Seasonal Technique 1. What we have Transformer table Transformer YEAR January February March April May June July August September October November December SUM OF EACH YEAR 1600 1400 1200 1000 800 600 400 200 0 Transformer sum of each year Year Transformer 1(2006) 9614 2(2007) 10784 3(2008) 11884 4(2009) 13002 5(2010) 13214 2006 2007 2008 2009 2010 779 845 857 917 887 802 739 881 956 892 818 871 937 1001 997 888 927 1159 1142 1118 898 1133 1072 1276 1197 902 1124 1246 1356 1256 916 1056 1198 1288 1202 708 889 922 1082 1170 695 857 798 877 982 708 772 879 1009 1297 716 751 945 1100 1163 784 820 990 998 1053 9614 10784 11884 13002 13214 2006 2007 2008 2009 2010 Transformer 15000 10000 5000 0 Transformer Then we want to forecast total transformer in 2011 by using Linear Trend Equation t Sum(Σ) t^2 1 2 3 4 5 15 y 1 4 9 16 25 55 ty 9,614 10,784 11,884 13,002 13,214 58,498 9,614 21,568 35,652 52,008 66,070 184,912 From equation Result: B=941.8 A=8874.2 Equation: Y=8874.2+941.8t Then try to forecast 2010 from this equation and check whether it works or not As the result, we get Y=8874.2+941.8(5) = 13,583 Therefore, the forecast of total transformer in 2010 is 13,583 which is not far from the actual (13,214) Use Seasonal Index to forecast each month 887 AVG(20062009) 849.50 Per month 943.42 Seasonal Index 0.90 1,019.23 (actualforecast)^2 17,486.07 956 892 844.50 943.42 0.90 1,013.24 14,698.14 937 1,001 997 906.75 943.42 0.96 1,087.92 8,267.14 927 1,159 1,142 1,118 1,029.00 943.42 1.09 1,234.60 13,595.57 898 1,133 1,072 1,276 1,197 1,094.75 943.42 1.16 1,313.49 13,569.28 June 902 1,124 1,246 1,356 1,256 1,157.00 943.42 1.23 1,388.18 17,470.27 July 916 1,056 1,198 1,288 1,202 1,114.50 943.42 1.18 1,337.18 18,274.56 August Septembe r October 708 889 922 1,082 1,170 900.25 943.42 0.95 1,080.13 8,077.51 695 857 798 877 982 806.75 943.42 0.86 967.94 197.59 708 772 879 1,009 1,297 842.00 943.42 0.89 1,010.24 82,233.38 November 716 751 945 1,100 1,163 878.00 943.42 0.93 1,053.43 12,005.72 December SUM OF YEAR 784 820 990 998 1,053 898.00 943.42 0.95 1,077.43 596.60 9,614 10,784 11,884 13,002 13,214 11,321.00 YEAR 2006 2007 2008 2009 2010 January 779 845 857 917 February 802 739 881 March 818 871 April 888 May 2010(F) 13,583.00 Sum (Σ) (actualforecast)^2 MSE 206,471.83 18,770.17 Moving Average (3 Months) YEAR 2009 January 917 February 956 March 1,001 April 1,142 May 1,276 June 1,356 July 1,288 August 1,082 September 877 October 1,009 November 1,100 December 998 (actual2010 2010(forecast) forecast)^2 887 1,035.67 22,101.78 892 995.00 10,609.00 997 925.67 5,088.44 1,118 925.33 37,120.44 1,197 1,002.33 37,895.11 1,256 1,104.00 23,104.00 1,202 1,190.33 136.11 1,170 1,218.33 2,336.11 982 1,209.33 51,680.44 1,297 1,118.00 32,041.00 1,163 1,149.67 177.78 1,053 1,147.33 8,898.78 Sum (Σ) (actualforecast)^2 231,189.00 MSE 21,017.18 Weight Moving Average (3 Months) We use Weight = 0.5 for the last month Weight = 0.3 for the last 2nd month Weight = 0.2 for the last 3rd month YEAR 2009 January 917 February 956 March 1,001 April 1,142 May 1,276 June 1,356 July 1,288 August 1,082 September 877 October 1,009 November 1,100 December 998 (actual2010 2010(forecast) forecast)^2 887 1,030.80 20678.44 892 962.90 5026.81 997 911.70 7276.09 1,118 943.50 30450.25 1,197 1,036.50 25760.25 1,256 1,133.30 15055.29 1,202 1,210.70 75.69 1,170 1,217.20 2227.84 982 1,196.80 46139.04 1,297 1,082.40 46053.16 1,163 1,177.10 198.81 1,053 1,167.00 12,996.00 Sum (Σ) (actualforecast)^2 211,937.67 MSE 19,267.06 We use Mean Squared Error (MSE) to measure accuracy for each technique MSE of Seasonal Index Technique = 18,770.17 MSE of Moving Average (3 Months) = 21,017.18 MSE of Weight Moving Average (3 Months) = 19,267.06 MSE of Seasonal Index Technique is the lowest, THE BEST then we try to apply to 2011 For the Equation: Y=8874.2+941.8t Put t=6 in the equation Year Transformer 1(2006) 9614 2(2007) 10784 3(2008) 11884 4(2009) 13002 5(2010) 13214 6(2011F) 14525 Then use 14525 as the sum of transformer in 2011 and use seasonal index then we will get this table YEAR January February March April May June July August September October November December 2006 2007 2008 779 845 857 802 739 881 818 871 937 888 927 1159 898 1133 1072 902 1124 1246 916 1056 1198 708 889 922 695 857 798 708 772 879 716 751 945 784 820 990 Transformer 2009 2010 Seasonal Index 917 887 956 892 1001 997 1142 1118 1276 1197 1356 1256 1288 1202 1082 1170 877 982 1009 1297 1100 1163 998 1053 0.90 0.90 0.96 1.09 1.16 1.23 1.18 0.95 0.86 0.89 0.93 0.95 Sum 2011(Forecast) 1,089.92 1,083.51 1,163.37 1,320.22 1,404.58 1,484.45 1,429.92 1,155.03 1,035.07 1,080.30 1,126.49 1,152.15 14,525.00 For the 3rd question What qualitative factors can be considered to improve the forecast experience? Don’t know LOL PS. I use only the first exhibit