1. The following table gives the actual demand for 4 weeks of a product. Actual
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1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)2 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)2 1 13 13.00 2 16 3 18 4 20 TOTAL = a) Using ? = 0.6, compute the exponentially smoothed forecast for weeks 2 through 4 and complete the table. b) Compute the Mean Squared Error . 2. The following table gives the the actaual demand for 4 weeks of a product. Ft = ?At-1 +(1-?)(Ft-1 + Tt-1) Tt = ?(Ft - Ft-1) + (1-?)Tt-1 ? = 0.3 ? = 0.4 FITt = Ft + Tt Actual De- Forecast with Week, t mand, At Smoothed forecast, Ft Trend, Tt trend, FITt 1 5 6.00 2.00 2 8 3 9 4 12 Using formulas above complete the table for forecast including trend. 1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)3 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)3 5 22.5 13.00 6 24.8 7 27.1 8 29.4 1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)3 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)3 5 22.5 13.00 6 24.8 7 27.1 8 29.4 TOTAL = a) Using ? = 0.6, compute the exponentially smoothed forecast for weeks 2 through 4 and complete the table. b) Compute the Mean Squared Error . 2. The following table gives the the actaual demand for 4 weeks of a product. Ft = ?At-1 +(1-?)(Ft-1 + Tt-1) Tt = ?(Ft - Ft-1) + (1-?)Tt-2 ? = 0.5 1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)2 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)2 1 13 13.00 2 16 3 18 4 20 TOTAL = a) Using ? = 0.6, compute the exponentially smoothed forecast for weeks 2 through 4 and complete the table. b) Compute the Mean Squared Error . 2. The following table gives the the actaual demand for 4 weeks of a product. Ft = ?At-1 +(1-?)(Ft-1 + Tt-1) Tt = ?(Ft - Ft-1) + (1-?)Tt-1 ? = 0.3 ? = 0.4 FITt = Ft + Tt Actual De- Forecast with Week, t mand, At Smoothed forecast, Ft Trend, Tt trend, FITt 1 5 6.00 2.00 2 8 3 9 4 12 Using formulas above complete the table for forecast including trend. 1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)3 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)3 5 22.5 13.00 6 24.8 7 27.1 8 29.4 1. The following table gives the actual demand for 4 weeks of a product. Actual De- Forecast (Error)3 Week, t mand, At Ft = Ft-1 + ?(A t-1 - Ft-1) (At - Ft)3 5 22.5 13.00 6 24.8 7 27.1 8 29.4 TOTAL = a) Using ? = 0.6, compute the exponentially smoothed forecast for weeks 2 through 4 and complete the table. b) Compute the Mean Squared Error . 2. The following table gives the the actaual demand for 4 weeks of a product. Ft = ?At-1 +(1-?)(Ft-1 + Tt-1) Tt = ?(Ft - Ft-1) + (1-?)Tt-2 ? = 0.5Explanation / Answer
ANS:1 Alpha=0.6 Week t Actual Demand At Ft Error Error Squared 1 13 13 0 -0.948 0.8987 2 16 14.8 1.2 0.252 0.0635 3 18 16.72 1.28 0.332 0.1102 4 20 18.688 1.312 0.364 0.1325 1.2049 t = 1 t = 2 t = 3 t = 4 s1 = x0 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 s1 = 13 s2 = ?x2 - 1 + (1 - ?)s2 - 1 s3 = ?x3 - 1 + (1 - ?)s3 - 1 s4 = ?x4 - 1 + (1 - ?)s4 - 1 s2 = 0.6(x1) + (1 - 0.6)s1 s3 = 0.6(x2) + (1 - 0.6)s2 s4 = 0.6(x3) + (1 - 0.6)s3 s2 = 0.6(x1) + (0.4)s1 s3 = 0.6(x2) + (0.4)s2 s4 = 0.6(x3) + (0.4)s3 s2 = 0.6(16) + (0.4)13 s3 = 0.6(18) + (0.4)14.8 s4 = 0.6(20) + (0.4)16.72 s2 = 9.6 + 5.2 s3 = 10.8 + 5.92 s4 = 12 + 6.688 s2 = 14.8 s3 = 16.72 s4 = 18.688 Mean of Squared Error 1.2049/4 = 0.301232 ANS:2 Alpha=0.3 Week t Actual Demand At Ft Error Error Squared 1 5 5 0 -1.972 3.8898 2 8 5.9 2.1 0.1278 0.0163 3 9 6.83 2.17 0.1978 0.0391 4 12 8.381 3.619 1.6468 2.7118 6.6570 t = 1 t = 2 t = 3 t = 4 s1 = x0 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 s1 = 5 s2 = ?x2 - 1 + (1 - ?)s2 - 1 s3 = ?x3 - 1 + (1 - ?)s3 - 1 s4 = ?x4 - 1 + (1 - ?)s4 - 1 s2 = 0.3(x1) + (1 - 0.3)s1 s3 = 0.3(x2) + (1 - 0.3)s2 s4 = 0.3(x3) + (1 - 0.3)s3 s2 = 0.3(x1) + (0.7)s1 s3 = 0.3(x2) + (0.7)s2 s4 = 0.3(x3) + (0.7)s3 s2 = 0.3(8) + (0.7)5 s3 = 0.3(9) + (0.7)5.9 s4 = 0.3(12) + (0.7)6.83 s2 = 2.4 + 3.5 s3 = 2.7 + 4.13 s4 = 3.6 + 4.781 s2 = 5.9 s3 = 6.83 s4 = 8.381 Mean of Squared Error 6.6570/4 = 1.664245188 ANS:2 Alpha=0.4 Week t Actual Demand At Ft Error Error Squared Trend t FiTt 1 5 5 0 -1.572 2.4712 2.00 10.00 2 8 6.2 1.8 0.228 0.0520 1.16 7.19 3 9 7.32 1.68 0.108 0.0117 0.80 5.86 4 12 9.192 2.808 1.236 1.5277 0.88 8.10 4.0625 t = 1 t = 2 t = 3 t = 4 s1 = x0 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 s1 = 5 s2 = ?x2 - 1 + (1 - ?)s2 - 1 s3 = ?x3 - 1 + (1 - ?)s3 - 1 s4 = ?x4 - 1 + (1 - ?)s4 - 1 s2 = 0.4(x1) + (1 - 0.4)s1 s3 = 0.4(x2) + (1 - 0.4)s2 s4 = 0.4(x3) + (1 - 0.4)s3 s2 = 0.4(x1) + (0.6)s1 s3 = 0.4(x2) + (0.6)s2 s4 = 0.4(x3) + (0.6)s3 s2 = 0.4(8) + (0.6)5 s3 = 0.4(9) + (0.6)6.2 s4 = 0.4(12) + (0.6)7.32 s2 = 3.2 + 3 s3 = 3.6 + 3.72 s4 = 4.8 + 4.392 s2 = 6.2 s3 = 7.32 s4 = 9.192 Mean of Squared Error 4.0625/4 = 1.015632 ANS:3 Alpha=0.6 Week t Actual Demand At Ft Error Error Squared 5 22.5 5 17.5 -1.522 -3.5257 6 24.8 6.2 18.6 -0.422 -0.0752 7 27.1 7.32 19.78 0.758 0.4355 8 29.4 9.192 20.208 1.186 1.6682 -1.4971 t = 1 t = 2 t = 3 t = 4 s1 = x0 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 st = ?xt - 1 + (1 - ?)st - 1 s1 = 22.5 s2 = ?x2 - 1 + (1 - ?)s2 - 1 s3 = ?x3 - 1 + (1 - ?)s3 - 1 s4 = ?x4 - 1 + (1 - ?)s4 - 1 s2 = .6(x1) + (1 - .6)s1 s3 = .6(x2) + (1 - .6)s2 s4 = .6(x3) + (1 - .6)s3 s2 = .6(x1) + (0.4)s1 s3 = .6(x2) + (0.4)s2 s4 = .6(x3) + (0.4)s3 s2 = .6(24.8) + (0.4)22.5 s3 = .6(27.1) + (0.4)23.88 s4 = .6(29.4) + (0.4)25.812 s2 = 14.88 + 9 s3 = 16.26 + 9.552 s4 = 17.64 + 10.3248 s2 = 23.88 s3 = 25.812 s4 = 27.9648 Mean of Squared Error (-1.4971)/4 = -0.3743
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