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2-2011=Revision-MIDTERM=CALCULATION

2-2011=Revision-MIDTERM=CALCULATION - 3 Forecasting No...

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3 3 Forecasting
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Chapter 3 Forecasting 2 No 2/118 National Scan, Inc., sells radio frequency inventory tags . Monthly sales for a seven-month period were as follows; Month Sales F M A M J J A S 20 0
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3 Month t t 2 Y Sales tY Feb. 1 1 19 19 Mar. 2 4 18 36 Apr. 3 9 15 45 May 4 16 20 80 Jun. 5 25 18 90 Jul. 6 36 22 132 Aug. 7 49 20 140 Sept.? 28 14 0 132 542 From Table 3–1 with n = 7, Σ t = 28, Σ t 2 = 140, ∑tY=542, ∑Y=132 50 . ) 28 ( 28 ) 140 ( 7 ) 132 ( 28 ) 542 ( 7 ) t ( t n Y t tY n b 2 2 = - - = - - = 86 . 16 7 ) 28 ( 50 . 132 n t b Y a = - = - = Forecast September sales volume (1) A Linear Equation No.2/11 8 Y t = 16.86 + .50 t , t=1,2,3,4,5,6,7,8,9 For Sept ember, t = 8 , and Y t = 16.86+.50(8) = 20.86 (000) For October , t = 9 , and Y t = 16.86+.50(9) = 21.36 (000) What is the forecast of October ? Y t = a + b t, t =1,2,3,4, Time Series A Linear Equation
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( Page 81 ) I. Simple Moving Average 4 n A A A A F n t t t t t - - - - + + + + = ........ 3 2 1 Moving period =4 for forecast of time period 6 , (n=4,t=6) Moving period = 6 for forecast of time period 10, (n=6, t=10) 6 4 5 6 7 8 9 10 A A A A A A F + + + + + = 4 2 3 4 5 6 A A A A F + + + = F t = Forecast for the coming period N = Number of periods to be averaged A t-1 = Actual occurrence in the past period for up to “n” periods No 2/118
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5 Forecast September sales volume (2) A Five-month moving average No 2/118 average moving in the periods of Number 1 period in value Actual average moving period MA period for time Forecast where MA 1 1 t = - = = = = = - = - n t A n t F n A F t t t n i i t t n A A A F n t t t t - - - + + = 2 1 Month Y Sales Feb. 19 =A 1 Mar. 18=A 2 Apr. 15=A 3 May 20=A 4 Jun. 18=A 5 Jul. 22=A 6 Aug. 20=A 7 19 5 20 22 18 20 15 MA 5 = + + + + = Page 81 Simple Moving Average Method What is the forecast for August? What is the forecast for July? =93/5=18.6 =90/5=18
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α 6 ) ( 1 1 1 - - - - + = t t t t F A F F α α = smoothing constant (alpha ), 0 < α < 1 Example an initial forecast for March (F 2 = 19(000) and an alpha ( ) =0.20 (c) (Page 83) No 2/118 (c) (Page 83) ) ( 1 1 1 - - - + = t t t A F F α α = smoothing constant (alpha ), 0 < α
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7 March 18=A 2 F 2 =19 April 15=A 3 F 3 =18.8= 19 + .20[18 – 19 ] F 3 = F 2 + .2(A 2 - F 2 ) ) ( 1 1 1 - - - - + = t t t t F A F F α an initial forecast for March (F 2 = 19(000) and an alpha ( α ) =0.20 F 4 = F 3 + .2(A 3 - F 3 ) May 20=A 4 F 4 =18.04 = 18.8 + .20[ 15 – 18.8] June 18=A 5 F 5 =18.43 = 18.04 + .20[ 20 – 18.04] F 5 = F 4 + .2(A 4 - F 4 ) No 2/118
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8 Month Actual Sales (000) Forecast = F(old) + .20[Actual F(old) ] March 18=A 2 F 2 =19 April 15=A 3 18.8= 19 + .20[ 18 – 19 ] May 20=A 4 18.04 = 18.8 + .20[ 15 – 18.8] June 18=A 5 18.43 = 18.04 + .20[ 20 – 18.04] July 22=A 6 18.34 = 18.43 + .20[ 18 – 18.43] August 20=A 7 19.07 = 18.34 + .20[ 22 – 18.34] Sep. 19.26 = 19.07 + .20[ 20 – 19.0] ) ( 1 1 1 - - - - + = t t t t F A F F α an initial forecast for March (F 2 = 19(000) and an alpha ( ) =0.20 α No 2/118
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9 (4) Naïve Forecast Uses a single previous value of a time series as the basis for a forecast The forecast for a time period is equal to the previous time period’s value 4) F 8 = A 7 =20 Forecast September sales volume Month Y Sales Feb. 19 =A 1 Mar. 18=A 2 Apr. 15=A 3 May 20=A 4 Jun. 18=A 5 Jul. 22=A 6 Aug. 20=A 7 Sep. ? No 2/118
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n t n t t t A w A w A w F - - - + + + = .. .......... 2 2 1 1 10 Page 83 Weighted Moving Average F t = w n A t - n + w n - 1 A t - ( n - 1) + ... + w 1 A t - 1 where w t = weight for period t , w t - 1 = weight for period t - 1, etc.
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