Lecture2 forecasting f06_604

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  • Lecture2 forecasting f06_604

    1. 1. CHAPTER 13FORECASTINGOutline• Forecasting and Choice of a Forecasting Methods• Methods for Stationary Series:– Simple and Weighted Moving Average– Exponential smoothing• Trend-Based Methods– Regression– Double Exponential Smoothing: Holt’s Method• A Method for Seasonality and Trend
    2. 2. Forecasting
    3. 3. Decisions Based on Forecasts• Production– Aggregate planning,inventory control,scheduling• Marketing– New productintroduction, sales-force allocation,promotions• Finance– Plant/equipmentinvestment, budgetaryplanning• Personnel– Workforce planning,hiring, layoff
    4. 4. Characteristics of Forecasts• Forecasts are alwayswrong; so considerboth expected valueand a measure offorecast error• Long-term forecastsare less accurate thanshort-term forecasts• Aggregate forecastsare more accurate thandisaggregate forecasts
    5. 5. Forecasting• Components of demand• Evaluation of forecasts• Time series: stationary series• Time series: trend– Linear regression– Double exponential smoothing• Time series: seasonality
    6. 6. Components of Demand• Average demand• Trend– Gradual shift in average demand• Seasonal pattern– Periodic oscillation in demand which repeats• Cycle– Similar to seasonal patterns, length andmagnitude of the cycle may vary• Random movements• Auto-correlation
    7. 7. QantityTime(a) Average: Data cluster about a horizontal line.Components of Demand
    8. 8. QuantityTime(b) Linear trend: Data consistently increase or decrease.Components of Demand
    9. 9. Components of DemandQuantity| | | | | | | | | | | |J F M A M J J A S O N DMonths(c) Seasonal influence: Data consistently showpeaks and valleys.Year 1
    10. 10. Components of DemandQuantity| | | | | | | | | | | |J F M A M J J A S O N DMonths(c) Seasonal influence: Data consistently showpeaks and valleys.Year 1Year 2
    11. 11. Components of Demand
    12. 12. Components of DemandQuantity| | | | | |1 2 3 4 5 6Years(c) Cyclical movements: Gradual changes overextended periods of time.
    13. 13. Components of Demand
    14. 14. DemandTimeTrendRandommovementDemandTimeTrend withseasonal patternComponents of Demand
    15. 15. Snow SkiingSeasonalLong term growth trendDemand for skiing products increasedsharply after the Nagano Olympics
    16. 16. Σ|Et |nΣEt2nRSFE = ΣEtMAD =MSE =MAPE =σ = MSEΣ[|Et | (100)]/AtnMeasures of Forecast ErrorEt = At - FtChoosing a MethodChoosing a MethodForecast ErrorForecast Error
    17. 17. AbsoluteError Absolute PercentMonth, Demand, Forecast, Error, Squared, Error, Error,t At Ft Et Et2|Et| (|Et|/At)(100)1 200 2252 240 2203 300 2854 270 2905 230 2506 260 2407 210 2508 275 240-TotalChoosing a MethodChoosing a MethodForecast ErrorForecast Error
    18. 18. MSE = =Measures of ErrorMAD = =MAPE = =RSFE =Choosing a MethodChoosing a MethodForecast ErrorForecast Error
    19. 19. Choosing a MethodChoosing a MethodForecast ErrorForecast ErrorRunning Sum Mean Absoluteof Forecast Errors DeviationMethod (RSFE - bias) (MAD)Simple moving averageThree-week (n = 3) 23.1 17.1Six-week (n = 6) 69.8 15.5Weighted moving average0.70, 0.20, 0.10 14.0 18.4Exponential smoothingα = 0.1 65.6 14.8α = 0.2 41.0 15.3
    20. 20. Choosing a MethodChoosing a MethodTracking SignalsTracking Signals Tracking signal =RSFEMAD+2.0 —+1.5 —+1.0 —+0.5 —0 —- 0.5 —- 1.0 —- 1.5 —| | | | |0 5 10 15 20 25Observation numberTrackingsignalControl limitControl limit
    21. 21. Choosing a MethodChoosing a MethodTracking SignalsTracking Signals Tracking signal =RSFEMAD+2.0 —+1.5 —+1.0 —+0.5 —0 —- 0.5 —- 1.0 —- 1.5 —| | | | |0 5 10 15 20 25Observation numberTrackingsignalControl limitControl limitOut of control
    22. 22. Choosing a MethodChoosing a MethodTracking SignalsTracking SignalsC o n t r o l L im itS p r e a d( N u m b e r o fM A D )E q u iv a le n tN u m b e r o f σ( σ = 1 .2 5 M A D )P e r c e n t a g e o fA r e a w it h inC o n t r o l L im it s± 1 .0 ± 0 .8 0 5 7 .6 2± 1 .5 ± 1 .2 0 7 6 .9 8± 2 .0 ± 1 .6 0 8 9 .0 4± 2 .5 ± 2 .0 0 9 5 .4 4± 3 .0 ± 2 .4 0 9 8 .3 6± 3 .5 ± 2 .8 0 9 9 .4 8± 4 .0 ± 3 .2 0 9 9 .8 6
    23. 23. Problem 13-2: Historical demand for a product is:Month Jan Feb Mar Apr May JunDemand 12 11 15 12 16 15a. Using a weighted moving average with weights of 0.60,0.30, and 0.10, find the July forecast.b. Using a simple three-month moving average, find the Julyforecast.c. Using single exponential smoothing with α=0.20 and a Juneforecast =13, find the July forecast.d. Using simple regression analysis, calculate the regressionequation for the preceding demand datae. Using regression equation in d, calculate the forecast inJuly
    24. 24. Problem 13-15: In this problem, you are to test the validity ofyour forecasting model. Here are the forecasts for a modelyou have been using and the actual demands thatoccurred:Week 1 2 3 4 5 6Forecast 800 850 950 950 1,000 975Actual 900 1,000 1,050 900 900 1,100Compute MAD and tracking signal. Then decide whether theforecasting model you have been using is givingreasonable results.
    25. 25. Methods for Stationary Series
    26. 26. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving AveragesWeek450 —430 —410 —390 —370 —Patientarrivals| | | | | |0 5 10 15 20 25 30Actual patientarrivals
    27. 27. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving AveragesActual patientarrivals450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30PatientWeek Arrivals1 4002 3803 411
    28. 28. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving AveragesActual patientarrivals450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30PatientWeek Arrivals1 4002 3803 411F4 =
    29. 29. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving AveragesActual patientarrivals450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30PatientWeek Arrivals2 3803 4114 415F5 =
    30. 30. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving Averages450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30Actual patientarrivals3-week MAforecast
    31. 31. Time Series MethodsTime Series MethodsSimple Moving AveragesSimple Moving AveragesWeek450 —430 —410 —390 —370 —Patientarrivals| | | | | |0 5 10 15 20 25 30Actual patientarrivals3-week MAforecast6-week MAforecast
    32. 32. Taco Bell determined thatthe demand for each 15-minute intervalcan be estimated from a 6-week simple movingaverage of sales.The forecast was used todetermine the number ofemployees needed.
    33. 33. Time Series MethodsTime Series MethodsWeighted Moving AverageWeighted Moving Average450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30Actual patientarrivals3-week MAforecast Weighted Moving AverageAssigned weightst-1 0.70t-2 0.20t-3 0.10F4 =
    34. 34. Time Series MethodsTime Series MethodsWeighted Moving AverageWeighted Moving Average450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30Actual patientarrivals3-week MAforecast Weighted Moving AverageAssigned weightst-1 0.70t-2 0.20t-3 0.10F5 =
    35. 35. Time Series MethodsTime Series MethodsExponential SmoothingExponential Smoothing450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30Exponential Smoothingα = 0.10Ft = α At-1 + (1 - α)Ft - 1
    36. 36. Time Series MethodsTime Series MethodsExponential SmoothingExponential Smoothing450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30Exponential Smoothingα = 0.10Ft = α At-1 + (1 - α)Ft - 1F3 = (400 + 380)/2=390A3 = 411
    37. 37. Time Series MethodsTime Series MethodsExponential SmoothingExponential Smoothing450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30F4 =Exponential Smoothingα = 0.10Ft = α At-1 + (1 - α)Ft - 1F3 = (400 + 380)/2=390A3 = 411
    38. 38. Time Series MethodsTime Series MethodsExponential SmoothingExponential SmoothingWeek450 —430 —410 —390 —370 —Patientarrivals| | | | | |0 5 10 15 20 25 30F4 =A4 = 415Exponential Smoothingα = 0.10Ft = α At + (1 - α)Ft - 1F5 =
    39. 39. Time Series MethodsTime Series MethodsExponential SmoothingExponential Smoothing450 —430 —410 —390 —370 —PatientarrivalsWeek| | | | | |0 5 10 15 20 25 30
    40. 40. Comparison of ExponentialComparison of ExponentialSmoothing and Simple MovingSmoothing and Simple MovingAverageAverage• Both Methods– Are designed for stationary demand– Require a single parameter– Lag behind a trend, if one exists– Have the same distribution of forecast error if)1/(2 +=α N
    41. 41. Comparison of ExponentialComparison of ExponentialSmoothing and Simple MovingSmoothing and Simple MovingAverageAverage• Moving average uses only the last N periodsdata, exponential smoothing uses all data• Exponential smoothing uses less memory andrequires fewer steps of computation; store onlythe most recent forecast!
    42. 42. Problem 13-20: Your manager is trying to determine whatforecasting method to use. Based upon the following historicaldata, calculate the following forecast and specify what procedureyou would utilize:Month 1 2 3 4 5 6 7 8 9 10 11 12Actual demand 62 65 67 68 71 73 76 78 78 80 84 85a. Calculate the three-month SMA forecast for periods 4-12b. Calculate the weighted three-month MA using weights of 0.50,0.30, and 0.20 for periods 4-12.c. Calculate the single exponential smoothing forecast for periods 2-12 using an initial forecast, F1=61 and α=0.30d. Calculate the exponential smoothing with trend componentforecast for periods 2-12 using T1=1.8,F1=60,α=0.30,δ=0.30e. Calculate MAD for the forecasts made by each technique inperiods 4-12. Which forecasting method do you prefer?
    43. 43. Trend-Based Methods
    44. 44. Turkeys have a long-term trend for increasing demand with aseasonal pattern. Sales are highest during September to Novemberand sales are lowest during December and January.
    45. 45. Linear RegressionLinear RegressionDependentvariableIndependent variableXY
    46. 46. Linear RegressionLinear RegressionDependentvariableIndependent variableXY Regressionequation:Y = a + bX
    47. 47. Linear RegressionLinear RegressionDependentvariableIndependent variableXYActualvalueof YValue of X usedto estimate YRegressionequation:Y = a + bX
    48. 48. Linear RegressionLinear RegressionDependentvariableIndependent variableXYActualvalueof YEstimate ofY fromregressionequationValue of X usedto estimate YRegressionequation:Y = a + bX
    49. 49. Linear RegressionLinear RegressionDependentvariableIndependent variableXYActualvalueof YEstimate ofY fromregressionequationValue of X usedto estimate YDeviation,or error{Regressionequation:Y = a + bX
    50. 50. Linear RegressionLinear RegressionSales AdvertisingMonth (000 units) (000 $)1 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0
    51. 51. Linear RegressionLinear RegressionSales, y Advertising, xMonth (000 units) (000 $)1 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0a = y - bx b =Σxy - nxyΣx2- n(x )2
    52. 52. a = y - bx b =Σxy - nxyΣx 2- nx 2Sales, y Advertising, xMonth (000 units) (000 $) xy x 21 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0Totaly= x =Linear RegressionLinear Regression
    53. 53. 300 —250 —200 —150 —100 —50b = 109.229Y =Sales(000s)| | | |1.0 1.5 2.0 2.5
    54. 54. Linear RegressionLinear RegressionSales, y Advertising, xMonth (000 units) (000 $) xy x 2y 21 264 2.5 660.0 6.252 116 1.3 150.8 1.693 165 1.4 231.0 1.964 101 1.0 101.0 1.005 209 2.0 418.0 4.00Total 855 8.2 1560.8 14.90y = 171 x = 1.64nΣxy - Σx Σy[nΣx 2-(Σx) 2][nΣy 2- (Σy) 2]r =
    55. 55. Linear RegressionLinear RegressionSales, y Advertising, xMonth (000 units) (000 $) xy x 2y 21 264 2.5 660.0 6.25 69,6962 116 1.3 150.8 1.69 13,4563 165 1.4 231.0 1.96 27,2254 101 1.0 101.0 1.00 10,2015 209 2.0 418.0 4.00 43,681Total 855 8.2 1560.8 14.90 164,259y= 171 x = 1.64r = 0.98 r 2= 0.96
    56. 56. Linear RegressionLinear RegressionForecast for Month 6:Advertising expenditure = $1750Y =
    57. 57. Time Series MethodsTime Series MethodsLinear Regression AnalysisLinear Regression Analysis| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1580 —70 —60 —50 —40 —30 —PatientarrivalsWeekYn = a + bXnwhereXn = Weekn
    58. 58. Time Series MethodsTime Series MethodsLinear Regression AnalysisLinear Regression Analysis| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1580 —70 —60 —50 —40 —30 —PatientarrivalsWeekYn = a + bXnwhereXn = Weekn
    59. 59. Time Series MethodsTime Series MethodsLinear Regression AnalysisLinear Regression Analysis• Standard error of estimate is computed asfollows:2)(12−−=∑=nYySniiiyx
    60. 60. Time Series MethodsTime Series MethodsLinear Regression AnalysisLinear Regression Analysis• An use of the standard error of estimate:– Suppose that a manager forecasts that the demandfor a product is 500 units and Syx is 20. If themanager wants to accept a stockout only 2% time,how many additional units should be held in theinventory?
    61. 61. • The method uses two smoothing constants αand δTime Series MethodsTime Series MethodsDouble Exponential SmoothingDouble Exponential SmoothingttttttttttTFTFFTAF+=−+−=−+=−−−−FITFIT1111)1()()1(δδαα
    62. 62. A Comparison of Methods606570758085900 5 10 15MonthsDemandActual3-Mo MA3-Mo WMAExp SmDouble Exp Sm
    63. 63. Methods for Seasonal Series
    64. 64. Quarter Year 1 Year 2 Year 3 Year 41 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215Total 1000 1200 1800 2200Average 250 300 450 550Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    65. 65. Quarter Year 1 Year 2 Year 3 Year 41 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215Total 1000 1200 1800 2200Average 250 300 450 550Seasonal Index =Actual DemandAverage DemandTime Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    66. 66. Quarter Year 1 Year 2 Year 3 Year 41 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215Total 1000 1200 1800 2200Average 250 300 450 550Seasonal Index = =Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    67. 67. Quarter Year 1 Year 2 Year 3 Year 41 45/250 = 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215Total 1000 1200 1800 2200Average 250 300 450 550Seasonal Index = =Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    68. 68. Quarter Year 1 Year 2 Year 3 Year 41 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    69. 69. Quarter Year 1 Year 2 Year 3 Year 41 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39Quarter Average Seasonal Index1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20234Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    70. 70. Quarter Average Seasonal Index Forecast1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20234Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650Time Series MethodsTime Series MethodsSeasonal InfluencesSeasonal Influences
    71. 71. Seasonal InfluencesSeasonal InfluencesPeriodDemand(a) Multiplicative influence| | | | | | | | | | | | | | | |0 2 4 5 8 10 12 14 16
    72. 72. Seasonal InfluencesSeasonal InfluencesPeriod| | | | | | | | | | | | | | | |0 2 4 5 8 10 12 14 16Demand(b) Additive influence
    73. 73. Time Series MethodsTime Series MethodsSeasonal Influences with TrendSeasonal Influences with TrendStep 1: Determine seasonal factors– Example: if the demands are quarterly, divide the average demand inQuarter 1 by the average quarterly demandStep 2: Deseasonalize the original data– Divide the original data by the seasonal factorsStep 3: Develop a regression line on deaseasonalized data– Find parameters a and b in Y=a+bX– Where– yi = deseasonalized data (not the original data)– xi = time; 1, 2, 3, …, n– n = Number of periods
    74. 74. Time Series MethodsTime Series MethodsSeasonal Influences with TrendSeasonal Influences with TrendStep 4: Make projection using regression line– For each i = n+1, n+2, …, compute yi by substituting a, b and xi inthe regression equation yi = a+bxiStep 5: Reseasonalize projection using seasonal factors– Multiply the projected values by the seasonal factors
    75. 75. Problem 13-21: Use regression analysis on deseasonalizeddemand to forecast demand in summer 2006, given thefollowing historical demand data:Year Season Actual Demand2004 Spring 205Summer 140Fall 375Winter 5752005 Spring 475Summer 275Fall 685Winter 965
    76. 76. Reading and Exercises• Chapter 13 pp. 518-539• Problems 1, 7, 13, 14,16

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