DEMAND FORECASTING II
2TREND PROJECTION METHOD1. Graphic method (fitting trend line by observation)2. Algebric (least squares)3. Smoothing metho...
3TimeValuesofDependentVariable(I) GRAPHIC METHODRandom InfluencesCyclical FluctuationSecular Trend
4TimeValuesofDependentVariableActualobservationGRAPHIC METHOD
5DeviationDeviationDeviationDeviationDeviationDeviationDeviationTimeValuesofDependentVariablePoint onthe lineActualobserva...
6DeviationDeviationDeviationDeviationDeviationDeviationDeviationTimeValuesofDependentVariablebxaYˆPoint onthe lineActualob...
7(II) LEAST SQUARES METHOD• Fitting a trend line to the data• Constant Rate of ChangeSt = So + bt• Where:– St value of tim...
8PeriodYear (t) Sales (S) S * t t^21991 1 300 300 11992 2 305 610 41993 3 315 945 91994 4 340 1360 161995 5 346 1730 25199...
9PeriodYear (t) Sales (S) S * t t^21991 1 300 300 11992 2 305 610 41993 3 315 945 91994 4 340 1360 161995 5 346 1730 25199...
10(III) SMOOTHING TECHNIQUES• Predicting values of a time series on the basis of someaverage of its past values• Used when...
11Quarter Actual Market 3 Quarter MovingShare (A) Average(F)1 202 223 234 24 21.675 18 23.006 23 21.677 19 21.678 17 20.00...
12Year Actual Market 3 Quarter Moving A - F (A - F)^2 5Share (A) Average(F) Av1 202 22 21.67 0.33 0.10893 23 23 0 04 24 21...
13Year Actual Market 3 Quarter Moving A - F (A - F)^2 5 Quarter Moving A - F (A - F)^2Share (A) Average(F) Average(F)1 202...
14nFA tt2)(RMSE =To decide on the better moving average forecast calculate theroot-mean-square error(RMSE) of each forecas...
15EXPONENTIAL SMOOTHING• Forecast for next period (ie, t) is a weighted average ofthe actual value in that period and fore...
16Year Demand (000 units)1 482 423 204 485 386 347 468 509 4810 5411 4012 44Find the exponentiallysmoothened time series u...
17Year Demand(000 units) (A)ExponentiallySmoothenedvalues(w = 0.1)(f t+1)A – (Ft +1){A – (Ft + 1)}21 48 482 42 47.43 20 44...
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demand forecasting

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demand forecasting

  1. 1. DEMAND FORECASTING II
  2. 2. 2TREND PROJECTION METHOD1. Graphic method (fitting trend line by observation)2. Algebric (least squares)3. Smoothing methods Moving average method Exponential smoothing
  3. 3. 3TimeValuesofDependentVariable(I) GRAPHIC METHODRandom InfluencesCyclical FluctuationSecular Trend
  4. 4. 4TimeValuesofDependentVariableActualobservationGRAPHIC METHOD
  5. 5. 5DeviationDeviationDeviationDeviationDeviationDeviationDeviationTimeValuesofDependentVariablePoint onthe lineActualobservationGRAPHIC METHOD
  6. 6. 6DeviationDeviationDeviationDeviationDeviationDeviationDeviationTimeValuesofDependentVariablebxaYˆPoint onthe lineActualobservationGRAPHIC METHOD
  7. 7. 7(II) LEAST SQUARES METHOD• Fitting a trend line to the data• Constant Rate of ChangeSt = So + bt• Where:– St value of time series to be forecasted for period t– So estimated value of time series in the base period– b is the absolute amount of growth per period– t time period for which series is to be forecastedS = nSo + b tS*t = So t + b t2
  8. 8. 8PeriodYear (t) Sales (S) S * t t^21991 1 300 300 11992 2 305 610 41993 3 315 945 91994 4 340 1360 161995 5 346 1730 251996 6 352 2112 361997 7 364 2548 491998 8 390 3120 641999 9 397 3573 812000 10 404 4040 1002001 11 418 4598 1212002 12 445 5340 144EXAMPLEAssuming the present trend continues, in which year would youexpect 1992 sales to be doubled?
  9. 9. 9PeriodYear (t) Sales (S) S * t t^21991 1 300 300 11992 2 305 610 41993 3 315 945 91994 4 340 1360 161995 5 346 1730 251996 6 352 2112 361997 7 364 2548 491998 8 390 3120 641999 9 397 3573 812000 10 404 4040 1002001 11 418 4598 1212002 12 445 5340 144n = 12 78 4376 30276 650St = So + btS = nSo + b tS*t = So t + b t2St = 281.39 + 12.81tSOLUTIONDouble of 1992 sales = 610So t = 25.65i.e. in 2017
  10. 10. 10(III) SMOOTHING TECHNIQUES• Predicting values of a time series on the basis of someaverage of its past values• Used when time series exhibit irregular or random variation– Moving Averages– Exponential Smoothing
  11. 11. 11Quarter Actual Market 3 Quarter MovingShare (A) Average(F)1 202 223 234 24 21.675 18 23.006 23 21.677 19 21.678 17 20.009 22 19.6710 23 19.3311 18 20.6712 23 21.00MOVING AVERAGE: EXAMPLE
  12. 12. 12Year Actual Market 3 Quarter Moving A - F (A - F)^2 5Share (A) Average(F) Av1 202 22 21.67 0.33 0.10893 23 23 0 04 24 21.67 2.33 5.435 18 21.67 -3.67 13.476 23 20.00 3.00 9.007 19 19.67 -0.67 0.458 17 19.33 -2.33 5.439 22 20.67 1.33 1.7710 23 21.00 2.00 4.0011 18 21.33 -3.33 11.0912 2350.63RMSE 2.05MOVING AVERAGE
  13. 13. 13Year Actual Market 3 Quarter Moving A - F (A - F)^2 5 Quarter Moving A - F (A - F)^2Share (A) Average(F) Average(F)1 202 22 21.67 0.33 0.10893 23 23 0 0 21.4 1.6 2.564 24 21.67 2.33 5.43 22.00 2.00 4.005 18 21.67 -3.67 13.47 21.40 -3.40 11.566 23 20.00 3.00 9.00 20.20 2.80 7.847 19 19.67 -0.67 0.45 19.80 -0.80 0.648 17 19.33 -2.33 5.43 20.80 -3.80 14.449 22 20.67 1.33 1.77 19.80 2.20 4.8410 23 21.00 2.00 4.00 20.60 2.40 5.7611 18 21.33 -3.33 11.0912 2350.63 51.64RMSE 2.05 2.07MOVING AVERAGE
  14. 14. 14nFA tt2)(RMSE =To decide on the better moving average forecast calculate theroot-mean-square error(RMSE) of each forecast and use themoving average which results in the smallest RMSE
  15. 15. 15EXPONENTIAL SMOOTHING• Forecast for next period (ie, t) is a weighted average ofthe actual value in that period and forecasted values ofthe time series in period (t - 1)0 1wSt = w Y t + (1 – w) S t-1
  16. 16. 16Year Demand (000 units)1 482 423 204 485 386 347 468 509 4810 5411 4012 44Find the exponentiallysmoothened time series usingsmoothing constant w = 0.1and w = 0.4
  17. 17. 17Year Demand(000 units) (A)ExponentiallySmoothenedvalues(w = 0.1)(f t+1)A – (Ft +1){A – (Ft + 1)}21 48 482 42 47.43 20 44.664 48 455 38 44.36 34 43.287 46 43.568 50 44.29 48 44.5810 54 45.5211 40 44.9612 44 44.86FindRMSE

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