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MGSC 625 Problem 12-9 & 12-15

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Question;Problem 12-15 Adjusted Exponentially Smoothed Forecasts Alpha 0.3 Beta 0.2 Ft +1 =?Dt + (1 -?)Ft AFt +1 = Ft +1 + Tt +1 Tt +1 =?(Ft +1 - Ft) + (1 -?) Tt Forecast Trend Adjusted Forecast Year Coat Sales (tons) Ft +1 Tt +1 AFt +1 1 4,260.00 "" 2 4,510.00 4,260.00 0 4,260.00 3 4,050.00 4,335.00 15 4,350.00 4 3,720.00 4,249.50 -5.1 4,244.40 5 3,900.00 4,090.65 -35.85 4,054.80 6 3,470.00 4,033.46 -40.119 3,993.34 7 2,890.00 3,864.42 -65.9025 3,798.52 8 3,100.00 3,572.09 -111.18711 3,460.91 3,430.47 -117.275265 3,313.19 MAD Forecast Year Coat Sales (tons) Ft +1 (Dt - Ft) |Dt - Ft| 1 4,260.00 4,260.00 2 4,510.00 4,260.00 250.00 250.00 3 4,050.00 4,335.00 -285.00 285.00 4 3,720.00 4,249.50 -529.50 529.5 5 3,900.00 4,090.65 -190.65 190.65 6 3,470.00 4,033.46 -563.45 563.45 7 2,890.00 3,864.42 -974.42 974.42 8 3,100.00 3,572.09 -472.09 472.09 3,430.47 -2,765.12 2,765.12 395.02 Linear trend line Year (x) Coat Sales (tons) (y) xy 1 4,260.00 4,260.00 1 2 4,510.00 9,020.00 4 3 4,050.00 12,150.00 9 4 3,720.00 14,880.00 16 5 3,900.00 19,500.00 25 6 3,470.00 20,820.00 36 7 2,890.00 20,230.00 49 8 3,100.00 24,800.00 64 36 29,900.00 125,660.00 204 x? = 4.5 ? = 3737.5 -211.67 a =? - b x? 4690 The linear trend line equation: y=4690-211.67x 166.2525 <395.02 The linear trend is more accuratethan the adjusted exponentialsmoothing forecast Year (x) Coat Sales (tons) (D) Forecase (Ft) |Dt - Ft| 1 4260 4478.33 218.33 2 4510 4266.66 243.34 3 4050 4054.99 4.99 4 3720 3843.32 123.32 5 3900 3631.65 268.35 6 3470 3419.98 50.02 7 2890 3208.31 318.31 8 3100 2996.64 103.36 1330.02Problem 12-9 Weights: 0.6, 0.2, 0.1 3 month Exponential Smoothing 3 Months moving avg. Weighted Alpha,? = 0.4 Period Demand Forecast Abs. Dev. Forecast Abs. Dev. Forecast Abs. Dev. 1 63.25 63.25 2 60.125 63.25 3.13 3 61.75 62.00 0.25 4 64.25 61.71 2.54 61.4125 2.8375 61.90 2.35 5 59.375 62.04 2.67 63.0875 3.7125 62.84 3.47 6 57.875 61.79 3.92 61.075 3.2 61.45 3.58 7 62.25 60.50 1.75 58.9625 3.2875 60.02 2.23 8 65.125 59.83 5.29 60.65 4.475 60.91 4.21 9 68.25 61.75 6.50 63.5375 4.7125 62.60 5.65 10 65.5 65.21 0.29 66.7125 1.2125 64.86 0.64 11 68.125 66.29 1.83 66.2875 1.8375 65.12 3.01 12 63.25 67.29 4.04 67.35 4.1 66.32 3.07 13 64.375 65.63 1.25 64.9375 0.5625 65.09 0.72 14 68.625 65.25 3.38 64.4125 4.2125 64.80 3.82 15 70.125 65.42 4.71 66.8125 3.3125 66.33 3.79 16 72.75 67.71 5.04 69.1 3.65 67.85 4.90 17 74.125 70.50 3.63 71.55 2.575 69.81 4.32 18 71.75 72.33 0.58 73.3125 1.5625 71.54 0.21 19 75.5 72.88 2.63 72.5625 2.9375 71.62 3.88 20 76.75 73.79 2.96 74.2375 2.5125 73.17 3.58 21 0 0.00 75.875 75.875 0.00 a. MAD = 3.12 b. MAD = 2.98 c. MAD = 3.14 d. Based on MAD, the 3 month weighted average method is best. Note: To be consistent we considered periods 4 to 21 for computing MAD.For exponential smoothing we treat the actual demand as the forcast for period 1.

 

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