Below is the sales data for Forever Young Boutique between March of Year 1 and J

Question

Below is the sales data for Forever Young Boutique between March of Year 1 and July of Year 5.

a) Optimize the smoothing constant in the Exponential smoothing technique to minimize MAD. Show the actual data points and the forecasts based on the optimized in one scatter plot (with lines) with appropriate legends and axes titles.  Exponential smoothing technique with a smoothing constant = 0.3 (forecast for March, year 1 = 4566.4).

b) Optimize and in the Trend adjusted exponential smoothing technique to minimize MAD. Show the actual data points and the forecasts based on the optimized in one scatter plot (with lines) with appropriate legends and axes titles . Trend adjusted exponential smoothing technique (with trend adjustment) with = 0.3 and = 0.5 (forecast without trend for March, year 1 = 4566.4; Trend for March, year 1 = 100)

Month Year 1 Year 2 Year 3 Year 4 Year 5 January 6381.07 11016.55 11965.68 10580.74 February 4405.83 8264.14 12761.98 13420.87 March 4566.4 9126.95 6843.95 18126.7 34476.27 April 6941.89 10970.45 20109.68 19092.9 19108.79 May 7047.23 10189.28 11148.64 15384.01 18109.54 June 6784.37 7043.85 8365.4 12237 13743.6 July 5814.23 6717.37 9469.08 13252.53 18339.25 August 6906.38 9139.72 10221 13819.77 September 8075.13 11315.19 15161.41 21755.64 October 7913.56 10838.4 17731.08 24838.1 November 9054.18 11150.94 17508.99 15955.6 December 14114.58 17592.2 27566.89 19370.7

Explanation / Answer

a)

For alpha = 0.3 we get

By minimizing MAD for forecast, we get alpha = 0.141367,

b)

For alpha = 0.3 and beta = 0.5, we get

By minimizing MAD for trend adjusted forecast, we get alpha = 0.135318 and beta = 0 ,

Period (i) Actual Sales (Ai) Forecast (Fi) Absolute Deviation (for Fi) 1 4566.4 4566.4 0 2 6941.89 4566.4 2375.49 3 7047.23 5279.047 1768.183 4 6784.37 5809.5019 974.8681 5 5814.23 6101.96233 287.73233 6 6906.38 6015.642631 890.737369 7 8075.13 6282.863842 1792.266158 8 7913.56 6820.543689 1093.016311 9 9054.18 7148.448582 1905.731418 10 14114.58 7720.168008 6394.411992 11 6381.07 9638.491605 3257.421605 12 4405.83 8661.265124 4255.435124 13 9126.95 7384.634587 1742.315413 14 10970.45 7907.329211 3063.120789 15 10189.28 8826.265447 1363.014553 16 7043.85 9235.169813 2191.319813 17 6717.37 8577.773869 1860.403869 18 9139.72 8019.652708 1120.067292 19 11315.19 8355.672896 2959.517104 20 10838.4 9243.528027 1594.871973 21 11150.94 9721.989619 1428.950381 22 17592.2 10150.67473 7441.525267 23 11016.55 12383.13231 1366.582313 24 8264.14 11973.15762 3709.017619 25 6843.95 10860.45233 4016.502334 26 20109.68 9655.501633 10454.17837 27 11148.64 12791.75514 1643.115143 28 8365.4 12298.8206 3933.4206 29 9469.08 11118.79442 1649.71442 30 10221 10623.88009 402.8800942 31 15161.41 10503.01607 4658.393934 32 17731.08 11900.53425 5830.545754 33 17508.99 13649.69797 3859.292028 34 27566.89 14807.48558 12759.40442 35 11965.68 18635.30691 6669.626906 36 12761.98 16634.41883 3872.438835 37 18126.7 15472.68718 2654.012816 38 19092.9 16268.89103 2824.008971 39 15384.01 17116.09372 1732.08372 40 12237 16596.4686 4359.468604 41 13252.53 15288.62802 2036.098023 42 13819.77 14677.79862 858.028616 43 21755.64 14420.39003 7335.249969 44 24838.1 16620.96502 8217.134978 45 15955.6 19086.10552 3130.505515 46 19370.7 18146.95386 1223.746139 47 10580.74 18514.0777 7933.337702 48 13420.87 16134.07639 2713.206392 49 34476.27 15320.11447 19156.15553 50 19108.79 21066.96113 1958.171132 51 18109.54 20479.50979 2369.969792 52 13743.6 19768.51885 6024.918855 53 18339.25 17961.0432 378.2068017 MAD = 3575.279551

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