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# HW Ch 4 - 4.2(a)No the data appear to have no consistent...

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(d) The three-year moving average appears to give better results. = + = + = = + = + - = July June August July (a) 0.2(Forecasting error) 42 0.2(40 – 42) 41.6 (b) 0.2(Forecasting error) 41.6 0.2(45 41.6) 42.3 F F F F 4.4 (c) The banking industry has a great deal of seasonality in its processing requirements 4.6 Y  Sales X  Period X 2 XY January 20 1 1 20 February 21 2 4 42 March 15 3 9 45 April 14 4 16 56 May 13 5 25 65 June 16 6 36 96 July 17 7 49 119 August 18 8 64 144 September 20 9 81 180 October 20 10 100 200 November 21 11 121 231 December 23 12 144 276 Sum  218 78 650 1474 Average    18.2    6.5 (a) 1 4.2 (a) No, the data appear to have no consistent pattern (see part d for graph). Year 1 2 3 4 5 6 7 8 9 10 11 Forecast Demand 7 9 5 9.0 13.0 8.0 12.0 13.0 9.0 11.0 7.0 (b) 3-year moving 7.0 7.7 9.0 10.0 11.0 11.0 11.3 11.0 9.0 (c) 3-year weighted 6.4 7.8 11.0 9.6 10.9 12.2 10.5 10.6 8.4

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CHAPTER 4 F O R E C A S T I N G 2 (b) [i] Naive The coming January = December = 23 [ii] 3-month moving (20 + 21 + 23)/3 = 21.33 [iii] 6-month weighted [(0.1 × 17) + (.1 × 18) + (0.1 × 20) + (0.2 × 20) + (0.2 × 21) + (0.3 × 23)]/1.0 = 20.6 [iv] Exponential smoothing with alpha = 0.3 = + - = = + - = = + - = = + - = 18 0.3(20 18) 18.6 18.6 0.3(20 18.6) 19.02 19.02 0.3(21 19.02) 19.6 19.6 0.3(23 19.6) 20.62 21 Oct Nov Dec Jan F F F F [v] Trend 78, 6.5, 218, 18.17 x x y = y = = = - = = = - = - = 2 1474 (12)(6.5)(18.2) 54.4 0.38 650 12(6.5) 143 18.2 0.38(6.5) 15.73 b a Forecast = 15.73 + .38(13) = 20.67, where next January is the 13th month. (c) Only trend provides an equation that can extend beyond one month + + = (96 88 90) (a) 91.3 3 4.8 Table for Problem 4.9 (a, b, c) Forecast |Error| Two-Month Three-Month Two-Month Three-Month Price per Moving Moving Moving Moving Month Chip Average Average Average Average January \$1.80 February 1.67 March 1.70 1.735 .035 April 1.85 1.685 1.723 .165 .127 May 1.90 1.775 1.740 .125 .160 June 1.87 1.875 1.817 .005 .053 July 1.80 1.885 1.873 .085 .073 August 1.83 1.835 1.857 .005 .027 September 1.70 1.815 1.833 .115 .133 October 1.65 1.765 1.777 .115 .127 November 1.70 1.675 1.727 .025 .027 December 1.75 1.675 1.683 .075 .067 Totals .750 .793
CHAPTER 4 F O R E C A S T I N G 3 + = (88 90) (b) 89 2 (c) Temperature 2 day M.A.  |Error| (Error) 2    Absolute % Error 93    — 94    — 93 93.5  0.5    0.25    100(.5/93)  = 0.54% 95 93.5  1.5     2.25    100(1.5/95)   = 1.58% 96 94.0  2.0    4.00    100(2/96)  = 2.08% 88 95.5  7.5    56.25    100(7.5/88)   = 8.52% 90 92.0  2.0    4.00    100(2/90)  = 2.22% 13.5 66.75 14.94% MAD = 13.5/5 = 2.7 (d) MSE = 66.75/5 = 13.35 (e) MAPE = 14.94%/5 = 2.99% (c) The forecasts are about the same. 4.10 Year 1 2 3 4 5 6 7 8 9 10 11 Forecast Demand 4 6 4 5.0 10.0 8.0 7.0 9.0 12.0 14.0 15.0 (a) 3-year moving 4.7 5.0 6.3 7.7 8.3 8.0 9.3 11.7 13.7 (b) 3-year weighted 4.5 5.0 7.3 7.8 8.0 8.3 10.0 12.3 14.0

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CHAPTER 4 F O R E C A S T I N G 4 4.13 (a) Exponential smoothing, α = 0.6: Exponential Absolute Year Demand Smoothing  α  = 0.6 Deviation 1 45 41 4.0 2 50 41.0 + 0.6(45–41) = 43.4 6.6 3 52 43.4 + 0.6(50–43.4) = 47.4 4.6 4 56 47.4 + 0.6(52–47.4) = 50.2 5.8 5 58 50.2 + 0.6(56–50.2) = 53.7 4.3 6 ? 53.7 + 0.6(58–53.7) = 56.3 Σ = 25.3 MAD = 5.06 Exponential smoothing, α = 0.9: Exponential Absolute Year Demand Smoothing  α  = 0.9 Deviation 1 45 41 4.0 2 50 41.0 + 0.9(45–41) = 44.6 5.4 3 52 44.6 + 0.9(50–44.6 ) = 49.5 2.5 4 56 49.5 + 0.9(52–49.5) = 51.8 4.2 5 58 51.8 + 0.9(56–51.8) = 55.6 2.4 6 ? 55.6 + 0.9(58–55.6) = 57.8 Σ = 18.5 MAD = 3.7 (b)
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HW Ch 4 - 4.2(a)No the data appear to have no consistent...

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