The following table contains the demand from the last 10 months:
MONTH | ACTUAL DEMAND |
1 | 33 |
2 | 29 |
3 | 32 |
4 | 33 |
5 | 35 |
6 | 32 |
7 | 35 |
8 | 42 |
9 | 44 |
10 | 45 |
a. Calculate the single exponential smoothing forecast for these data using an α of 0.10 and an initial forecast (F1) of 33. (Round your answers to 2 decimal places.)
b. Calculate the exponential smoothing with trend forecast for these data using an α of 0.10, a δ of 0.20, an initial trend forecast (T1) of 1.00, and an initial exponentially smoothed forecast (F1) of 32. (Round your answers to 2 decimal places.)
c-1. Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your answers to 2 decimal places.)
c-2. Which is best?
Exponential smoothing with trend forecast
Single exponential smoothing forecast
(a)
Forecast |
33 |
33 |
32.6 |
32.54 |
32.59 |
32.83 |
32.74 |
32.97 |
33.87 |
34.89 |
(b)
Smoothed Forecast, Ft |
33 |
33.9 |
33.41 |
33.27 |
33.24 |
33.42 |
33.28 |
33.45 |
34.30 |
35.27 |
(c-1)
3.98 |
MAD |
3.95 |
MAD |
(c-2) Exponential smoothing with trend forecast
Alpha | 0.1 | ||||||
Data | Forecasts and Error Analysis | ||||||
Period | Demand | Forecast | Error | Absolute | Squared | Abs Pct Err | |
Period 1 | 33 | 33 | 0 | 0 | 0 | 00.00% | |
Period 2 | 29 | 33 | -4 | 4 | 16 | 13.79% | |
Period 3 | 32 | 32.6 | -0.6 | 0.6 | 0.36 | 01.88% | |
Period 4 | 33 | 32.54 | 0.46 | 0.46 | 0.2116 | 01.39% | |
Period 5 | 35 | 32.59 | 2.414 | 2.414 | 5.827396 | 06.90% | |
Period 6 | 32 | 32.83 | -0.8274 | 0.8274 | 0.684591 | 02.59% | |
Period 7 | 35 | 32.74 | 2.25534 | 2.25534 | 5.086559 | 06.44% | |
Period 8 | 42 | 32.97 | 9.029806 | 9.029806 | 81.5374 | 21.50% | |
Period 9 | 44 | 33.87 | 10.12683 | 10.12683 | 102.5526 | 23.02% | |
Period 10 | 45 | 34.89 | 10.11414 | 10.11414 | 102.2959 | 0.2247587 | |
Total | 28.97271 | 39.82751 | 314.556 | 99.98% | |||
Average | 2.897271 | 3.98 | 31.4556 | 10.00% | |||
Bias | MAD | MSE | MAPE | ||||
SE | 6.270526 | ||||||
Next period | 35.8972714 |
Alpha | 0.1 | ||||||||
Beta | 0.2 | ||||||||
Data | Forecasts and Error Analysis | ||||||||
Period | Demand | Smoothed Forecast, Ft | Smoothed Trend, Tt | Forecast Including Trend, FITt | Error | Absolute | Squared | Abs Pct Err | |
Period 1 | 33 | 33 | 1 | 34 | 0 | 0 | 0 | 00.00% | |
Period 2 | 29 | 33.9 | 0.98 | 34.88 | -4.9 | 4.9 | 24.01 | 16.90% | |
Period 3 | 32 | 33.41 | -1.41 | 1.41 | 1.9881 | 04.41% | |||
Period 4 | 33 | 33.27 | -0.269 | 0.269 | 0.072361 | 00.82% | |||
Period 5 | 35 | 33.24 | 1.7579 | 1.7579 | 3.090212 | 05.02% | |||
Period 6 | 32 | 33.42 | -1.41789 | 1.41789 | 2.010412 | 04.43% | |||
Period 7 | 35 | 33.28 | 1.723899 | 1.723899 | 2.971828 | 04.93% | |||
Period 8 | 42 | 33.45 | 8.551509 | 8.551509 | 73.12831 | 20.36% | |||
Period 9 | 44 | 34.30 | 9.696358 | 9.696358 | 94.01936 | 22.04% | |||
Period 10 | 45 | 35.27 | 9.726722 | 9.726722 | 94.60913 | 0.216149 | |||
Total | 23.4595 | 39.45328 | 295.8997 | 100.51% | |||||
Average | 2.34595 | 3.95 | 29.58997 | 10.05% | |||||
Bias | MAD | MSE | MAPE | ||||||
SE | 6.081732 |
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