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Sales of computers at the electronics store over the past 10 weeks are shown in the table below:
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Demand | 19 | 23 | 28 | 37 | 26 | 30 | 35 | 24 | 26 | 30 |
Part A: The forecast for weeks 2 through 10 using exponential with data = 0.60 and a week 1 initial forecast of 19.0 are:
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Demand | 19 | 23 | 28 | 37 | 26 | 30 | 35 | 24 | 26 | 30 |
| Forecast | 19 |
Part B: For the forecast developed using exponential smoothing, the mean average deviation = ________
Expert Answer
Initial forecast (forecast for week 1) = 19
The formula to calculate forecast for a period = Ft + (At – Ft) where,
Ft=Forecast of previous period
=smoothing constant
At=Actual demand for previous period
Using the above formula the forecast for week 2 through 10 is calculated below
Week 2 = 19 + 0.60(19-19) = 19
Week 3 = 19 + 0.60(23-19) = 21.4
Week 4 = 21.4 + 0.60(28-21.4) = 25.36
Week 5 = 25.36+ 0.60(37-25.36) = 32.34
Week 6 = 32.34 + 0.60(26-32.34) = 28.53
Week 7 = 28.53 + 0.60(30-28.53) = 29.41
Week 8 = 29.41 + 0.60(35-29.41) = 32.76
Week 9 = 32.76 + 0.60(24-32.76) = 27.50
Week 10 = 27.50 + 0.60(26-27.50) = 26.6
B) Absolute deviation is the absolute value of the difference betwwen the Forecasted value and actual value.This can be calculated with the formula Absolute deviation = | Forecast demand – Actual demand |
Using the above formula the absolute deviations for week 1 through 10 is calculated below:
Week 1 = | 19 – 19 | = 0
Week 2 = | 19 – 23 | = |-4| = 4
Week 3 = | 21.4 – 28 | = |-6.6| = 6.6
Week 4 = | 25.36 – 37 | = |-11.64| =11.64
Week 5 = | 32.34 – 26 | = 6.34
Week 6 = | 28.53 – 30 | = |-1.47| = 1.47
Week 7 = | 29.41 – 35 | = |-5.59| = 5.59
Week 8 = | 32.76 – 24 | = 8.76
Week 9 = | 27.50 – 26 | = 1.5
Week 10 = | 26.6 – 30 | = |-3.4| = 3.4
Mean Absolute Deviation = Sum of the absolute deviations of all the weeks / Number of weeks
= (0+4+6.6+11.64+6.34+1.47+5.59+8.76+1.5+3.4) / 10
= 49.3 / 10
= 4.93
