8.Implement the results

4. © 2009 Prentice-Hall, Inc. 5 – 4 Introduction These steps are a systematic way of initiating, designing, and implementing a forecasting system When used regularly over time, data is collected routinely and calculations performed automatically There is seldom one superior forecasting system Different organizations may use different techniques Whatever tool works best for a firm is the one they should use

5. © 2009 Prentice-Hall, Inc. 5 – 5 Regression Analysis Multiple Regression Moving Average Exponential Smoothing Trend Projections Decomposition Delphi Methods Jury of Executive Opinion Sales Force Composite Consumer Market Survey Time-Series Methods Qualitative Models Causal Methods Forecasting Models Forecasting Techniques Figure 5.1

6. © 2009 Prentice-Hall, Inc. 5 – 6 Time-Series Models Time-series models attempt to predict the future based on the past Common time-series models are Moving average Exponential smoothing Trend projections Decomposition Regression analysis is used in trend projections and one type of decomposition model

7. © 2009 Prentice-Hall, Inc. 5 – 7 Causal Models Causal models Causal models use variables or factors that might influence the quantity being forecasted The objective is to build a model with the best statistical relationship between the variable being forecast and the independent variables Regression analysis is the most common technique used in causal modeling

8. © 2009 Prentice-Hall, Inc. 5 – 8 Qualitative Models Qualitative models Qualitative models incorporate judgmental or subjective factors Useful when subjective factors are thought to be important or when accurate quantitative data is difficult to obtain Common qualitative techniques are Delphi method Jury of executive opinion Sales force composite Consumer market surveys

9. © 2009 Prentice-Hall, Inc. 5 – 9 Qualitative Models Delphi Method respondents decision makers Delphi Method – an iterative group process where (possibly geographically dispersed) respondents provide input to decision makers Jury of Executive Opinion Jury of Executive Opinion – collects opinions of a small group of high-level managers, possibly using statistical models for analysis Sales Force Composite Sales Force Composite – individual salespersons estimate the sales in their region and the data is compiled at a district or national level Consumer Market Survey Consumer Market Survey – input is solicited from customers or potential customers regarding their purchasing plans

10. © 2009 Prentice-Hall, Inc. 5 – 10 Scatter Diagrams Radios Televisions Compact Discs Scatter diagrams are helpful when forecasting time-series data because they depict the relationship between variables.

11. © 2009 Prentice-Hall, Inc. 5 – 11 Scatter Diagrams Wacker Distributors wants to forecast sales for three different products YEARTELEVISION SETSRADIOSCOMPACT DISC PLAYERS 1250300110 2250310100 3250320120 4250330140 5250340170 6250350150 7250360160 8250370190 9250380200 10250390190 Table 5.1

12. © 2009 Prentice-Hall, Inc. 5 – 12 Scatter Diagrams Figure 5.2 330 – 250 – 200 – 150 – 100 – 50 – |||||||||| 012345678910 Time (Years) Annual Sales of Televisions (a) Sales appear to be constant over time Sales = 250 A good estimate of sales in year 11 is 250 televisions

13. © 2009 Prentice-Hall, Inc. 5 – 13 Scatter Diagrams Sales appear to be increasing at a constant rate of 10 radios per year Sales = 290 + 10(Year) A reasonable estimate of sales in year 11 is 400 televisions 420 – 400 – 380 – 360 – 340 – 320 – 300 – 280 – |||||||||| 012345678910 Time (Years) Annual Sales of Radios (b) Figure 5.2

14. © 2009 Prentice-Hall, Inc. 5 – 14 Scatter Diagrams This trend line may not be perfectly accurate because of variation from year to year Sales appear to be increasing A forecast would probably be a larger figure each year 200 – 180 – 160 – 140 – 120 – 100 – |||||||||| 012345678910 Time (Years) Annual Sales of CD Players (c) Figure 5.2

15. © 2009 Prentice-Hall, Inc. 5 – 15 Measures of Forecast Accuracy We compare forecasted values with actual values to see how well one model works or to compare models Forecast error = Actual value – Forecast value mean absolute deviation MAD One measure of accuracy is the mean absolute deviation ( MAD )

16. © 2009 Prentice-Hall, Inc. 5 – 16 Measures of Forecast Accuracy naïve Using a naïve forecasting model YEAR ACTUAL SALES OF CD PLAYERS FORECAST SALES ABSOLUTE VALUE OF ERRORS (DEVIATION), (ACTUAL – FORECAST) 1110—— 2100110|100 – 110| = 10 3120100|120 – 110| = 20 4140120|140 – 120| = 20 5170140|170 – 140| = 30 6150170|150 – 170| = 20 7160150|160 – 150| = 10 8190160|190 – 160| = 30 9200190|200 – 190| = 10 10190200|190 – 200| = 10 11—190— Sum of |errors| = 160 MAD = 160/9 = 17.8 Table 5.2

17. © 2009 Prentice-Hall, Inc. 5 – 17 Measures of Forecast Accuracy naïve Using a naïve forecasting model YEAR ACTUAL SALES OF CD PLAYERS FORECAST SALES ABSOLUTE VALUE OF ERRORS (DEVIATION), (ACTUAL – FORECAST) 1110—— 2100110|100 – 110| = 10 3120100|120 – 110| = 20 4140120|140 – 120| = 20 5170140|170 – 140| = 30 6150170|150 – 170| = 20 7160150|160 – 150| = 10 8190160|190 – 160| = 30 9200190|200 – 190| = 10 10190200|190 – 200| = 10 11—190— Sum of |errors| = 160 MAD = 160/9 = 17.8 Table 5.2

18. © 2009 Prentice-Hall, Inc. 5 – 18 Measures of Forecast Accuracy There are other popular measures of forecast accuracy mean squared error The mean squared error mean absolute percent error The mean absolute percent error bias And bias is the average error and tells whether the forecast tends to be too high or too low and by how much. Thus, it can be negative or positive.

19. © 2009 Prentice-Hall, Inc. 5 – 19 Measures of Forecast Accuracy YearActual CD SalesForecast Sales|Actual -Forecast| 1110 210011010 312010020 414012020 517014030 615017020 716015010 819016030 920019010 19020010 11190 Sum of |errors|160 MAD17.8

20. © 2009 Prentice-Hall, Inc. 5 – 20 Hospital Days Forecast Error Example Ms. Smith forecasted total hospital inpatient days last year. Now that the actual data are known, she is reevaluating her forecasting model. Compute the MAD, MSE, and MAPE for her forecast. MonthForecastActual JAN250243 FEB320315 MAR275286 APR260256 MAY250241 JUN275298 JUL300292 AUG325333 SEP320326 OCT350378 NOV365382 DEC380396

21. © 2009 Prentice-Hall, Inc. 5 – 21 Hospital Days Forecast Error Example ForecastActual|error|error 2 |error/actual| JAN250243 7490.03 FEB320315 5250.02 MAR275286 111210.04 APR260256 4160.02 MAY250241 9810.04 JUN275298 235290.08 JUL300292 8640.03 AUG325333 8640.02 SEP320326 6360.02 OCT350378 287840.07 NOV365382 172890.04 DEC380396 162560.04 AVERAGE MAD= 11.83 MSE= 192.83 MAPE=.0381*100 = 3.81

22. © 2009 Prentice-Hall, Inc. 5 – 22 Time-Series Forecasting Models A time series is a sequence of evenly spaced events (weekly, monthly, quarterly, etc.) Time-series forecasts predict the future based solely of the past values of the variable Other variables, no matter how potentially valuable, are ignored

23. © 2009 Prentice-Hall, Inc. 5 – 23 Decomposition of a Time-Series A time series typically has four components 1.Trend T 1.Trend ( T ) is the gradual upward or downward movement of the data over time 2.Seasonality S 2.Seasonality ( S ) is a pattern of demand fluctuations above or below trend line that repeats at regular intervals 3.Cycles C 3.Cycles ( C ) are patterns in annual data that occur every several years 4.Random variations R 4.Random variations ( R ) are “blips” in the data caused by chance and unusual situations

24. © 2009 Prentice-Hall, Inc. 5 – 24 Decomposition of a Time-Series Average Demand over 4 Years Trend Component Actual Demand Line Time Demand for Product or Service |||| YearYearYearYear 1234 Seasonal Peaks Figure 5.3

25. © 2009 Prentice-Hall, Inc. 5 – 25 Decomposition of a Time-Series There are two general forms of time-series models The multiplicative model Demand = T x S x C x R The additive model Demand = T + S + C + R Models may be combinations of these two forms Forecasters often assume errors are normally distributed with a mean of zero

26. © 2009 Prentice-Hall, Inc. 5 – 26 Moving Averages Moving averages Moving averages can be used when demand is relatively steady over time The next forecast is the average of the most recent n data values from the time series The most recent period of data is added and the oldest is dropped This methods tends to smooth out short-term irregularities in the data series

27. © 2009 Prentice-Hall, Inc. 5 – 27 Moving Averages Mathematically where = forecast for time period t + 1 = actual value in time period t n = number of periods to average

28. © 2009 Prentice-Hall, Inc. 5 – 28 Wallace Garden Supply Example Wallace Garden Supply wants to forecast demand for its Storage Shed They have collected data for the past year They are using a three-month moving average to forecast demand ( n = 3)

29. © 2009 Prentice-Hall, Inc. 5 – 29 Wallace Garden Supply Example Table 5.3 MONTHACTUAL SHED SALESTHREE-MONTH MOVING AVERAGE January10 February12 March13 April16 May19 June23 July26 August30 September28 October18 November16 December14 January— (12 + 13 + 16)/3 = 13.67 (13 + 16 + 19)/3 = 16.00 (16 + 19 + 23)/3 = 19.33 (19 + 23 + 26)/3 = 22.67 (23 + 26 + 30)/3 = 26.33 (26 + 30 + 28)/3 = 28.00 (30 + 28 + 18)/3 = 25.33 (28 + 18 + 16)/3 = 20.67 (18 + 16 + 14)/3 = 16.00 (10 + 12 + 13)/3 = 11.67

30. © 2009 Prentice-Hall, Inc. 5 – 30 Weighted Moving Averages Weighted moving averages Weighted moving averages use weights to put more emphasis on recent periods Often used when a trend or other pattern is emerging Mathematically where w i = weight for the ith observation

31. © 2009 Prentice-Hall, Inc. 5 – 31 Weighted Moving Averages Both simple and weighted averages are effective in smoothing out fluctuations in the demand pattern in order to provide stable estimates Problems Increasing the size of n smoothes out fluctuations better, but makes the method less sensitive to real changes in the data Moving averages can not pick up trends very well – they will always stay within past levels and not predict a change to a higher or lower level

32. © 2009 Prentice-Hall, Inc. 5 – 32 Wallace Garden Supply Example Wallace Garden Supply decides to try a weighted moving average model to forecast demand for its Storage Shed They decide on the following weighting scheme WEIGHTS APPLIEDPERIOD 3Last month 2Two months ago 1Three months ago 6 3 x Sales last month + 2 x Sales two months ago + 1 X Sales three months ago Sum of the weights

33. © 2009 Prentice-Hall, Inc. 5 – 33 Wallace Garden Supply Example Table 5.4 MONTHACTUAL SHED SALES THREE-MONTH WEIGHTED MOVING AVERAGE January10 February12 March13 April16 May19 June23 July26 August30 September28 October18 November16 December14 January— [(3 X 13) + (2 X 12) + (10)]/6 = 12.17 [(3 X 16) + (2 X 13) + (12)]/6 = 14.33 [(3 X 19) + (2 X 16) + (13)]/6 = 17.00 [(3 X 23) + (2 X 19) + (16)]/6 = 20.50 [(3 X 26) + (2 X 23) + (19)]/6 = 23.83 [(3 X 30) + (2 X 26) + (23)]/6 = 27.50 [(3 X 28) + (2 X 30) + (26)]/6 = 28.33 [(3 X 18) + (2 X 28) + (30)]/6 = 23.33 [(3 X 16) + (2 X 18) + (28)]/6 = 18.67 [(3 X 14) + (2 X 16) + (18)]/6 = 15.33

34. © 2009 Prentice-Hall, Inc. 5 – 34 Wallace Garden Supply Example Program 5.1A

35. © 2009 Prentice-Hall, Inc. 5 – 35 Wallace Garden Supply Example Program 5.1B

36. © 2009 Prentice-Hall, Inc. 5 – 36 Exponential Smoothing Exponential smoothing Exponential smoothing is easy to use and requires little record keeping of data It is a type of moving average New forecast =Last period’s forecast +  (Last period’s actual demand – Last period’s forecast) smoothing constant Where  is a weight (or smoothing constant) with a value between 0 and 1 inclusive A larger  gives more importance to recent data while a smaller value gives more importance to past data

37. © 2009 Prentice-Hall, Inc. 5 – 37 Exponential Smoothing Mathematically where F t +1 = new forecast (for time period t + 1) F t = pervious forecast (for time period t)  = smoothing constant (0 ≤  ≤ 1) Y t = pervious period’s actual demand The idea is simple – the new estimate is the old estimate plus some fraction of the error in the last period

38. © 2009 Prentice-Hall, Inc. 5 – 38 Exponential Smoothing Example In January, February’s demand for a certain car model was predicted to be 142 Actual February demand was 153 autos Using a smoothing constant of  = 0.20, what is the forecast for March? New forecast (for March demand)= 142 + 0.2(153 – 142) = 144.2 or 144 autos If actual demand in March was 136 autos, the April forecast would be New forecast (for April demand)= 144.2 + 0.2(136 – 144.2) = 142.6 or 143 autos

39. © 2009 Prentice-Hall, Inc. 5 – 39 Selecting the Smoothing Constant Selecting the appropriate value for  is key to obtaining a good forecast The objective is always to generate an accurate forecast The general approach is to develop trial forecasts with different values of  and select the  that results in the lowest MAD

40. © 2009 Prentice-Hall, Inc. 5 – 40 Port of Baltimore Example QUARTER ACTUAL TONNAGE UNLOADED FORECAST USING  =0.10 FORECAST USING  =0.50 1180175 2168175.5 = 175.00 + 0.10(180 – 175)177.5 3159174.75 = 175.50 + 0.10(168 – 175.50)172.75 4175173.18 = 174.75 + 0.10(159 – 174.75)165.88 5190173.36 = 173.18 + 0.10(175 – 173.18)170.44 6205175.02 = 173.36 + 0.10(190 – 173.36)180.22 7180178.02 = 175.02 + 0.10(205 – 175.02)192.61 8182178.22 = 178.02 + 0.10(180 – 178.02)186.30 9?178.60 = 178.22 + 0.10(182 – 178.22)184.15 Table 5.5 Exponential smoothing forecast for two values of 

41. © 2009 Prentice-Hall, Inc. 5 – 41 Selecting the Best Value of  QUARTER ACTUAL TONNAGE UNLOADED FORECAST WITH  = 0.10 ABSOLUTE DEVIATIONS FOR  = 0.10 FORECAST WITH  = 0.50 ABSOLUTE DEVIATIONS FOR  = 0.50 11801755 ….. 1755…. 2168175.57.5..177.59.5.. 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 8182178.223.78186.304.3.. Sum of absolute deviations82.4598.63 MAD = Σ|deviations| =10.31 MAD =12.33 n Table 5.6 Best choice

42. © 2009 Prentice-Hall, Inc. 5 – 42 Port of Baltimore Example Program 5.2A

43. © 2009 Prentice-Hall, Inc. 5 – 43 Port of Baltimore Example Program 5.2B

44. © 2009 Prentice-Hall, Inc. 5 – 44 PM Computer: Moving Average Example PM Computer assembles customized personal computers from generic parts The owners purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal. It is important that they develop a good forecast of demand for their computers so they can purchase component parts efficiently.

45. © 2009 Prentice-Hall, Inc. 5 – 45 PM Computers: Data PeriodMonthActual Demand 1Jan37 2Feb40 3Mar41 4Apr37 5May45 6June50 7July43 8Aug47 9Sept56 Compute a 2-month moving average Compute a 3-month weighted average using weights of 4,2,1 for the past three months of data Compute an exponential smoothing forecast using  = 0.7, previous forecast of 40 Using MAD, what forecast is most accurate?

46. © 2009 Prentice-Hall, Inc. 5 – 46 PM Computers: Moving Average Solution MAD Exponential smoothing resulted in the lowest MAD.

47. © 2009 Prentice-Hall, Inc. 5 – 47 Exponential Smoothing with Trend Adjustment Like all averaging techniques, exponential smoothing does not respond to trends A more complex model can be used that adjusts for trends The basic approach is to develop an exponential smoothing forecast then adjust it for the trend Forecast including trend ( FIT t ) =New forecast ( F t ) + Trend correction ( T t )

48. © 2009 Prentice-Hall, Inc. 5 – 48 Exponential Smoothing with Trend Adjustment The equation for the trend correction uses a new smoothing constant  T t is computed by where T t +1 =smoothed trend for period t + 1 T t =smoothed trend for preceding period  =trend smooth constant that we select F t +1 =simple exponential smoothed forecast for period t + 1 F t =forecast for pervious period

49. © 2009 Prentice-Hall, Inc. 5 – 49 Selecting a Smoothing Constant As with exponential smoothing, a high value of  makes the forecast more responsive to changes in trend A low value of  gives less weight to the recent trend and tends to smooth out the trend Values are generally selected using a trial-and- error approach based on the value of the MAD for different values of  first-order smoothing Simple exponential smoothing is often referred to as first-order smoothing second-order double smoothingHolt’s method Trend-adjusted smoothing is called second-order, double smoothing, or Holt’s method

50. © 2009 Prentice-Hall, Inc. 5 – 50 Trend Projection Trend projection fits a trend line to a series of historical data points The line is projected into the future for medium- to long-range forecasts Several trend equations can be developed based on exponential or quadratic models The simplest is a linear model developed using regression analysis

51. © 2009 Prentice-Hall, Inc. 5 – 51 Trend Projection Trend projections are used to forecast time- series data that exhibit a linear trend. A trend line is simply a linear regression equation in which the independent variable (X) is the time period Least squares may be used to determine a trend projection for future forecasts. Least squares determines the trend line forecast by minimizing the mean squared error between the trend line forecasts and the actual observed values. The independent variable is the time period and the dependent variable is the actual observed value in the time series.

52. © 2009 Prentice-Hall, Inc. 5 – 52 Trend Projection The mathematical form is where = predicted value b 0 = intercept b 1 = slope of the line X = time period (i.e., X = 1, 2, 3, …, n )

53. © 2009 Prentice-Hall, Inc. 5 – 53 Trend Projection Value of Dependent Variable Time * * * * * * * Dist 2 Dist 4 Dist 6 Dist 1 Dist 3 Dist 5 Dist 7 Figure 5.4

54. © 2009 Prentice-Hall, Inc. 5 – 54 Midwestern Manufacturing Company Example Midwestern Manufacturing Company has experienced the following demand for it’s electrical generators over the period of 2001 – 2007 YEARELECTRICAL GENERATORS SOLD 200174 200279 200380 200490 2005105 2006142 2007122 Table 5.7

55. © 2009 Prentice-Hall, Inc. 5 – 55 Midwestern Manufacturing Company Example Program 5.3A Notice code instead of actual years

56. © 2009 Prentice-Hall, Inc. 5 – 56 Midwestern Manufacturing Company Example Program 5.3B r 2 says model predicts about 80% of the variability in demand Significance level for F -test indicates a definite relationship

57. © 2009 Prentice-Hall, Inc. 5 – 57 Midwestern Manufacturing Company Example The forecast equation is To project demand for 2008, we use the coding system to define X = 8 (sales in 2008)= 56.71 + 10.54(8) = 141.03, or 141 generators Likewise for X = 9 (sales in 2009)= 56.71 + 10.54(9) = 151.57, or 152 generators

58. © 2009 Prentice-Hall, Inc. 5 – 58 Midwestern Manufacturing Company Example Generator Demand Year 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – ||||||||| 200120022003200420052006200720082009 Actual Demand Line Trend Line Figure 5.5

59. © 2009 Prentice-Hall, Inc. 5 – 59 Midwestern Manufacturing Company Example Program 5.4A

60. © 2009 Prentice-Hall, Inc. 5 – 60 Midwestern Manufacturing Company Example Program 5.4B

61. © 2009 Prentice-Hall, Inc. 5 – 61 Seasonal Variations Recurring variations over time may indicate the need for seasonal adjustments in the trend line A seasonal index indicates how a particular season compares with an average season When no trend is present, the seasonal index can be found by dividing the average value for a particular season by the average of all the data

62. © 2009 Prentice-Hall, Inc. 5 – 62 Seasonal Variations Eichler Supplies sells telephone answering machines Data has been collected for the past two years sales of one particular model They want to create a forecast that includes seasonality

63. © 2009 Prentice-Hall, Inc. 5 – 63 Seasonal Variations MONTH SALES DEMAND AVERAGE TWO- YEAR DEMAND MONTHLY DEMAND AVERAGE SEASONAL INDEX YEAR 1YEAR 2 January8010090940.957 February857580940.851 March809085940.904 April11090100941.064 May115131123941.309 June120110115941.223 July100110105941.117 August11090100941.064 September859590940.957 October758580940.851 November857580940.851 December80 940.851 Total average demand = 1,128 Seasonal index = Average two-year demand Average monthly demand Average monthly demand = = 94 1,128 12 months Table 5.8

64. © 2009 Prentice-Hall, Inc. 5 – 64 Seasonal Variations The calculations for the seasonal indices are Jan.July Feb.Aug. Mar.Sept. Apr.Oct. MayNov. JuneDec.

65. © 2009 Prentice-Hall, Inc. 5 – 65 Regression with Trend and Seasonal Components Multiple regression Multiple regression can be used to forecast both trend and seasonal components in a time series One independent variable is time Dummy independent variables are used to represent the seasons The model is an additive decomposition model where X 1 = time period X 2 = 1 if quarter 2, 0 otherwise X 3 = 1 if quarter 3, 0 otherwise X 4 = 1 if quarter 4, 0 otherwise

66. © 2009 Prentice-Hall, Inc. 5 – 66 Regression with Trend and Seasonal Components Program 5.6A

67. © 2009 Prentice-Hall, Inc. 5 – 67 Regression with Trend and Seasonal Components Program 5.6B (partial)

68. © 2009 Prentice-Hall, Inc. 5 – 68 Regression with Trend and Seasonal Components The resulting regression equation is Using the model to forecast sales for the first two quarters of next year These are different from the results obtained using the multiplicative decomposition method Use MAD and MSE to determine the best model

69. © 2009 Prentice-Hall, Inc. 5 – 69 Regression with Trend and Seasonal Components American Airlines original spare parts inventory system used only time-series methods to forecast the demand for spare parts This method was slow to responds to even moderate changes in aircraft utilization let alone major fleet expansions They developed a PC-based system named RAPS which uses linear regression to establish a relationship between monthly part removals and various functions of monthly flying hours The computation now takes only one hour instead of the days the old system needed Using RAPS provided a one time savings of $7 million and a recurring annual savings of nearly $1 million

70. © 2009 Prentice-Hall, Inc. 5 – 70 Monitoring and Controlling Forecasts Tracking signals Tracking signals can be used to monitor the performance of a forecast Tacking signals are computed using the following equation where

71. © 2009 Prentice-Hall, Inc. 5 – 71 Monitoring and Controlling Forecasts Acceptable Range Signal Tripped Upper Control Limit Lower Control Limit 0 MAD s + – Time Figure 5.7 Tracking Signal

72. © 2009 Prentice-Hall, Inc. 5 – 72 Monitoring and Controlling Forecasts Positive tracking signals indicate demand is greater than forecast Negative tracking signals indicate demand is less than forecast Some variation is expected, but a good forecast will have about as much positive error as negative error Problems are indicated when the signal trips either the upper or lower predetermined limits This indicates there has been an unacceptable amount of variation Limits should be reasonable and may vary from item to item

73. © 2009 Prentice-Hall, Inc. 5 – 73 Regression with Trend and Seasonal Components How do you decide on the upper and lower limits? Too small a value will trip the signal too often and too large will cause a bad forecast Plossl & Wight – use maximums of ±4 MADs for high volume stock items and ±8 MADs for lower volume items One MAD is equivalent to approximately 0.8 standard deviation so that ±4 MADs =3.2 s.d. For a forecast to be “in control”, 89% of the errors are expected to fall within ±2 MADs, 98% with ±3 MADs or 99.9% within ±4 MADs whenever the errors are approximately normally distributed

74. © 2009 Prentice-Hall, Inc. 5 – 74 Kimball’s Bakery Example Tracking signal for quarterly sales of croissants TIME PERIOD FORECAST DEMAND ACTUAL DEMANDERRORRSFE |FORECAST| | ERROR| CUMULATIVE ERRORMAD TRACKING SIGNAL 110090–10 10 10.0–1 210095–5–155157.5–2 3100115+150153010.00 4110100–10 104010.0–1 5110125+15+5155511.0+0.5 6110140+30+35308514.2+2.5

75. © 2009 Prentice-Hall, Inc. 5 – 75 Forecasting at Disney The Disney chairman receives a daily report from his main theme parks that contains only two numbers – the forecast of yesterday’s attendance at the parks and the actual attendance The Disney chairman receives a daily report from his main theme parks that contains only two numbers – the forecast of yesterday’s attendance at the parks and the actual attendance An error close to zero (using MAPE as the measure) is expected The annual forecast of total volume conducted in 1999 for the year 2000 resulted in a MAPE of 0

76. © 2009 Prentice-Hall, Inc. 5 – 76 Using The Computer to Forecast Spreadsheets can be used by small and medium-sized forecasting problems More advanced programs (SAS, SPSS, Minitab) handle time-series and causal models May automatically select best model parameters Dedicated forecasting packages may be fully automatic May be integrated with inventory planning and control