Chapter 12Forecasting
Lecture Outline• Strategic Role of Forecasting in Supply ChainManagement• Components of Forecasting Demand• Time Series Me...
Forecasting• Predicting the future• Qualitative forecast methods• subjective• Quantitative forecast methods• based on math...
Supply Chain Management• Accurate forecasting determines inventory levelsin the supply chain• Continuous replenishment• su...
The Effect of Inaccurate ForecastingCopyright 2011 John Wiley & Sons, Inc. 12-5
Forecasting• Quality Management• Accurately forecasting customer demand is a key toproviding good quality service• Strateg...
Types of Forecasting Methods• Depend on• time frame• demand behavior• causes of behaviorCopyright 2011 John Wiley & Sons, ...
Time Frame• Indicates how far into the future is forecast• Short- to mid-range forecast• typically encompasses the immedia...
Demand Behavior• Trend• a gradual, long-term up or down movement ofdemand• Random variations• movements in demand that do ...
Forms of Forecast MovementCopyright 2011 John Wiley & Sons, Inc. 12-10Time(a) TrendTime(d) Trend with seasonal patternTime...
Forecasting Methods• Time series• statistical techniques that use historical demand datato predict future demand• Regressi...
Qualitative Methods• Management, marketing, purchasing, andengineering are sources for internal qualitativeforecasts• Delp...
Forecasting ProcessCopyright 2011 John Wiley & Sons, Inc. 12-136. Check forecastaccuracy with one ormore measures4. Select...
Time Series• Assume that what has occurred in the past willcontinue to occur in the future• Relate the forecast to only on...
Moving Average• Naive forecast• demand in current period is used as next period’sforecast• Simple moving average• uses ave...
Moving Average: Naïve ApproachCopyright 2011 John Wiley & Sons, Inc. 12-16Jan 120Feb 90Mar 100Apr 75May 110June 50July 75A...
Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-17MAn =ni = 1Dinwheren = number of periods inthe moving ave...
3-month Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-18Jan 120Feb 90Mar 100Apr 75May 110June 50July 75Au...
5-month Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-19MA5 =5i = 1Di5=90 + 110 + 130+75+505= 91 orders f...
Smoothing EffectsCopyright 2011 John Wiley & Sons, Inc. 12-20150 –125 –100 –75 –50 –25 –0 – | | | | | | | | | | |Jan Feb M...
Weighted Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-21• Adjusts moving average method to more closelyreflect ...
Weighted Moving Average ExampleCopyright 2011 John Wiley & Sons, Inc. 12-22MONTH WEIGHT DATAAugust 17% 130September 33% 11...
Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-23• Averaging method• Weights most recent data more strongl...
Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-24Ft +1 = Dt + (1 - )Ftwhere:Ft +1 = forecast for next peri...
0.0 1.0If = 0.20, then Ft +1 = 0.20 Dt + 0.80 FtIf = 0, then Ft +1 = 0 Dt + 1 Ft = FtForecast does not reflect recent data...
Exponential Smoothing (α=0.30)Copyright 2011 John Wiley & Sons, Inc. 12-26F2 = D1 + (1 - )F1= (0.30)(37) + (0.70)(37)= 37F...
Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-27FORECAST, Ft + 1PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)1 Ja...
Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-2870 –60 –50 –40 –30 –20 –10 –0 – | | | | | | | | | | | | |...
Adjusted Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-29AFt +1 = Ft +1 + Tt +1whereT = an exponentially ...
Adjusted Exponential Smoothing (β=0.30)Copyright 2011 John Wiley & Sons, Inc. 12-30PERIOD MONTH DEMAND1 Jan 372 Feb 403 Ma...
Adjusted Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-31FORECAST TREND ADJUSTEDPERIOD MONTH DEMAND Ft +1...
Adjusted Exponential SmoothingForecastsCopyright 2011 John Wiley & Sons, Inc. 12-3270 –60 –50 –40 –30 –20 –10 –0 – | | | |...
Linear Trend LineCopyright 2011 John Wiley & Sons, Inc. 12-33y = a + bxwherea = interceptb = slope of the linex = time per...
Least Squares ExampleCopyright 2011 John Wiley & Sons, Inc. 12-34x(PERIOD) y(DEMAND) xy x21 73 37 12 40 80 43 41 123 94 37...
Least Squares ExampleCopyright 2011 John Wiley & Sons, Inc. 12-35x = = 6.5y = = 46.42b = = =1.72a = y - bx= 46.42 - (1.72)...
Copyright 2011 John Wiley & Sons, Inc. 12-36Linear trend line y = 35.2 + 1.72xForecast for period 13 y = 35.2 + 1.72(13) =...
Seasonal AdjustmentsCopyright 2011 John Wiley & Sons, Inc. 12-37 Repetitive increase/ decrease in demand Use seasonal fa...
Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-382002 12.6 8.6 6.3 17.5 45.02003 14.1 10.3 7.5 18.2 50.12004...
Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-39SF1 = (S1) (F5) = (0.28)(58.17) = 16.28SF2 = (S2) (F5) = (0...
Forecast Accuracy• Forecast error• difference between forecast and actual demand• MAD• mean absolute deviation• MAPD• mean...
Mean Absolute Deviation (MAD)Copyright 2011 John Wiley & Sons, Inc. 12-41wheret = period numberDt = demand in period tFt =...
Copyright 2011 John Wiley & Sons, Inc. 12-42MAD Example1 37 37.00 – –2 40 37.00 3.00 3.003 41 37.90 3.10 3.104 37 38.83 -1...
MAD CalculationCopyright 2011 John Wiley & Sons, Inc. 12-43Dt - FtnMAD === 4.8553.3911
Other Accuracy MeasuresCopyright 2011 John Wiley & Sons, Inc. 12-44Mean absolute percent deviation (MAPD)MAPD =|Dt - Ft|Dt...
Comparison of ForecastsCopyright 2011 John Wiley & Sons, Inc. 12-45FORECAST MAD MAPD E (E)Exponential smoothing ( = 0.30) ...
Forecast Control• Tracking signal• monitors the forecast to see if it is biased high or low• 1 MAD ≈ 0.8 б• Control limits...
Tracking Signal ValuesCopyright 2011 John Wiley & Sons, Inc. 12-471 37 37.00 – – –2 40 37.00 3.00 3.00 3.003 41 37.90 3.10...
Tracking Signal PlotCopyright 2011 John Wiley & Sons, Inc. 12-483 –2 –1 –0 –-1 –-2 –-3 –| | | | | | | | | | | | |0 1 2 3 4...
Statistical Control ChartsCopyright 2011 John Wiley & Sons, Inc. 12-49=(Dt - Ft)2n - 1 Using we can calculate statistical...
Statistical Control ChartsCopyright 2011 John Wiley & Sons, Inc. 12-50Errors18.39 –12.24 –6.12 –0 –-6.12 –-12.24 –-18.39 –...
Time Series Forecasting Using Excel• Excel can be used to develop forecasts:• Moving average• Exponential smoothing• Adjus...
Exponentially Smoothed and AdjustedExponentially Smoothed ForecastsCopyright 2011 John Wiley & Sons, Inc. 12-52=B5*(C11-C1...
Demand and Exponentially SmoothedForecastCopyright 2011 John Wiley & Sons, Inc. 12-53Click on “Insert” then “Line”
Data Analysis OptionCopyright 2011 John Wiley & Sons, Inc. 12-54
Forecasting With Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-55
Forecasting With OM ToolsCopyright 2011 John Wiley & Sons, Inc. 12-56
Regression Methods• Linear regression• mathematical technique that relates a dependentvariable to an independent variable ...
Linear RegressionCopyright 2011 John Wiley & Sons, Inc. 12-58y = a + bx a = y - b xb =wherea = interceptb = slope of the l...
Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-59x y(WINS) (ATTENDANCE) xy x24 36.3 145.2 166 40.1 240...
Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-60x = = 6.125y = = 43.36b === 4.06a = y - bx= 43.36 - (...
Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-61| | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 1060,000 –50...
Correlation and Coefficient ofDetermination• Correlation, r• Measure of strength of relationship• Varies between -1.00 and...
n xy - x y[n x2 - ( x)2] [n y2 - ( y)2]r =Coefficient of determinationr2 = (0.947)2 = 0.897r =(8)(2,167.7) - (49)(346.9)[(...
Regression Analysis With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-64=INTERCEPT(B5:B12,A5:A12)=CORREL(B5:B12,A5:A12)=...
Regression Analysis with ExcelCopyright 2011 John Wiley & Sons, Inc. 12-65
Regression Analysis With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-66
Multiple RegressionCopyright 2011 John Wiley & Sons, Inc. 12-67Study the relationship of demand to two or moreindependent ...
Multiple Regression With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-68r2, the coefficientof determinationRegression eq...
Multiple Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-69y = 19,094.42 + 3560.99 x1 + .0368 x2y = 19,094.42 ...
Copyright 2011 John Wiley & Sons, Inc. 12-70Copyright 2011 John Wiley & Sons, Inc.All rights reserved. Reproduction or tra...
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C12

  1. 1. Chapter 12Forecasting
  2. 2. Lecture Outline• Strategic Role of Forecasting in Supply ChainManagement• Components of Forecasting Demand• Time Series Methods• Forecast Accuracy• Time Series Forecasting Using Excel• Regression MethodsCopyright 2011 John Wiley & Sons, Inc. 12-2
  3. 3. Forecasting• Predicting the future• Qualitative forecast methods• subjective• Quantitative forecast methods• based on mathematical formulasCopyright 2011 John Wiley & Sons, Inc. 12-3
  4. 4. Supply Chain Management• Accurate forecasting determines inventory levelsin 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• JIT (just-in-time)• VMI (vendor-managed inventory)• stockless inventoryCopyright 2011 John Wiley & Sons, Inc. 12-4
  5. 5. The Effect of Inaccurate ForecastingCopyright 2011 John Wiley & Sons, Inc. 12-5
  6. 6. Forecasting• Quality Management• Accurately forecasting customer demand is a key toproviding good quality service• Strategic Planning• Successful strategic planning requires accurateforecasts of future products and marketsCopyright 2011 John Wiley & Sons, Inc. 12-6
  7. 7. Types of Forecasting Methods• Depend on• time frame• demand behavior• causes of behaviorCopyright 2011 John Wiley & Sons, Inc. 12-7
  8. 8. Time Frame• Indicates how far into the future is forecast• Short- to mid-range forecast• typically encompasses the immediate future• daily up to two years• Long-range forecast• usually encompasses a period of time longer thantwo yearsCopyright 2011 John Wiley & Sons, Inc. 12-8
  9. 9. Demand Behavior• Trend• a gradual, long-term up or down movement ofdemand• 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 demandoccurring periodicallyCopyright 2011 John Wiley & Sons, Inc. 12-9
  10. 10. Forms of Forecast MovementCopyright 2011 John Wiley & Sons, Inc. 12-10Time(a) TrendTime(d) Trend with seasonal patternTime(c) Seasonal patternTime(b) CycleDemandDemandDemandDemandRandommovement
  11. 11. Forecasting Methods• Time series• statistical techniques that use historical demand datato predict future demand• Regression methods• attempt to develop a mathematical relationshipbetween demand and factors that cause its behavior• Qualitative• use management judgment, expertise, and opinion topredict future demandCopyright 2011 John Wiley & Sons, Inc. 12-11
  12. 12. Qualitative Methods• Management, marketing, purchasing, andengineering are sources for internal qualitativeforecasts• Delphi method• involves soliciting forecasts about technologicaladvances from expertsCopyright 2011 John Wiley & Sons, Inc. 12-12
  13. 13. Forecasting ProcessCopyright 2011 John Wiley & Sons, Inc. 12-136. Check forecastaccuracy with one ormore measures4. Select a forecastmodel that seemsappropriate for data5. Develop/computeforecast for period ofhistorical data8a. Forecast overplanning horizon9. Adjust forecast basedon additional qualitativeinformation and insight10. Monitor resultsand measure forecastaccuracy8b. Select newforecast model oradjust parameters ofexisting model7.Is accuracy offorecastacceptable?1. Identify thepurpose of forecast3. Plot data and identifypatterns2. Collect historicaldataNoYes
  14. 14. Time Series• Assume that what has occurred in the past willcontinue to occur in the future• Relate the forecast to only one factor - time• Include• moving average• exponential smoothing• linear trend lineCopyright 2011 John Wiley & Sons, Inc. 12-14
  15. 15. Moving Average• Naive forecast• demand in current period is used as next period’sforecast• Simple moving average• uses average demand for a fixed sequence of periods• stable demand with no pronounced behavioralpatterns• Weighted moving average• weights are assigned to most recent dataCopyright 2011 John Wiley & Sons, Inc. 12-15
  16. 16. Moving Average: Naïve ApproachCopyright 2011 John Wiley & Sons, Inc. 12-16Jan 120Feb 90Mar 100Apr 75May 110June 50July 75Aug 130Sept 110Oct 90ORDERSMONTH PER MONTH-1209010075110507513011090Nov -FORECAST
  17. 17. Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-17MAn =ni = 1Dinwheren = number of periods inthe moving averageDi = demand in period i
  18. 18. 3-month Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-18Jan 120Feb 90Mar 100Apr 75May 110June 50July 75Aug 130Sept 110Oct 90Nov -ORDERSMONTH PER MONTHMA3 =3i = 1Di3=90 + 110 + 1303= 110 orders for Nov–––103.388.395.078.378.385.0105.0110.0MOVINGAVERAGE
  19. 19. 5-month Simple Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-19MA5 =5i = 1Di5=90 + 110 + 130+75+505= 91 orders for NovJan 120Feb 90Mar 100Apr 75May 110June 50July 75Aug 130Sept 110Oct 90Nov -ORDERSMONTH PER MONTH–––––99.085.082.088.095.091.0MOVINGAVERAGE
  20. 20. Smoothing EffectsCopyright 2011 John Wiley & Sons, Inc. 12-20150 –125 –100 –75 –50 –25 –0 – | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct NovActualOrdersMonth5-month3-month
  21. 21. Weighted Moving AverageCopyright 2011 John Wiley & Sons, Inc. 12-21• Adjusts moving average method to more closelyreflect data fluctuationsWMAn =i = 1Wi DiwhereWi = the weight for period i,between 0 and 100percentWi = 1.00n
  22. 22. Weighted Moving Average ExampleCopyright 2011 John Wiley & Sons, Inc. 12-22MONTH WEIGHT DATAAugust 17% 130September 33% 110October 50% 90WMA3 =3i = 1Wi Di= (0.50)(90) + (0.33)(110) + (0.17)(130)= 103.4 ordersNovember Forecast
  23. 23. Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-23• Averaging method• Weights most recent data more strongly• Reacts more to recent changes• Widely used, accurate method
  24. 24. Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-24Ft +1 = Dt + (1 - )Ftwhere:Ft +1 = forecast for next periodDt = actual demand for present periodFt = previously determined forecast forpresent period= weighting factor, smoothing constant
  25. 25. 0.0 1.0If = 0.20, then Ft +1 = 0.20 Dt + 0.80 FtIf = 0, then Ft +1 = 0 Dt + 1 Ft = FtForecast does not reflect recent dataIf = 1, then Ft +1 = 1 Dt + 0 Ft = DtForecast based only on most recent dataEffect of Smoothing ConstantCopyright 2011 John Wiley & Sons, Inc. 12-25
  26. 26. Exponential Smoothing (α=0.30)Copyright 2011 John Wiley & Sons, Inc. 12-26F2 = D1 + (1 - )F1= (0.30)(37) + (0.70)(37)= 37F3 = D2 + (1 - )F2= (0.30)(40) + (0.70)(37)= 37.9F13 = D12 + (1 - )F12= (0.30)(54) + (0.70)(50.84)= 51.79PERIOD MONTH DEMAND1 Jan 372 Feb 403 Mar 414 Apr 375 May 456 Jun 507 Jul 438 Aug 479 Sep 5610 Oct 5211 Nov 5512 Dec 54
  27. 27. Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-27FORECAST, Ft + 1PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)1 Jan 37 – –2 Feb 40 37.00 37.003 Mar 41 37.90 38.504 Apr 37 38.83 39.755 May 45 38.28 38.376 Jun 50 40.29 41.687 Jul 43 43.20 45.848 Aug 47 43.14 44.429 Sep 56 44.30 45.7110 Oct 52 47.81 50.8511 Nov 55 49.06 51.4212 Dec 54 50.84 53.2113 Jan – 51.79 53.61
  28. 28. Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-2870 –60 –50 –40 –30 –20 –10 –0 – | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13ActualOrdersMonth= 0.50= 0.30
  29. 29. Adjusted Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-29AFt +1 = Ft +1 + Tt +1whereT = an exponentially smoothed trend factorTt +1 = (Ft +1 - Ft) + (1 - ) TtwhereTt = the last period trend factor= a smoothing constant for trend0 ≤ ≤
  30. 30. Adjusted Exponential Smoothing (β=0.30)Copyright 2011 John Wiley & Sons, Inc. 12-30PERIOD MONTH DEMAND1 Jan 372 Feb 403 Mar 414 Apr 375 May 456 Jun 507 Jul 438 Aug 479 Sep 5610 Oct 5211 Nov 5512 Dec 54T3 = (F3 - F2) + (1 - ) T2= (0.30)(38.5 - 37.0) + (0.70)(0)= 0.45AF3 = F3 + T3 = 38.5 + 0.45= 38.95T13 = (F13 - F12) + (1 - ) T12= (0.30)(53.61 - 53.21) + (0.70)(1.77)= 1.36AF13 = F13 + T13 = 53.61 + 1.36 = 54.97
  31. 31. Adjusted Exponential SmoothingCopyright 2011 John Wiley & Sons, Inc. 12-31FORECAST TREND ADJUSTEDPERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +11 Jan 37 37.00 – –2 Feb 40 37.00 0.00 37.003 Mar 41 38.50 0.45 38.954 Apr 37 39.75 0.69 40.445 May 45 38.37 0.07 38.446 Jun 50 38.37 0.07 38.447 Jul 43 45.84 1.97 47.828 Aug 47 44.42 0.95 45.379 Sep 56 45.71 1.05 46.7610 Oct 52 50.85 2.28 58.1311 Nov 55 51.42 1.76 53.1912 Dec 54 53.21 1.77 54.9813 Jan – 53.61 1.36 54.96
  32. 32. Adjusted Exponential SmoothingForecastsCopyright 2011 John Wiley & Sons, Inc. 12-3270 –60 –50 –40 –30 –20 –10 –0 – | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13ActualDemandPeriodForecast ( = 0.50)Adjusted forecast ( = 0.30)
  33. 33. Linear Trend LineCopyright 2011 John Wiley & Sons, Inc. 12-33y = a + bxwherea = interceptb = slope of the linex = time periody = forecast fordemand for period xb =a = y - b xwheren = number of periodsx = = mean of the x valuesy = = mean of the y valuesxy - nxyx2 - nx2xnyn
  34. 34. Least Squares ExampleCopyright 2011 John Wiley & Sons, Inc. 12-34x(PERIOD) y(DEMAND) xy x21 73 37 12 40 80 43 41 123 94 37 148 165 45 225 256 50 300 367 43 301 498 47 376 649 56 504 8110 52 520 10011 55 605 12112 54 648 14478 557 3867 650
  35. 35. Least Squares ExampleCopyright 2011 John Wiley & Sons, Inc. 12-35x = = 6.5y = = 46.42b = = =1.72a = y - bx= 46.42 - (1.72)(6.5) = 35.23867 - (12)(6.5)(46.42)650 - 12(6.5)2xy - nxyx2 - nx2781255712
  36. 36. Copyright 2011 John Wiley & Sons, Inc. 12-36Linear trend line y = 35.2 + 1.72xForecast for period 13 y = 35.2 + 1.72(13) = 57.56 units70 –60 –50 –40 –30 –20 –10 – | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13ActualDemandPeriodLinear trend line
  37. 37. Seasonal AdjustmentsCopyright 2011 John Wiley & Sons, Inc. 12-37 Repetitive increase/ decrease in demand Use seasonal factor to adjust forecastSeasonal factor = Si =DiD
  38. 38. Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-382002 12.6 8.6 6.3 17.5 45.02003 14.1 10.3 7.5 18.2 50.12004 15.3 10.6 8.1 19.6 53.6Total 42.0 29.5 21.9 55.3 148.7DEMAND (1000’S PER QUARTER)YEAR 1 2 3 4 TotalS1 = = = 0.28D1D42.0148.7S2 = = = 0.20D2D29.5148.7S4 = = = 0.37D4D55.3148.7S3 = = = 0.15D3D21.9148.7
  39. 39. Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-39SF1 = (S1) (F5) = (0.28)(58.17) = 16.28SF2 = (S2) (F5) = (0.20)(58.17) = 11.63SF3 = (S3) (F5) = (0.15)(58.17) = 8.73SF4 = (S4) (F5) = (0.37)(58.17) = 21.53y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17For 2005
  40. 40. Forecast Accuracy• Forecast error• difference between forecast and actual demand• MAD• mean absolute deviation• MAPD• mean absolute percent deviation• Cumulative error• Average error or biasCopyright 2011 John Wiley & Sons, Inc. 12-40
  41. 41. Mean Absolute Deviation (MAD)Copyright 2011 John Wiley & Sons, Inc. 12-41wheret = period numberDt = demand in period tFt = forecast for period tn = total number of periods= absolute valueDt - FtnMAD =
  42. 42. Copyright 2011 John Wiley & Sons, Inc. 12-42MAD Example1 37 37.00 – –2 40 37.00 3.00 3.003 41 37.90 3.10 3.104 37 38.83 -1.83 1.835 45 38.28 6.72 6.726 50 40.29 9.69 9.697 43 43.20 -0.20 0.208 47 43.14 3.86 3.869 56 44.30 11.70 11.7010 52 47.81 4.19 4.1911 55 49.06 5.94 5.9412 54 50.84 3.15 3.15557 49.31 53.39PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
  43. 43. MAD CalculationCopyright 2011 John Wiley & Sons, Inc. 12-43Dt - FtnMAD === 4.8553.3911
  44. 44. Other Accuracy MeasuresCopyright 2011 John Wiley & Sons, Inc. 12-44Mean absolute percent deviation (MAPD)MAPD =|Dt - Ft|DtCumulative errorE = etAverage errorE =etn
  45. 45. Comparison of ForecastsCopyright 2011 John Wiley & Sons, Inc. 12-45FORECAST MAD MAPD E (E)Exponential smoothing ( = 0.30) 4.85 9.6% 49.31 4.48Exponential smoothing ( = 0.50) 4.04 8.5% 33.21 3.02Adjusted exponential smoothing 3.81 7.5% 21.14 1.92( = 0.50, = 0.30)Linear trend line 2.29 4.9% – –
  46. 46. 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 frequentlyCopyright 2011 John Wiley & Sons, Inc. 12-46Tracking signal = =(Dt - Ft)MADEMAD
  47. 47. Tracking Signal ValuesCopyright 2011 John Wiley & Sons, Inc. 12-471 37 37.00 – – –2 40 37.00 3.00 3.00 3.003 41 37.90 3.10 6.10 3.054 37 38.83 -1.83 4.27 2.645 45 38.28 6.72 10.99 3.666 50 40.29 9.69 20.68 4.877 43 43.20 -0.20 20.48 4.098 47 43.14 3.86 24.34 4.069 56 44.30 11.70 36.04 5.0110 52 47.81 4.19 40.23 4.9211 55 49.06 5.94 46.17 5.0212 54 50.84 3.15 49.32 4.85DEMAND FORECAST, ERROR E =PERIOD Dt Ft Dt - Ft (Dt - Ft) MAD–1.002.001.623.004.255.016.007.198.189.2010.17TRACKINGSIGNALTS3 = = 2.006.103.05
  48. 48. Tracking Signal PlotCopyright 2011 John Wiley & Sons, Inc. 12-483 –2 –1 –0 –-1 –-2 –-3 –| | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12Trackingsignal(MAD)PeriodExponential smoothing ( = 0.30)Linear trend line
  49. 49. Statistical Control ChartsCopyright 2011 John Wiley & Sons, Inc. 12-49=(Dt - Ft)2n - 1 Using we can calculate statisticalcontrol limits for the forecast error Control limits are typically set at 3
  50. 50. Statistical Control ChartsCopyright 2011 John Wiley & Sons, Inc. 12-50Errors18.39 –12.24 –6.12 –0 –-6.12 –-12.24 –-18.39 –| | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12PeriodUCL = +3LCL = -3
  51. 51. Time Series Forecasting Using Excel• Excel can be used to develop forecasts:• Moving average• Exponential smoothing• Adjusted exponential smoothing• Linear trend lineCopyright 2011 John Wiley & Sons, Inc. 12-51
  52. 52. Exponentially Smoothed and AdjustedExponentially Smoothed ForecastsCopyright 2011 John Wiley & Sons, Inc. 12-52=B5*(C11-C10)+(1-B5)*D10=C10+D10=ABS(B10-E10)=SUM(F10:F20)=G22/11
  53. 53. Demand and Exponentially SmoothedForecastCopyright 2011 John Wiley & Sons, Inc. 12-53Click on “Insert” then “Line”
  54. 54. Data Analysis OptionCopyright 2011 John Wiley & Sons, Inc. 12-54
  55. 55. Forecasting With Seasonal AdjustmentCopyright 2011 John Wiley & Sons, Inc. 12-55
  56. 56. Forecasting With OM ToolsCopyright 2011 John Wiley & Sons, Inc. 12-56
  57. 57. Regression Methods• Linear regression• mathematical technique that relates a dependentvariable to an independent variable in the form of alinear equation• Correlation• a measure of the strength of the relationship betweenindependent and dependent variablesCopyright 2011 John Wiley & Sons, Inc. 12-57
  58. 58. Linear RegressionCopyright 2011 John Wiley & Sons, Inc. 12-58y = a + bx a = y - b xb =wherea = interceptb = slope of the linex = = mean of the x datay = = mean of the y dataxy - nxyx2 - nx2xnyn
  59. 59. Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-59x y(WINS) (ATTENDANCE) xy x24 36.3 145.2 166 40.1 240.6 366 41.2 247.2 368 53.0 424.0 646 44.0 264.0 367 45.6 319.2 495 39.0 195.0 257 47.5 332.5 4949 346.7 2167.7 311
  60. 60. Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-60x = = 6.125y = = 43.36b === 4.06a = y - bx= 43.36 - (4.06)(6.125)= 18.46498346.98xy - nxy2x2 - nx2(2,167.7) - (8)(6.125)(43.36)(311) - (8)(6.125)2
  61. 61. Linear Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-61| | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 1060,000 –50,000 –40,000 –30,000 –20,000 –10,000 –Linear regression line, y= 18.46 + 4.06xWins, xAttendance,yy = 18.46 + 4.06(7)= 46.88, or 46,880Attendance forecast for 7 wins
  62. 62. Correlation and Coefficient ofDetermination• Correlation, r• Measure of strength of relationship• Varies between -1.00 and +1.00• Coefficient of determination, r2• Percentage of variation in dependent variableresulting from changes in the independent variableCopyright 2011 John Wiley & Sons, Inc. 12-62
  63. 63. n xy - x y[n x2 - ( x)2] [n y2 - ( y)2]r =Coefficient of determinationr2 = (0.947)2 = 0.897r =(8)(2,167.7) - (49)(346.9)[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]r = 0.947Computing CorrelationCopyright 2011 John Wiley & Sons, Inc. 12-63
  64. 64. Regression Analysis With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-64=INTERCEPT(B5:B12,A5:A12)=CORREL(B5:B12,A5:A12)=SUM(B5:B12)
  65. 65. Regression Analysis with ExcelCopyright 2011 John Wiley & Sons, Inc. 12-65
  66. 66. Regression Analysis With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-66
  67. 67. Multiple RegressionCopyright 2011 John Wiley & Sons, Inc. 12-67Study the relationship of demand to two or moreindependent variablesy = 0 + 1x1 + 2x2 … + kxkwhere0 = the intercept1, … , k = parameters for theindependent variablesx1, … , xk = independent variables
  68. 68. Multiple Regression With ExcelCopyright 2011 John Wiley & Sons, Inc. 12-68r2, the coefficientof determinationRegression equationcoefficients for x1 and x2
  69. 69. Multiple Regression ExampleCopyright 2011 John Wiley & Sons, Inc. 12-69y = 19,094.42 + 3560.99 x1 + .0368 x2y = 19,094.42 + 3560.99 (7) + .0368 (60,000)= 46,229.35
  70. 70. Copyright 2011 John Wiley & Sons, Inc. 12-70Copyright 2011 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation of thiswork beyond that permitted in section 117 of the 1976United States Copyright Act without express permissionof the copyright owner is unlawful. Request for furtherinformation should be addressed to the PermissionDepartment, John Wiley & Sons, Inc. The purchasermay make back-up copies for his/her own use only andnot for distribution or resale. The Publisher assumes noresponsibility for errors, omissions, or damages causedby the use of these programs or from the use of theinformation herein.

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