4 1 a 374 368 381 374 33 pints 3 b Week of August 31 September September September September October 5 Pints Used 360 389 410 381 368 374 7 14 21 28 Weighted Moving Average 381 1 38 1 368 3 110 4 374 6 224 4 372 9 Forecast 372 9 c Week of Pints Forecast August 31 September September September September October 5 360 389 410 381 368 374 360 360 365 8 374 64 375 912 374 3296 7 14 21 28 Forecasting Error 0 29 44 2 6 36 7 912 3296 The forecast is 374 2 4 6 January February March April May June July August September October November December Sum Average a Y Sales X Period 20 21 15 14 13 16 17 18 20 20 21 23 1 2 3 4 5 6 7 8 9 10 11 12 218 18 2 78 6 5 X2 1 4 9 16 25 36 49 64 81 100 121 144 XY 20 42 45 56 65 96 119 144 180 200 231 276 650 1474 Error 20 0 5 8 8 84 1 272 1 5824 06592 Forecast 360 365 8 374 64 375 912 374 3296 374 2636 b Naive The coming January December 23 3 month moving 20 21 23 3 21 33 6 month weighted 0 1 17 1 18 0 1 20 0 2 20 0 2 21 0 3 23 20 6 Exponential smoothing with alpha 0 3 FOct 18 0 3 20 18 18 6 FNov 18 6 0 3 20 18 6 19 02 FDec 19 02 0 3 21 19 02 19 6 FJan 19 6 0 3 23 19 6 20 62 21 Trend x 78 x 6 5 y 218 y 18 17 1474 12 6 5 18 2 54 4 0 38 650 12 6 5 2 143 a 18 2 0 38 6 5 15 73 b 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 4 10 Year Demand a 3 year moving b 3 year weighted 4 11 1 2 3 4 6 4 Year 1 2 3 Demand Exp Smoothing 4 5 6 0 4 7 4 0 5 1 4 5 6 5 0 10 0 8 0 4 7 5 0 6 3 4 5 5 0 7 3 4 5 6 5 0 10 0 8 0 4 8 4 8 6 4 7 8 9 10 11 Forecast 7 0 7 7 7 8 9 0 8 3 8 0 12 0 8 0 8 3 14 0 9 3 10 0 15 0 11 7 12 3 13 7 14 0 7 8 9 10 11 Forecast 7 0 6 9 9 0 6 9 12 0 7 5 14 0 8 9 15 0 10 4 11 8 4 13 a Exponential smoothing 0 6 Year 1 2 3 4 5 6 Demand 45 50 52 56 58 Exponential Absolute Smoothing 0 6 Deviation 41 4 0 41 0 0 6 45 41 43 4 6 6 43 4 0 6 50 43 4 47 4 4 6 47 4 0 6 52 47 4 50 2 5 8 50 2 0 6 56 50 2 53 7 4 3 53 7 0 6 58 53 7 56 3 25 3 MAD 5 06 Exponential smoothing 0 9 Year 1 2 3 4 5 6 Demand Exponential Smoothing 0 9 Absolute Deviation 45 50 52 56 58 41 41 0 0 9 45 41 44 6 44 6 0 9 50 44 6 49 5 49 5 0 9 52 49 5 51 8 51 8 0 9 56 51 8 55 6 55 6 0 9 58 55 6 57 8 4 0 5 4 2 5 4 2 2 4 18 5 MAD 3 7 b 3 year moving average Year Demand 1 2 3 4 5 45 50 52 56 58 6 Three Year Moving Average Absolute Deviation 45 50 52 3 49 50 52 56 3 52 7 52 56 58 3 55 3 7 5 3 12 3 MAD 6 2 c Trend projection Year Demand 1 2 3 4 5 6 3 2 MAD 0 64 45 50 52 56 58 Trend Projection 42 6 42 6 42 6 42 6 42 6 42 6 3 2 3 2 3 2 3 2 3 2 3 2 1 2 3 4 5 6 45 8 49 0 52 2 55 4 58 6 61 8 Absolute Deviation 0 8 1 0 0 2 0 6 0 6 Y a bX b XY nXY X 2 nX 2 a Y bX X Y XY X2 1 2 3 4 5 45 50 52 56 58 45 100 156 224 290 1 4 9 16 25 2 Then X 15 Y 261 XY 815 X 55 X 3 Y 52 2 Therefore 815 5 3 52 2 b 3 2 55 5 3 3 a 52 20 3 20 3 42 6 Y6 42 6 3 2 6 61 8 4 14 Comparing the results of the forecasting methodologies for Problem 4 13 Forecast Methodology MAD Exponential smoothing 0 6 5 06 Exponential smoothing 0 9 3 7 3 year moving average 6 2 Trend projection 0 64 Based on a mean absolute deviation criterion the trend projection is to be preferred over the exponential smoothing with 0 6 exponential smoothing with 0 9 or the 3 year moving average forecast methodologies 4 17 Year Sales 2001 2002 2003 2004 450 495 518 563 2005 2006 584 Forecast Exponential Smoothing 0 6 410 0 410 434 470 6 499 0 499 537 4 565 6 Absolute Deviation 0 6 450 410 434 0 0 6 495 434 470 6 0 6 518 470 6 0 6 563 499 537 4 0 6 584 537 4 40 0 61 0 47 4 64 0 46 6 259 MAD 51 8 Forecast Exponential Year Sales 2001 2002 2003 2004 450 495 518 563 2005 584 2006 Absolut e Deviatio n Smoothing 0 9 410 0 410 446 490 1 515 2 515 2 558 2 558 2 581 4 0 9 450 410 446 0 0 9 495 446 490 1 0 9 518 490 1 40 0 49 0 27 9 47 8 0 9 563 515 2 25 8 0 9 584 558 2 190 5 MAD 38 1 Refer to Solved Problem 4 1 For 0 3 absolute deviations for 2001 2005 are 40 0 73 0 74 1 96 9 88 8 respectively So the MAD 372 8 5 74 6 MAD 0 3 74 6 MAD 0 6 51 8 MAD 0 9 38 1 Because it gives the lowest MAD the smoothing constant of 0 9 gives the most accurate forecast 4 24 a Graph of Demand The observations obviously do not form a straight line but do tend to cluster about a straight line over the range shown b Least Squares Regression Y a bX b XY …